the renormalized electron mass in non relativistic quantum electrodynamics abstract this work addresses the problem of infrared mass renormalization for a non relativistic electron minimally coupled to the quantized electromagnetic field the standard translationally invariant system of an electron in non relativistic qed we assume that the interaction of the electron with the quantized electromagnetic field is subject to an ultraviolet regularization and an infrared regularization parametrized by 0 for the value p 0 of the conserved total momentum of electron and photon field bounds on the renormalized mass are established which are uniform in 0 and the existence of a ground state is proved for p 0 sufficiently small bounds on the renormalized mass are derived for any fixed 0 a key ingredient of our proofs is the operator theoretic renormalization group based on the isospectral smooth feshbach map it provides an explicit finite algorithm for determining the renormalized electron mass at p 0 to any given precision

spectra of digraphs in this primarily expository paper we survey classical and some more recent results on the spectra of digraphs equivalently the spectra of 0 1 matrices with emphasis on the spectral radius

periodicity in bilinear lattices and the coxeter formalism abstract we introduce and study in detail so called circulant coxeter periodic elements and circulant families in a bilinear lattice k as well as their dual versions called anti circulant we show that they form a natural environment for a systematic explanation of certain cyclotomic factors of the coxeter polynomial k of k and in consequence of coxeter polynomials of algebras of finite global dimension we discuss the properties of quadratic forms induced by circulant and anti circulant families moreover we interpret the results in the language of representation theory of algebras and point out applications facts concerning tubular families in auslander reiten quivers and quadratic forms of algebras abstract considerations in bilinear lattices are illustrated with a collection of non trivial examples arising from module and derived categories the results show that techniques of linear algebra and number theory provide efficient tools for explaining various representation theoretic facts

the mass shell of the nelson model without cut offs abstract the massless nelson model describes non relativistic spinless quantum particles interacting with a relativistic massless scalar quantum field the interaction is linear in the field we analyze its one particle sector first we construct the renormalized mass shell of the non relativistic particle for an arbitrarily small infrared cut off that turns off the interaction with the low energy modes of the field no ultraviolet cut off is imposed second we implement a suitable bogolyubov transformation of the hamiltonian in the infrared regime this transformation depends on the total momentum of the system and is non unitary as the infrared cut off is removed for the transformed hamiltonian we construct the mass shell in the limit where both the ultraviolet and the infrared cut off are removed the limiting fibre hamiltonians are obtained by convergence in the norm resolvent sense our approach is constructive and leads to explicit expansion formulae which are amenable to rigorously control the s matrix elements

the kth largest eigenvalue of a tree abstract let k t be the k th eigenvalue of a tree x the largest integer not greater than x it is shown that a tree with n vertices has k t n 2 k for 2 k n 2 and this upper bound is best possible for n 1 mod k

bifurcations and internal resonances in space curved rods abstract the paper discusses a geometrically non linear model of space curved beams the timoshenko type model is used which includes the shear effects and rotatory inertia the motion of the system is described by a non linear matrix equation which accounts for non linearities up to the second order to solve the non linear problem discretization methods based on the galerkin method are used and the resulting non linear eigenvalue problem is then solved by the continuation methods the analysis of the discretized problem allows the study of the bifurcations of solutions the post bifurcation analysis is used to explain the phenomenon of internal resonance which is of much importance in the prediction of the dynamic response of the analyzed systems the approach is illustrated by numerical examples which consider the free vibration of beams and circular arches with different boundary conditions

bounds on the kth eigenvalues of trees and forests abstract we prove the upper bound k t n k 1 for the kth largest eigenvalue of a tree t 1 k n 2 and show that this bound is best possible when n 0 mod k we further obtain the strict inequality t 1 k 1 t 1 k t t 1 where t n k for the case n 0 mod k 2 k n 2 our upper bound is also proved to be the best possible upper bound for the kth largest eigenvalues of the forests in all cases

