pinecone/core-2020-05-10-deduplication huggingface dataset:
Implications of Conformal Invariance in Field Theories for General
  Dimensions

The requirements of conformal invariance for two and three point functions
for general dimension $d$ on flat space are investigated. A compact group
theoretic construction of the three point function for arbitrary spin fields is
presented and it is applied to various cases involving conserved vector
operators and the energy momentum tensor. The restrictions arising from the
associated conservation equations are investigated. It is shown that there are,
for general $d$, three linearly independent conformal invariant forms for the
three point function of the energy momentum tensor, although for $d=3$ there
are two and for $d=2$ only one. The form of the three point function is also
demonstrated to simplify considerably when all three points lie on a straight
line. Using this the coefficients of the conformal invariant point functions
are calculated for free scalar and fermion theories in general dimensions and
for abelian vector fields when $d=4$. Ward identities relating three and two
point functions are also discussed. This requires careful analysis of the
singularities in the short distance expansion and the method of differential
regularisation is found convenient. For $d=4$ the coefficients appearing in the
energy momentum tensor three point function are related to the coefficients of
the two possible terms in the trace anomaly for a conformal theory on a curved
space background.Comment: 46 pages (plain TeX with use of AMS fonts), DAMTP/93-31 (minor
  corrections and additions
A renormalization group approach to Hamiltonian light-front field theory

A perturbative renormalization group is formulated for the study of
Hamiltonian light-front field theory near a critical Gaussian fixed point. The
only light-front renormalization group transformations found that can be
approximated by dropping irrelevant operators and using perturbation theory
near Gaussian fixed volumes, employ invariant-mass cutoffs. These cutoffs
violate covariance and cluster decomposition, and allow functions of
longitudinal momenta to appear in all relevant, marginal, and irrelevant
operators. These functions can be determined by insisting that the Hamiltonian
display a coupling constant coherence, with the number of couplings that
explicitly run with the cutoff scale being limited and all other couplings
depending on this scale only through perturbative dependence on the running
couplings. Examples are given that show how coupling coherence restores Lorentz
covariance and cluster decomposition, as recently speculated by Wilson and the
author. The ultimate goal of this work is a practical Lorentz metric version of
the renormalization group, and practical renormalization techniques for
light-front quantum chromodynamics.Comment: TEX with macros included. 11 figures available upon request. 120
  pages. Ohio State preprint OSU-NT-93-11
Canonical Transformations in Quantum Mechanics

Quantum canonical transformations are defined algebraically outside of a
Hilbert space context. This generalizes the quantum canonical transformations
of Weyl and Dirac to include non-unitary transformations. The importance of
non-unitary transformations for constructing solutions of the Schr\"odinger
equation is discussed. Three elementary canonical transformations are shown
both to have quantum implementations as finite transformations and to generate,
classically and infinitesimally, the full canonical algebra. A general
canonical transformation can be realized quantum mechanically as a product of
these transformations. Each transformation corresponds to a familiar tool used
in solving differential equations, and the procedure of solving a differential
equation is systematized by the use of the canonical transformations. Several
examples are done to illustrate the use of the canonical transformations. [This
is an extensively revised version of hep-th-9205080: the first third of the
paper is new material; the notation has been simplified, and further discussion
has been added to the remainder.]Comment: 43 pages, LaTeX, McGill Univ. 92-29, Imperial-TP-92-93-31,
  NSF-ITP-93-6
Functional Integral Approach to the N-Flavor Schwinger Model

We study massless QED_2 with N flavors using path integrals. We identify the
sector that is generated by the N^2 classically conserved vector currents. One
of them (the U(1) current) creates a massive particle, while the others create
massless ones. We show that the mass spectrum obeys a Witten-Veneziano type
formula. Two theorems on n-point functions clarify the structure of the Hilbert
space. Evaluation of the Fredenhagen-Marcu order parameter indicates that a
confining force exists only between charges that are integer multiples of +/-
Ne, whereas charges that are nonzero mod(N) screen their confining forces and
lead to non-vacuum sectors. Finally we identify operators that violate
clustering, and decompose the theory into clustering theta vacua.Comment: 28 pages, MPI-Ph/93-5
Dynamics of Interfaces in Superconductors

