Related papers: A new generalized Wick theorem in conformal field …

We present various generalizations of the Dirac formalism. The different-parity solutions of the Weinberg's 2(2J+1)-component equations are found. On this basis, generalizations of the Bargmann-Wigner (BW) formalism are proposed. Relations…

We analyze the commutation relations of light-ray operators in conformal field theories. We first establish the algebra of light-ray operators built out of higher spin currents in free CFTs and find explicit expressions for the…

I review three different problems occuring in two dimensional field theory: 1) classification of conformal field theories; 2) construction of lattice integrable realizations of the latter; 3) solutions to the WDVV equations of topological…

We consider scalar field theory in the D-dimensional space with nontrivial metric and local action functional of most general form. It is possible to construct for this model a generalization of renormalization procedure and RG-equations.…

We present a general theory of mixing for an arbitrary number of fields with integer or half-integer spin. The time dynamics of the interacting fields is solved and the Fock space for interacting fields is explicitly constructed. The…

This is the revised version of the second paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. The theory will be illustrated in upcoming papers by applications to Floer Theory,…

The reductions of conformal field theories which lead to generalized abelian cosets are studied. Primary fields and correlation functions of arbitrary abelian coset conformal field theory are explicitly expressed in terms of those of the…

For a generic $\Ww$ algebra, we give an algorithmic procedure for factoring out all fields of dimension $1/2$, both bosonic and fermionic, and some fields of dimension $1$. This generalizes and makes more explicit the Goddard-Schwimmer…

We show how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective…

We establish a direct connection between two fundamental topics: one in probability theory and one in quantum field theory. The first topic is the problem of pointwise multiplication of random Schwartz distributions which has been the…

We consider application of the analytic functional approach to the conformal field theories associated with mean field theory and Wilson-Fisher fixed point. We study the constraints imposed by the crossing symmetry on the coefficients of…

In this work we present the formal background used to develop the methods used in earlier works to extend the truncated Wigner representation of quantum and atom optics in order to address multi-time problems. The truncated Wigner…

We present a new technique for putting general boson fields into ant-Wick ordered form. The anti-Wick map associates an operator with a given function of complex variables, and we show that it may be realized as composition of a mapping to…

We define generalized vector fields, and contraction and Lie derivatives with respect to them. Generalized commutators are also defined.

We consider a theory of fermions interacting with a (in general, non-Abelian) gauge field. The theory is assumed to be essentially inhomogeneous, which might be provided by non-trivial background fields interacting with both fermions and…

Vertex algebras provide an axiomatic algebraic description of the operator product expansion (OPE) of chiral fields in 2-dimensional conformal field theory. Vertex Lie algebras (= Lie conformal algebras) encode the singular part of the OPE,…

We explain how to incorporate the action of local integrals of motion into the fermionic basis for the sine-Gordon model and its UV CFT. The examples up to the level 4 are presented. Numerical computation support the results. Possible…

Following on from previous work we derive the non-linear differential equations of more general correlators of U(1) twist fields in two-dimensional massive Dirac theory. Using the conserved charges of the double copy model equations…

Operator product expansions (OPE) for the product of a scalar field with its conjugate are presented as infinite sums of bilocal fields V_k (x_1, x_2) of dimension (k,k). For a {\it globally conformal invariant} (GCI) theory we write down…

We revisit the most general theory for a massive vector field with derivative self-interactions, extending previous works on the subject to account for terms having trivial total derivative interactions for the longitudinal mode. In the…