inflation algorithm for loop free non negative edge bipartite graphs of corank at least two we continue the study of finite connected loop free edge bipartite graphs with m 3m 3 vertices a class of signed graphs we started in simson 2013 48 and m g siorek et al 2016 19 by means of the non symmetric gram matrix g mm z of its symmetric gram matrix g 12 g g tr mm 12z and the gram quadratic form q zm zq zm z in particular we study connected non negative edge bipartite graphs with n r 3n r 3 vertices of corank r 2r 2 in the sense that the symmetric gram matrix g mn r z g mn r z of is positive semi definite of rank n 1n 1 the edge bipartite graphs of corank r 2r 2 are studied up to the weak gram zz congruence z z where z z means that g btr g bg btr g b for some b mn r z b mn r z such that det b 1det b 1 our main result of the paper asserts that given a connected edge bipartite graph with n r 3n r 3 vertices of corank r 2r 2 there exists a suitably chosen sequence t of the inflation operators of the form tab such that the composite operator t reduces to a connected bigraph d n r such that zd n r and d n r is one of the canonical r vertex extensions a n r n 1n 1 d n r n 4n 4 e 6 r e 7 r and e 8 r with n rn r vertices of the simply laced dynkin diagrams an dn e6 e7 e8an dn e6 e7 e8 with n 1n 1 vertices the algorithm constructs also a matrix b mn r z b mn r z with det b 1det b 1 defining the weak gram zz congruence zd n r that is satisfying the equation gd n r btr g b

positive commutators in non equilibrium quantum statistical mechanics the method of positive commutators developed for zero temperature problems over the last twenty years has been an essential tool in the spectral analysis of hamiltonians in quantum mechanics we extend this method to positive temperatures i e to non equilibrium quantum statistical mechanics we use the positive commutator technique to give an alternative proof of a fundamental property of a certain class of large quantum systems called return to equilibrium this property says that equilibrium states are asymptotically stable if a system is slightly perturbed from its equilibrium state then it converges back to that equilibrium state as time goes to infinity

tame algebras and tits quadratic forms abstract we solve a long standing problem concerning the connection between the tameness of simply connected algebras and the weak nonnegativity of the associated tits integral quadratic forms and derive some consequences

coxeter energy of graphs abstract we study the concept of the coxeter energy of graphs and digraphs quivers as an analogue of gutman s adjacency energy which has applications in theoretical chemistry and is a recently widely investigated graph invariant coxeter energy ce g of a di graph g is defined to be the sum of the absolute values of all complex eigenvalues of the coxeter matrix associated with g our main inspiration for the study comes from the coxeter formalism appearing in group theory lie theory representation theory of algebras mathematical physics and other contexts we focus on the coxeter energy of trees and we prove that the path resp the maximal star has the smallest resp the greatest coxeter energy among all trees resp two large subclasses of trees with fixed number of vertices we provide several other related results as the characterization of trees with second smallest and second greatest coxeter energy bounds for coxeter energy and general facts on coxeter spectra of graphs extending known results e g for salem trees and for certain special real coxeter eigenvalues of trees additionally we discuss few other energy like quantities for the coxeter spectra of di graphs including coxeter energy normalized by the trace of the coxeter matrix and the quantities derived from variants of coulson integral formula

on products and line graphs of signed graphs their eigenvalues and energy abstract in this article we examine the adjacency and laplacian matrices and their eigenvalues and energies of the general product non complete extended p sum or neps of signed graphs we express the adjacency matrix of the product in terms of the kronecker matrix product and the eigenvalues and energy of the product in terms of those of the factor graphs for the cartesian product we characterize balance and compute expressions for the laplacian eigenvalues and laplacian energy we give exact results for those signed planar cylindrical and toroidal grids which are cartesian products of signed paths and cycles we also treat the eigenvalues and energy of the line graphs of signed graphs and the laplacian eigenvalues and laplacian energy in the regular case with application to the line graphs of signed grids that are cartesian products and to the line graphs of all positive and all negative complete graphs