The dynamics of an interface between the normal and superconducting phases
under nonstationary external conditions is studied within the framework of the
time-dependent Ginzburg-Landau equations of superconductivity, modified to
include thermal fluctuations. An equation of motion for the interface is
derived in two steps. First, the method of matched asymptotic expansions is
used to derive a diffusion equation for the magnetic field in the normal phase,
with nonlinear boundary conditions at the interface. These boundary conditions
are a continuity equation which relates the gradient of the field at the
interface to the normal velocity of the interface, and a modified Gibbs-Thomson
boundary condition for the field at the interface. Second, the boundary
integral method is used to integrate out the magnetic field in favor of an
equation of motion for the interface. This equation of motion, which is highly
nonlinear and nonlocal, exhibits a diffusive instability (the Mullins-Sekerka
instability) when the superconducting phase expands into the normal phase
(i.e., when the external field is reduced below the critical field). In the
limit of infinite diffusion constant the equation of motion becomes local in
time, and can be derived variationally from a static energy functional which
includes the bulk free energy difference between the two phases, the
interfacial energy, and a long range self-interaction of the interface of the
Biot-Savart form. In this limit the dynamics is identicalComment: 22 pages, Revtex 3.0, no figure
Hermiticity and the Cohomology Condition in Topological Yang-Mills
  Theory

The symmetries of the topological Yang-Mills theory are studied in the
Hamiltonian formalism and the generators of the twisted N=2 superPoincar\'e
algebra are explicitly constructed. Noting that the twisted Lorentz generators
do not generate the Lorentz symmetry of the theory, we relate the two by
extracting from the latter the twisted version of the internal SU(2) generator.
The hermiticity properties of the various generators are also considered
throughout, and the boost generators are found to be non-hermitian. We then
recover the BRST cohomology condition on physical states from representation
theory arguments.Comment: 19 pages, MIT-CTP 223
Level-Rank Duality of WZW Theories and Isomorphisms of N=2 Coset Models

Mappings between certain infinite series of N=2 superconformal coset models
are constructed. They make use of level-rank dualities for B, C and D type
theories. While the WZW level-rank dualities do not constitute isomorphisms of
the theories, they lead to level-rank dualities of N=2 coset models that
preserve the cft properties in such a manner that the coset models related by
duality are expected to be isomorphic as conformal field theories. The
construction also gives some further insight in the nature of the resolution of
field identification fixed points of coset theories.Comment: 50 pages, NIKHEF-H/93-16a. (Contrary to the claim in the original
  version of this paper, our results in sections 3 through 5 are in perfect
  agreement with those of ref. [4]. We are grateful to the authors of ref. [4]
  for extensive explanation of their notation and apologize for having
  misrepresented their work.
The weak electroweak phase transition

We present a detailed analysis of the phase transition in the standard model
at finite temperature. Using an improved perturbation theory, where plasma
masses are determined from a set of one-loop gap equations, we evaluate the
effective potential $V_{eff}(\varphi,T)$ in next-to-leading order, i.e.,
including terms cubic in the gauge coupling $g$, the scalar self-coupling
$\lambda^{1/2}$ and the top-quark Yukawa coupling $f_t$. The gap equations
yield a non-vanishing magnetic plasma mass for the gauge bosons, originating
from the non-abelian self-interactions. We discuss in detail size and origin of
higher order effects and conclude that the phase transition is weakly
first-order up to Higgs masses of about $70\ GeV$, above which our calculation
is no longer self-consistent. For larger Higgs masses even an approximation
containing all $g^4$ contributions to $V_{eff}$ is not sufficient, at least a
full calculation to order $g^6$ is needed. These results turn out to be rather
insensitive to the top-quark mass in the range $m_t=100\ -\ 180\ GeV$. Using
Langer's theory of metastability we calculate the nucleation rate of critical
droplets and discuss some aspects of the cosmological electroweak phase
transition.Comment: LaTeX, 45 pages, 13 figures [not included, can be sent upon
  request],DESY 93-02
Phase Space Quantum Mechanics on the Anti-De Sitter Spacetime and its
  Poincar\'e Contraction

