An Introduction to Yangian Symmetries
We review some aspects of the quantum Yangians as symmetry algebras of two-dimensional quantum field theories. The plan of these notes is the following: 
 
1 
 
The classical Heisenberg model: 
 
 
 
 
 
 
 
 
 
Non-Abelian symmetries; 
 
 
The generators of the symmetries and the semi-classical Yangians; 
 
 
An alternative presentation of the semi-classical Yangians; 
 
 
Digression on Poisson-Lie groups. 
 
 
Non-Abelian symmetries and the quantum Yangians; 
 
 
The transfer matrix and an alternative presentation of the Yangians; 
 
 
Digression on the double Yangians. 
 
 
 
 
 
2 
 
The quantum Heisenberg chain: 
 
 
 
 
 
 
 
 
 
Non-Abelian symmetries and the quantum Yangians; 
 
 
The transfer matrix and an alternative presentation of the Yangians; 
 
 
Digression on the double Yangians.

title: Logarithmic Yangians in WZW Models
abstract: A new action of the Yangians in the WZW models is displayed. Its structure is generic and level-independent. This Yangian is the natural extension at the conformal point of the one unraveled in massive theories with current algebras. Hopefully, this new symmetry of WZW models will lead to a deeper understanding of the integrable structure of conformal field theories and their deformations.

title: Anomalous scaling in the N-point functions of a passive scalar.
abstract: A recent analysis of the 4-point correlation function of the passive scalar advected by a time-decorrelated random flow is extended to the N-point case. It is shown that all stationary-state inertial-range correlations are dominated by homogeneous zero modes of singular operators describing their evolution. We compute analytically the zero modes governing the N-point structure functions and the anomalous dimensions corresponding to them to the linear order in the scaling exponent of the 2-point function of the advecting velocity field. The implications of these calculations for the dissipation correlations are discussed.

title: Differential equations for sine-Gordon correlation functions at the free fermion point
abstract: We demonstrate that for the sine-Gordon theory at the free fermion point, the 2-point correlation functions of the fields eiαΦ for 0 < α < 1 can be parameterized in terms of a solution to the sinh-Gordon equation. This result is derived by summing over intermediate multiparticle states and using the form factors to express this as a Fredholm determinant. The proof of the differential equations relies on a Z2 graded multiplication law satisfied by the integral operators of the Fredholm determinant. Using this methodology, we give a new proof of the differential equations which govern the spin and disorder field correlations in the Ising model.

title: New Lax pair for 2D dimensionally reduced gravity
abstract: Using a Lax pair based on the affine SL(2,) Kac-Moody algebra, we solve two-dimensional reduced vacuum Einstein's equations. We obtain explicit determinant formulae for metric coefficients with no quadrature left. This Lax connection also allows a new approach to the Poisson algebra of two-dimensional reduced gravity. In particular, we show that it leads to pure c-number r-matrices and modified Yang-Baxter equations. We explain how one can construct classical observables within this framework.

title: AFFINE SOLITONS: A RELATION BETWEEN TAU FUNCTIONS, DRESSING AND BÄCKLUND TRANSFORMATIONS
abstract: We reconsider the construction of solitons by dressing transformations in the sine-Gordon model. We show that the N-soliton solutions are in the orbit of the vacuum, and we identify the elements in the dressing group which allow us to build the N-soliton solutions from the vacuum solution. The dressed τ functions can be computed in two different ways: either using adjoint actions in the affine Lie algebra , and this gives the relation with the Backlund transformations, or using the level-one representations of the affine Lie algebra , and this directly gives the formulae for the τ functions in terms of vertex operators.

title: Measurement of the CKM matrix element $|V_{ub}|$ with $B \to \rho e \nu$ decays

title: Measurement of the inclusive charmless semileptonic branching ratio of B mesons and determination of |V ub|.
abstract: We report a measurement of the inclusive charmless semileptonic branching fraction of B mesons in a sample of 89 x 10(6) (-)BB events recorded with the BABAR detector at the Upsilon(4S) resonance. Events are selected by fully reconstructing the decay of one B meson and identifying a charged lepton from the decay of the other B meson. The number of signal events is extracted from the mass distribution of the hadronic system accompanying the lepton and is used to determine the ratio of branching fractions B((-)B-->X(u)lnu;)/B((-)B-->Xlnu;)=[2.06+/-0.25(stat)+/-0.23(syst)+/-0.36(theo)]x10(-2). Using the measured branching fraction for inclusive semileptonic B decays, we find B((-)B-->X(u)lnu;)=[2.24+/-0.27(stat)+/-0.26(syst)+/-0.39(theo)]x10(-3) and derive the Cabibbo-Kobayashi-Maskawa matrix element |V(ub)|=[4.62+/-0.28(stat)+/-0.27(syst)+/-0.48(theo)]x10(-3).

title: Observation of time-reversal violation in the B0 meson system.
abstract: Although CP violation in the B meson system has been well established by the B factories, there has been no direct observation of time-reversal violation. The decays of entangled neutral B mesons into definite flavor states (B(0) or B(0)), and J/ψK(L)(0) or ccK(S)(0) final states (referred to as B(+) or B(-)), allow comparisons between the probabilities of four pairs of T-conjugated transitions, for example, B(0) → B(-) and B(-) → B(0), as a function of the time difference between the two B decays. Using 468 × 10(6) BB pairs produced in Υ(4S) decays collected by the BABAR detector at SLAC, we measure T-violating parameters in the time evolution of neutral B mesons, yielding ΔS(T)(+) = -1.37 ± 0.14(stat) ± 0.06(syst) and ΔS(T)(-) = 1.17 ± 0.18(stat) ± 0.11(syst). These nonzero results represent the first direct observation of T violation through the exchange of initial and final states in transitions that can only be connected by a T-symmetry transformation.

title: Laser Wakefield Acceleration of Particle in a Plasma
abstract: A review of the present situation and perspectives, in particular in the scope of a multi-Tev linear accelerator.

title: Branching fractions in $B \to \phi$ h and search for direct CP violation in $B^\pm \to \phi K^\pm$