renormalization group analysis of spectral problems in quantum field theory abstract in this paper we present a self contained and detailed exposition of the new renormalization group technique proposed in 1 2 its main feature is that the renormalization group transformation acts directly on a space of operators rather than on objects such as a propagator the partition function or correlation functions we apply this renormalization transformation to a hamiltonian describing the physics of an atom interacting with the quantized electromagnetic field and we prove that excited atomic states turn into resonances when the coupling between electrons and field is nonvanishing

on the sum of the laplacian eigenvalues of a tree given an n vertex graph g v e the laplacian spectrum of g is the set of eigenvalues of the laplacian matrix l d a where d and a denote the diagonal matrix of vertex degrees and the adjacency matrix of g respectively in this paper we study the laplacian spectrum of trees more precisely we find a new upper bound on the sum of the k largest laplacian eigenvalues of every n vertex tree where k 1 n this result is used to establish that the n vertex star has the highest laplacian energy over all n vertex trees which answers affirmatively to a question raised by radenkovic and gutman 10

on spectral radii of coxeter transformations let t be a finite tree and dt the maximal branching degree of its vertices let t be the spectral radius of a coxeter transformation defined by t t hen t 4dt 6

spectral theory of pauli fierz operators abstract we study spectral properties of pauli fierz operators which are commonly used to describe the interaction of a small quantum system with a bosonic free field we give precise estimates of the location and multiplicity of the singular spectrum of such operators applications of these estimates which will be discussed elsewhere concern spectral and ergodic theory of non relativistic qed our proof has two ingredients the feshbach method which is developed in an abstract framework and mourre theory applied to the operator restricted to the sector orthogonal to the vacuum

on the cauchy problem for gross pitaevskii hierarchies the purpose of this paper is to investigate the cauchy problem for the gross pitaevskii infinite linear hierarchy of equations on rn n 1 we prove local existence and uniqueness of solutions in certain sobolev type spaces h of sequences of marginal density operators with n 2 in particular we give a clear discussion of all cases n 2 which covers the local well posedness problem for the gross pitaevskii hierarchy in this situation

normal modes of a non linear clamped clamped beam abstract non linear modal analysis approach based on invariant manifold method proposed earlier by shaw and pierre journal of sound and vibration 164 85 124 is utilized here to obtain the non linear normal modes of a clamped clamped beam for large amplitude displacements the results obtained for the fundamental normal mode are compared with the corresponding reported experimental and theoretical studies the effects of modal coupling are examined in greater detail the limitation of the present method for analyzing non linear behavior is highlighted

infrared renormalization in non relativistic qed and scaling criticality abstract we consider a spin 1 2 electron in the framework of non relativistic quantum electrodynamics qed let h p denote the fiber hamiltonian corresponding to the conserved total momentum p r 3 of the electron and the photon field regularized by a fixed ultraviolet cutoff in the interaction term and an infrared regularization parametrized by 0 1 ultimately our goal is to remove the latter by taking 0 we prove that there exists a constant 0 0 1 independent of 0 such that for all p 1 3 and all values of the finestructure constant 0 0 there exists a ground state eigenvalue of multiplicity two at the bottom of the essential spectrum moreover we prove that the renormalized electron mass satisfies 1 m ren p 1 c uniformly in 0 in units where the bare mass has the value 1 and we prove the existence of the renormalized mass in the limit 0 our analysis uses the isospectral renormalization group method of bach frohlich sigal introduced in v bach j frohlich i m sigal quantum electrodynamics of confined non relativistic particles adv math 137 2 1998 299 395 v bach j frohlich i m sigal renormalization group analysis of spectral problems in quantum field theory adv math 137 1998 205 298 and further developed in v bach t chen j frohlich i m sigal smooth feshbach map and operator theoretic renormalization group methods j funct anal 203 1 2003 44 92 v bach t chen j frohlich i m sigal the renormalized electron mass in non relativistic qed j funct anal 243 2 2007 426 535 the limit 0 determines a scaling critical or endpoint type renormalization group problem in which the interaction is strictly marginal of scale independent size a main result of this paper is the development of a method that provides rigorous control of the renormalization of a strictly marginal quantum field theory characterized by a non trivial scaling limit the key ingredients entering this analysis include a hierarchy of exact algebraic cancelation identities exploiting the spatial and gauge symmetries of the model and a combination of the isospectral renormalization group method with the strong induction principle

