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The main principles of two-dimensional quantum field theories, in particular two-dimensional QCD and gravity are reviewed. We study non-perturbative aspects of these theories which make them particularly valuable for testing ideas of…

We present detailed analytical calculations for an 1D Ising ring of arbitrary number of spin-1/2 particles, in order to reveal entanglement properties of the stationary states. We show that the ground state and specific eigenstates of the…

One of the simplest examples of a PT-symmetric quantum system is the scaling Yang-Lee model, a quantum field theory with cubic interaction and purely imaginary coupling. We give a historical review of some facts about this model in d <= 2…

The study of noncommutative solitons is greatly facilitated if the field equations are integrable, i.e. result from a linear system. For the example of a modified but integrable U(n) sigma model in 2+1 dimensions we employ the dressing…

We present a quantum theory for the dynamic structure factors in non-equilibrium, correlated, two-component systems such as plasmas or warm dense matter. Using this general framework, we derive expressions for effective local field…

The paper is devoted to integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also…

We revisit one of the earliest proposals for deformed dispersion relations in the light of recent results on dynamical dimensional reduction and production of cosmological fluctuations. Depending on the specification of the measure of…

In this lecture, we survey a number of recent results and developments regarding the representation theory of infinite-dimensional quantum groups (quantum affine algebras and related algebras), as well as their connections with cluster…

A recently conjectured relashionship between UV and IR cutoffs in an effective field theory without quantum gravity is generalized in the presence of large extra dimensions. Estimates for the corrections to the usual calculation of…

We study the form factors of local operators of integrable QFT's between states with finite energy density. These states arise, for example, at finite temperature, or from a generalized Gibbs ensemble. We generalize Smirnov's form factor…

I describe how integrable quantum field theories in 2 spacetime dimensions are characterized by infinite dimensional quantum group symmetries, namely the q-deformations of affine Lie algebras, and their Yangian limit. These symmetries can…

We consider the problem of the characteristics of mass spectra in the doubly symmetric theory of fields transforming under the proper Lorentz group representations decomposable into an infinite direct sum of finite-dimensional irreducible…

We combine spectral- and split representations to factorize multi-loop momentum space diagrams, in the Schwinger-Keldysh formulation for cosmological correlators, with massive scalars in the loop. This allows us to extend the resummation of…

We classify and relate unitary irreducible representations (UIRs) of the Carroll and dipole groups, i.e., we define elementary quantum Carroll and fracton particles and establish a correspondence between them. Whenever possible, we express…

The partition function with boundary conditions for various two-dimensional Ising models is examined and previously unobserved properties of conformal invariance and universality are established numerically.

A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…

In this PhD thesis we investigate some properties of one-dimensional quantum systems, focusing on two important aspects of integrable models: Their entanglement properties at equilibrium and their dynamical correlators after a quantum…

The general boundary formulation of quantum field theory is applied to a massive scalar field in two dimensional Rindler space. The field is quantized according to both the Schr\"odinger-Feynman quantization prescription and the holomorphic…

Using Quantum Field Theory we derive a general formula for the double inclusive spectra of photons radiated by a system in local equilibrium. The derived expression differs significantly from the one mostly used up to now in photon…

We discuss an application of the method of the angular quantization to reconstruction of form-factors of local fields in massive integrable models. The general formalism is illustrated with examples of the Klein-Gordon, sinh-Gordon and…