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Quantum Field Theory (QFT) developed in Rindler space-time and its thermal properties are analyzed by means of quantum groups approach. The quantum deformation parameter, labelling the unitarily inequivalent representations, turns out to be…
We define a notion of formal quantum field theory and associate a formal quantum field theory to K-theoretical intersection theories on Hilbert schemes of points on algebraic surfaces. This enables us to find an effective way to compute…
We provide an axiomatic framework for Quantum Field Theory at finite temperature which implies the existence of general analyticity properties of the $ n $-point functions; the latter parallel the properties derived from the usual Wightman…
The concept of definability of quantum fields in a set-theoretical foundation is introduced. We propose an axiomatic set theory and then derive a nonlinear sigma model and the Schroedinger equation in a Lagrangian form; this follows…
In recent years, a method for computing spin dynamics at infinite temperature (spinDMFT) was developed. It utilizes the ideas of dynamical mean-field theory for fermions: single-site approximation and a self-consistency condition to…
There has been significant progress in our understanding of finite-temperature field theory over the past decade. In this paper, we review the progress in perturbative thermal field theory focusing on thermodynamic quantities. We first…
An introductory theory of frames on finite dimensional quaternion Hilbert spaces is demonstrated along the lines of their complex counterpart.
This is a pedagogical review on recent progress in the exact evaluation of physical quantities in interacting quantum systems at finite temperatures. 1D quantum spin chains are discussed in detail as typical examples.
We consider finite temperature correlation functions in massive integrable Quantum Field Theory. Using a regularization by putting the system in finite volume, we develop a novel approach (based on multi-dimensional residues) to the form…
We discuss the $\phi^6 $ theory defined in $D=2+1$-dimensional space-time and assume that the system is in equilibrium with a thermal bath at temperature $\beta^{-1}$. We use the $ 1/N $ expansion and the method of the composite operator…
Plan of this report is given below: 1. Motivation from Physical and Mathematical Point of View; 2. Differential Calculi on Finite Groups; 3. Metrics; 4. Lagrangian Field Theory and Symplectic Structure; 5. Scalar Field Theory and Spectral…
A new approach is demonstrated that QFTs can be UV finite if they are viewed as the low energy effective theories of a fundamental underlying theory (that is complete and well-defined in all respects) according to the nowaday's standard…
Within the framework of generalized free field theory at nonzero temperature we address the problem of current conservation. The formalism of thermo field dynamics is used to derive a conserved and thermodynamically consistent physical…
Establishing a description for confinement is not something simple. In order to try to understand a little about this phenomenon, we will explore the thermodynamics of models that try to describe it in terms of propagators with violation of…
A comprehensive introduction to two-dimensional conformal field theory is given.
Scalar field theory at finite temperature is investigated via an improved renormalization group prescription which provides an effective resummation over all possible non-overlapping higher loop graphs. Explicit analyses for the lambda…
We propose a fractional variant of Mellin's transform which may find an application in the Conformal Field Theory. Its advantage is the presence of an arbitrary parameter which may substantially simplify calculations and help adjusting…
In this paper, we study the question of quantization of quantum field theories in a general light-front frame. We quantize scalar, fermion as well as gauge field theories in a systematic manner carrying out the Hamiltonian analysis…
In this chapter I discuss the impact of concepts of Quantum Field Theory in modern Condensed Physics. Although the interplay between these two areas is certainly not new, the impact and mutual cross-fertilization has certainly grown…
At high temperatures a four dimensional field theory is reduced to a three dimensional field theory. In this letter we consider the $\phi^4$ theory whose parameters are chosen so that a thermal phase transition occurs at a high temperature.…