smooth feshbach map and operator theoretic renormalization group methods abstract a new variant of the isospectral feshbach map defined on operators in hilbert space is presented it is constructed with the help of a smooth partition of unity instead of projections and is therefore called smooth feshbach map it is an effective tool in spectral and singular perturbation theory as an illustration of its power a novel operator theoretic renormalization group method is described and applied to analyze a general class of hamiltonians on fock space the main advantage of the new renormalization group method over its predecessors is its technical simplicity which it owes to the use of the smooth feshbach map

symbolic computation of strong gram congruences for cox regular positive edge bipartite graphs with loops abstract the paper can be viewed as a second part of the author s paper simson 2018 43 our main aim is to construct symbolic algorithms for the coxeter spectral classification of a class of signed graphs called edge bipartite graphs with n 2 vertices we started in simson 2013 37 and bocian et al 2014 6 more precisely we construct algorithms for the classification up to the strong gram z congruence z of all finite connected cox regular edge bipartite graphs with at least one loop bigraphs for short that are positive in the sense that the associated symmetric gram matrix g 1 2 g g t r m n 1 2 z is positive definite where g m n z is the non symmetric gram matrix of defined in section 1 and z means that there is a z invertible matrix b m n z such that g b t r g b we recall from 43 that every such a bigraph with a loop is strongly gram z congruent with a bigraph d that is one of the positive cox regular bigraphs b n n 2 c n n 3 f 4 m 4 g 2 presented in section 1 here by applying the geometry of mesh root system technique we construct symbolic algorithms that compute the correspondence d and the set gl n z d of all z invertible matrices b m n z defining the strong gram z congruence z d for any connected positive bigraph with n 2 vertices and at least one loop

the trace of the coxeter matrix and hochschild cohomology abstract for a basic finite dimensional k algebra of finite global dimension over an algebraically closed field k the coxeter matrix is defined the following formula is shown trm i 1 i dim k h i where tr is the trace and hi is the ith hochschild cohomology space

a lock free material finite element for non linear oscillations of laminated plates abstract the objective of the present paper is to propose an efficient accurate and robust four node shear flexible composite plate element with six degrees of freedom per node to investigate the non linear oscillatory behavior of unsymmetrical laminated plates the degrees of freedom considered are three displacement u v w along x y and z axis two rotations x y abouty and x axis and twist xy the elementc employs coupled displacement field which is derived using moment shear equilibrium and in plane equilibrium of composite strips along the x andy axis the displacement field so derived not only depend on the element co ordinates but are a function of extensional bending extensional bending and transverse shear stiffness coefficients as well a bi cubic polynomial distribution with 16 generalized undetermined coefficients for the transverse displacement is assumed the element stiffness and mass matrices are computed numerically by employing 3 3 gauss legendre product rules the element is found to be free of shear locking and does not exhibit any spurious modes the element is found to be free of shear locking and does not exhibit any spurious modes in order to compute the non linear frequencies linear mode shape corresponding to fundamental frequency is assumed as the spatial distribution and non linear finite element equations are reduced to a single non linear second order ordinary differential equation this equation is solved by employing direct numerical integration method a series of numerical examples is solved to demonstrate the efficacy of the proposed material finite element