In this work we propose an alternative description of the quantum mechanics
of a massive and spinning free particle in anti-de~Sitter spacetime, using a
phase space rather than a spacetime representation. The regularizing character
of the curvature appears clearly in connection with a notion of localization in
phase space which is shown to disappear in the zero curvature limit. We show in
particular how the anti-de~Sitter optimally localized (coherent) states
contract to plane waves as the curvature goes to zero. In the first part we
give a detailed description of the classical theory {\it \a la Souriau\/}. This
serves as a basis for the quantum theory which is constructed in the second
part using methods of geometric quantization. The invariant positive K\"ahler
polarization that selects the anti-de~Sitter quantum elementary system is shown
to have as zero curvature limit the Poincar\'e polarization which is no longer
K\"ahler. This phenomenon is then related to the disappearance of the notion of
localization in the zero curvature limit.Comment: 37 pgs+3 figures (not included), PlainTeX, Preprint CRM-183
Relativistic three-particle dynamical equations: I. Theoretical
  development

Starting from the two-particle Bethe-Salpeter equation in the ladder
approximation and integrating over the time component of momentum, we rederive
three dimensional scattering integral equations satisfying constraints of
relativistic unitarity and covariance, first derived by Weinberg and by
Blankenbecler and Sugar. These two-particle equations are shown to be related
by a transformation of variables. Hence we show how to perform and relate
identical dynamical calculation using these two equations. Similarly, starting
from the Bethe-Salpeter-Faddeev equation for the three-particle system and
integrating over the time component of momentum, we derive several three
dimensional three-particle scattering equations satisfying constraints of
relativistic unitarity and covariance. We relate two of these three-particle
equations by a transformation of variables as in the two-particle case. The
three-particle equations we derive are very practical and suitable for
performing relativistic scattering calculations.Comment: 30 pages, Report # IFT P.070/93, [Text in Latex, e-mail:
  tomio@ift.uesp.ansp.br ; FAX: 55-11-288-8224
Relativistic three-particle dynamical equations: II. Application to the
  trinucleon system

We calculate the contribution of relativistic dynamics on the
neutron-deuteron scattering length and triton binding energy employing five
sets trinucleon potential models and four types of three-dimensional
relativistic three-body equations suggested in the preceding paper. The
relativistic correction to binding energy may vary a lot and even change sign
depending on the relativistic formulation employed. The deviations of these
observables from those obtained in nonrelativistic models follow the general
universal trend of deviations introduced by off- and on-shell variations of
two- and three-nucleon potentials in a nonrelativistic model calculation.
Consequently, it will be difficult to separate unambiguously the effect of off-
and on-shell variations of two- and three- nucleon potentials on low-energy
three-nucleon observables from the effect of relativistic dynamics.Comment: 15 pages, [Text and one postscript figure included, e-mail:
  tomio@ift.uesp.ansp.br; Fax: 55-11-288 8224] Report # IFT P.069/9
Fermionic Field Theory and Gauge Interactions on Random Lattices

Random-lattice fermions have been shown to be free of the doubling problem if
there are no interactions or interactions of a non-gauge nature. However, gauge
interactions impose stringent constraints as expressed by the Ward-Takahashi
identities which could revive the free-field suppressed doubler modes in loop
diagrams. After introducing a formulation for fermions on a new kind of random
lattice, we compare random, naive and Wilson fermions in two dimensional
Abelian background gauge theory. We show that the doublers are revived for
random lattices in the continuum limit, while demonstrating that gauge
invariance plays the critical role in this revival. Some implications of the
persistent doubling phenomenon on random lattices are also discussed.Comment: 16 A4 pages, UM-P-93/0
Non-Abelian Chern-Simons Quantum Mechanics and Non-Abelian Aharonov-Bohm
  Effect