quantum electrodynamics of confined nonrelativistic particles abstract we consider a system of finitely many nonrelativistic quantum mechanical electrons bound to static nuclei the electrons are minimally coupled to the quantized electromagnetic field but we impose an ultraviolet cutoff on the electromagnetic vector potential appearing in covariant derivatives and the interactions between the radiation field and electrons localized very far from the nuclei are turned off for a class of hamiltonians we prove exponential localization of bound states establish the existence of a ground state and derive sufficient conditions for its uniqueness furthermore we show that excited bound states of the unperturbed system become unstable and turn into resonances when the electrons are coupled to the radiation field to this end we develop a novel renormalization transformation which acts directly on the space of hamiltonians

a gram classification of non negative corank two loop free edge bipartite graphs we continue the coxeter spectral study of finite connected loop free edge bipartite graphs with m 2 3 vertices a class of signed graphs started in simson 2013 49 by means of the non symmetric gram matrix g mm 2 z of its symmetric gram matrix g 12 g g tr mm 2 12z the gram quadratic form q zm 2 z and the coxeter spectrum specc c i e the complex spectrum of the coxeter matrix cox g g tr gl m 2 z in the present paper we study non negative edge bipartite graphs of corank two in the sense that the symmetric gram matrix g mm 2 z of is positive semi definite of rank m 1 one of our aims is to get a complete classification of all connected corank two loop free edge bipartite graphs with m 2 3 vertices up to the weak gram z congruence z where z means that g btr g b for some b mm 2 z such that det b 1 by one vertex extensions of the simply laced euclidean diagrams a m m 1 d m m 4 e 6 e 7 e 8 we construct a family of connected loop free corank two diagrams a m 2 d m 2 e 6 2 e 7 2 e 8 2 called simply extended euclidean diagrams such that they classify all connected corank two loop free edge bipartite graphs with m 2 3 vertices up to the weak gram z congruence z a structure of connected corank two loop free edge bipartite graphs is described it is shown that every such contains a connected positive edge bipartite subgraph that is z congruent with a simply laced dynkin diagram dyn called the dynkin type of such that is a two point extension u w of along two roots u w of the positive definite gram form q zm z this yields a combinatorial algorithm u w u w allowing us to construct all connected corank two loop free edge bipartite graphs with m 2 3 vertices and d dyn from the triples u w where is positive of the dynkin type d and u w are roots of the positive definite gram form q zm z

a power series solution for the non linear vibration of beams a power series solution is presented for the non linear free vibration of beams with restrained ends the analysis is based on transforming the time variable into an oscillating time which allows the motion of the beam assumed to be periodic to be expressed as a double power series that is convergent for all time a recurrence relation is used to determine the series coefficients with the initial movement satisfying the boundary conditions as its basis results are obtained for simply supported and clamped beams and compared with available solutions

continuous renormalization group analysis of spectral problems in quantum field theory the isospectral renormalization group is a powerful method to analyze the spectrum of operators in quantum field theory it was introduced in 1995 see 2 4 and since then it has been used to prove several results for non relativistic quantum electrodynamics after the introduction of the method there have been many works in which extensions simplifications or clarifications are presented see 7 11 13 in this paper we present a new approach in which we construct a flow of operators parametrized by a continuous variable in the positive real axis while this is in contrast to the discrete iteration used before this is more in spirit of the original formulation of the renormalization group introduced in theoretical physics in 1974 22 the renormalization flow that we construct can be expressed in a simple way it can be viewed as a single application of the feshbach schur map with a clever selection of the spectral parameter another advantage of the method is that there exists a flow function for which the renormalization group that we present is the orbit under this flow of an initial hamiltonian this opens the possibility to study the problem using different techniques coming from the theory of evolution equations

bounds related to coxeter spectral measures of graphs abstract let m be a real square matrix we give upper bounds for the sum of the absolute values of the real part of the eigenvalues of m quantity in some particular cases known as real energy of m from these results we obtain a combinatorial bound for the real energy of the coxeter matrix q of a tree digraph q with n vertices e r e q min n 2 a b c d 2 where a is the number of edges b and c are respectively the number of bifurcation and congregation paths of q as defined below d i 1 n i 1 i 2 with i the degree of a vertex i and where the minimum is taken over all possible orientations of edges in q as particular case we consider dynkin euclidean and star graphs obtaining practical bounds for the real coxeter energy of these classes of digraphs