We construct a classical action for a system of $N$ point-like sources which
carry SU(2) non-Abelian charges coupled to non-Abelian Chern-Simons gauge
fields, and develop a quantum mechanics for them. Adopting the coherent state
quantization and solving the Gauss' constraint in an appropriately chosen
gauge, we obtain a quantum mechanical Hamiltonian given in terms of the
Knizhnik-Zamolodchikov connection. Then we study the non-Abelian Aharonov-Bohm
effect, employing the obtained Hamiltonian for two-particle sector. An explicit
evaluation of the differential cross section for the non-Abelian Aharonov-Bohm
scattering is given.Comment: 32 pages, Revtex 2.0, two figures available upon request, SNUTP-93/8
Two-Dimensional Gravity and Nonlinear Gauge Theory

We review nonlinear gauge theory and its application to two-dimensional
gravity. We construct a gauge theory based on nonlinear Lie algebras, which is
an extension of the usual gauge theory based on Lie algebras. It is a new
approach to generalization of the gauge theory. The two-dimensional gravity is
derived from nonlinear Poincar{\' e} algebra, which is the new Yang-Mills like
formulation of the gravitational theory. As typical examples, we investigate
$R^2$ gravity with dynamical torsion and generic form of 'dilaton' gravity. The
supersymmetric extension of this theory is also discussed.Comment: 35 pages, phyzzx, RIMS-95
Renormalizability of Effective Scalar Field Theory

We present a comprehensive discussion of the consistency of the effective
quantum field theory of a single $Z_2$ symmetric scalar field. The theory is
constructed from a bare Euclidean action which at a scale much greater than the
particle's mass is constrained only by the most basic requirements; stability,
finiteness, analyticity, naturalness, and global symmetry. We prove to all
orders in perturbation theory the boundedness, convergence, and universality of
the theory at low energy scales, and thus that the theory is perturbatively
renormalizable in the sense that to a certain precision over a range of such
scales it depends only on a finite number of parameters. We then demonstrate
that the effective theory has a well defined unitary and causal analytic
S--matrix at all energy scales. We also show that redundant terms in the
Lagrangian may be systematically eliminated by field redefinitions without
changing the S--matrix, and discuss the extent to which effective field theory
and analytic S--matrix theory are actually equivalent. All this is achieved by
a systematic exploitation of Wilson's exact renormalization group flow
equation, as used by Polchinski in his original proof of the renormalizability
of conventional $\varphi^4$-theory.Comment: 80 pages, TeX, OUTP-93-23P, CERN-TH.7067/93. Many minor revisions,
  and several new paragraph
Functional Schroedinger Equation for Fermions in External Gauge Fields

We discuss the functional Schroedinger picture for fermions in external
fields for both stationary and time-dependent problems. We give formal results
for the ground state and the solution of the time-dependent Schroedinger
equation for QED in arbitrary dimensions, while more explicit results are
obtained in two dimensions. For both the massless and massive Schwinger model
we give an explicit expression for the ground state functional as well as for
the expectation values of energy, electric and axial charge. We also give the
corresponding results for non-abelian fields. We solve the functional
Schroedinger equation for a constant external field in four dimensions and
obtain the amount of particle creation. We solve the Schroedinger equation for
arbitrary external fields for massless QED in two dimensions and make a careful
discussionof the anomalous particle creation rate. Finally, we discuss some
subtleties connected with the interpretation of the quantized Gauss constraint.Comment: 44 pages, LaTex File, preprint Freiburg THEP-94/2 and ETH-TH/93-17,
  hep-th/9306161, corrected version (in particular the particle production
Poisson Bracket on the Space of Histories

We extend the Poisson bracket from a Lie bracket of phase space functions to
a Lie bracket of functions on the space of canonical histories and investigate
the resulting algebras. Typically, such extensions define corresponding Lie
algebras on the space of Lagrangian histories via pull back to a space of
partial solutions. These are the same spaces of histories studied with regard
to path integration and decoherence. Such spaces of histories are familiar from
path integration and some studies of decoherence. For gauge systems, we extend
both the canonical and reduced Poisson brackets to the full space of histories.
We then comment on the use of such algebras in time reparameterization
invariant systems and systems with a Gribov ambiguity, though our main goal is
to introduce concepts and techniques for use in a companion paper.Comment: 25 pages REVTEX, CGPG-93/8-4 (minor changes made
The Generalized Peierls Bracket

We first extend the Peierls algebra of gauge invariant functions from the
space ${\cal S}$ of classical solutions to the space ${\cal H}$ of histories
used in path integration and some studies of decoherence. We then show that it
may be generalized in a number of ways to act on gauge dependent functions on
${\cal H}$. These generalizations (referred to as class I) depend on the choice
of an ``invariance breaking term," which must be chosen carefully so that the
gauge dependent algebra is a Lie algebra. Another class of invariance breaking
terms is also found that leads to an algebra of gauge dependent functions, but
only on the space ${\cal S}$ of solutions. By the proper choice of invariance
breaking term, we can construct a generalized Peierls algebra that agrees with
any gauge dependent algebra constructed through canonical or gauge fixing
methods, as well as Feynman and Landau ``gauge." Thus, generalized Peierls
algebras present a unified description of these techniques. We study the
properties of generalized Peierls algebras and their pull backs to spaces of
partial solutions and find that they may posses constraints similar to the
canonical case. Such constraints are always first class, and quantization may
proceed accordingly.Comment: 30 pages REVTEX, CGPG-93/8-5 (significant mistake in earlier version
  corrected
Manin pairs and topological field theory

Kazama has described an extension of the N=2 superconformal algebra in which
the operator product of G^- with itself is singular. In this paper, we relate
actions of this chiral algebra to Drinfeld's theory of Manin pairs, or
equivalently, quasi-Lie bialgebras. We also show how to couple topological
conformal field theories with this symmetry to topological gravity. As an
application, we demonstrate the equivalence of the SL(2)/SL(2) model to a
deformed SL(2)/SO(2) model tensored with a free field theory. (Revisions
correct some minor errors.)Comment: 36 page
On the emergence of gauge structures and generalized spin when
  quantizing on a coset space

It has been known for some time that there are many inequivalent
quantizations possible when the configuration space of a system is a coset
space G/H. Viewing this classical system as a constrained system on the group
G, we show that these inequivalent quantizations can be recovered from a
generalization of Dirac's approach to the quantization of such a constrained
system within which the classical first class constraints (generating the
H-action on G) are allowed to become anomalous (second class) when quantizing.
The resulting quantum theories are characterized by the emergence of a
Yang-Mills connection, with quantized couplings, and new 'spin' degrees of
{}freedom. Various applications of this procedure are presented in detail:
including a new account of how spin can be described within a path-integral
formalism, and how on S^4 chiral spin degrees of {}freedom emerge, coupled to a
BPST instanton.Comment: 64 pages, plain TeX, DIAS-STP-93-1
On "asymptotically flat" space-times with $G_{2}$-invariant Cauchy
  surfaces

In this paper we study space-times which evolve out of Cauchy data
$(\Sigma,{}^3g,K)$ invariant under the action of a two-dimensional commutative
Lie group. Moreover $(\Sigma,{}^3g,K)$ are assumed to satisfy certain
completeness and asymptotic flatness conditions in spacelike directions. We
show that asymptotic flatness and energy conditions exclude all topologies and
group actions except for a cylindrically symmetric $R^3$, or a periodic
identification thereof along the $z$-axis. We prove that asymptotic flatness,
energy conditions and cylindrical symmetry exclude the existence of compact
trapped surfaces. Finally we show that the recent results of Christodoulou and
Tahvildar-Zadeh concerning global existence of a class of wave-maps imply that
strong cosmic censorship holds in the class of asymptotically flat
cylindrically symmetric electro-vacuum space-times.Comment: 33 pages, Latex (with amssymbols), Garching preprint MPA 797; texing
  problems correcte