mean field dynamics of a quantum tracer particle interacting with a boson gas abstract we consider the dynamics of a heavy quantum tracer particle coupled to a non relativistic boson field in r 3 the pair interactions of the bosons are of mean field type with coupling strength proportional to 1 n where n is the expected particle number assuming that the mass of the tracer particle is proportional to n we derive generalized hartree equations in the limit n moreover we prove the global well posedness of the associated cauchy problem for sufficiently weak interaction potentials

convergent expansions in non relativistic qed analyticity of the ground state we consider the ground state of an atom in the framework of non relativistic qed we show that the ground state as well as the ground state energy are analytic functions of the coupling constant which couples to the vector potential under the assumption that the atomic hamiltonian has a non degenerate ground state moreover we show that the corresponding expansion coefficients are precisely the coefficients of the associated raleigh schrodinger series as a corollary we obtain that in a scaling limit where the ultraviolet cutoff is of the order of the rydberg energy the ground state and the ground state energy have convergent power series expansions in the fine structure constant with dependent coefficients which are finite for 0

the energy of a graph abstract the energy e g of a simple graph g is defined to be the sum of the absolute values of the eigen values of g if g is a k regular graph on n vertices then e g k k n 1 n k b 2 and this bound is sharp it is shown that for each 0 there exist infinitely many n for each of which there exists a k regular graph g of order n with k e g b 2 two graphs with the same number of vertices are equienergetic if they have the same energy we show that for any positive integer n 3 there exist two equienergetic graphs of order 4n that are not cospectral

renormalization analysis for degenerate ground states abstract we consider a hamilton operator which describes a finite dimensional quantum mechanical system with degenerate eigenvalues coupled to a field of relativistic bosons we show that the ground state projection and the ground state energy are analytic functions of the coupling constant in a cone with apex at the origin provided a mild infrared assumption holds to show the result operator theoretic renormalization is used and extended to degenerate situations

structure and a coxeter dynkin type classification of corank two non negative posets inspired by famous results of drozd 1974 13 nazarova ro ter 1975 42 and bondarenko stepochkina 2005 8 on the importance of finite posets i with the non negative tits quadratic form q i zi z in the representation theory we study the finite non negative posets i of corank two that is such posets i that the symmetric gram matrix gi 12 ci citr mi q of i is positive semi definite of corank two where ci mi z is the incidence matrix of i a structure of such posets is described in the paper it is shown that every such a poset i can be obtained in a natural way from a corank zero poset j and a pair of roots of j following main ideas of the coxeter spectral analysis of posets we associate with any connected corank two poset i the incidence quadratic form qi zi z the coxeter matrix coxi ci ci tr the coxeter polynomial coxi t det t e coxi z t its complex coxeter spectrum specci the coxeter number ci n the reduced coxeter number c i n the incidence defect homomorphism i zi kerqi zi and a simply laced dynkin diagram dyni in particular we study the question when the coxeter spectrum specci of i together with dyni determines the incidence matrix ci of i hence the poset i uniquely up to a z congruence by applying linear algebra techniques and a combinatorial computer aided analysis of posets we prove that the question has an affirmative answer for connected corank two posets i with at most 15 elements a complete list of such posets is presented and their coxeter type invariants are computed it follows that i 6 there is only one such a poset i of cardinality 6 and 8 such posets of cardinality 7 up to the poset duality i iop the existence of a i mesh translation quiver ri kerqi i on the set ri kerqi is discussed where ri v zi qi v 1 is the set of roots of qi

tubes in derived categories and cyclotomic factors of the coxeter polynomial of an algebra let be a k algebra of finite global dimension we study tubular families in the auslander reiten quiver of the bounded derived category db satisfying certain natural axioms in particular we precisely describe their influence on the cyclotomic factors of the coxeter polynomial of and discuss several numerical limitations for their possible shapes moreover we show that our results provide an alternative relatively simple proof of non trivial classical facts concerning tubular families in module categories and also extend them slightly

on the two largest eigenvalues of trees abstract very little is known about upper bounds for the largest eigenvalues of a tree that depend only on the vertex number starting from a classical upper bound for the largest eigenvalue some refinements can be obtained by successively removing trees from consideration the results can be used to characterize those trees that maximize the second largest eigenvalue this corrects a result from the literature and it includes a proof of a conjecture of neumaier the main tool for this endeavor is the theory of partial engenvectors

classification of hyperbolic dynkin diagrams root lengths and weyl group orbits we give a criterion for a dynkin diagram equivalently a generalized cartan matrix to be symmetrizable this criterion is easily checked on the dynkin diagram we obtain a simple proof that the maximal rank of a dynkin diagram of compact hyperbolic type is 5 while the maximal rank of a symmetrizable dynkin diagram of compact hyperbolic type is 4 building on earlier classification results of kac kobayashi morita li and sacliolu we present the 238 hyperbolic dynkin diagrams in ranks 3 10 142 of which are symmetrizable for each symmetrizable hyperbolic generalized cartan matrix we give a symmetrization and hence the distinct lengths of real roots in the corresponding root system for each such hyperbolic root system we determine the disjoint orbits of the action of the weyl group on real roots it follows that the maximal number of disjoint weyl group orbits on real roots in a hyperbolic root system is 4

analyticity of the self energy in total momentum of an atom coupled to the quantized radiation field abstract we study a neutral atom with a non vanishing electric dipole moment coupled to the quantized electromagnetic field for a sufficiently small dipole moment and small momentum p the one particle self energy of an atom is proven to be a real analytic function of its momentum the main ingredient of our proof is a suitable form of the feshbach schur spectral renormalization group

on the mahler measure of the coxeter polynomial of an algebra abstract let a be a finite dimensional algebra over an algebraically closed field k assume a is a basic connected and triangular algebra with n pairwise non isomorphic simple modules we consider the coxeter transformation a t as the automorphism of the grothendieck group k 0 a induced by the auslander reiten translation in the derived category der b mod a of the module category mod a of finite dimensional left a modules we say that a is of cyclotomic type if the characteristic polynomial a of a is a product of cyclotomic polynomials equivalently if the mahler measure m a 1 in 6 we have considered many examples of algebras of cyclotomic type in the representation theory literature in this paper we study the mahler measure of the coxeter polynomial of accessible algebras in 1933 d h lehmer found that the polynomial t 10 t 9 t 7 t 6 t 5 t 4 t 3 t 1 has mahler measure 0 1 176280 and he asked whether there exist any smaller values exceeding 1 in this paper we prove that for any accessible algebra a either m a 1 or m b 0 for some convex subcategory b of a we introduce interlaced tower of algebras a m a n with m n 2 satisfying a s 1 t 1 a s t a s 1 for m 1 s n 1 we prove that if spec a n s 1 r and a n is not of cyclotomic type then m a m m a n we construct several examples

functional integral representations of the pauli fierz model with spin 1 2 a feynman kac type formula for a levy and an infinite dimensional gaussian random process associated with a quantized radiation field is derived in particular a functional integral representation of e thpf generated by the pauli fierz hamiltonian with spin 1 2 in non relativistic quantum electrodynamics is constructed when no external potential is applied hpf turns translation invariant and it is decomposed as a direct integral hpf r3 hpf p dp the functional integral representation of e thpf p is also given although all these hamiltonians include spin nevertheless the kernels obtained for the path measures are scalar rather than matrix expressions as an application of the functional integral representations energy comparison inequalities are derived