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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…
We discuss the properties of bound states in finite-bandwidth waveguide QED beyond the Rotating Wave Approximation or excitation number conserving light-matter coupling models. Therefore, we extend the \emph{standard} calculations to a…
The multiscale entanglement renormalization ansatz is applied to the study of boundary critical phenomena. We compute averages of local operators as a function of the distance from the boundary and the surface contribution to the ground…
A knowledge of nonpertubative propagators is often needed when the standard perturbative methods are not applicable. An example of this is the bound state problem in field theory. While a nonperturbative result is valuable by itself, it is…
It is explained how field-theoretic methods and the dynamic renormalisation group (RG) can be applied to study the universal scaling properties of systems that either undergo a continuous phase transition or display generic scale…
The dynamics of classical field theories is usually governed by field equations, but when fields are constrained to bounded domains it is also dependent on its boundary conditions. Usually boundary conditions are constrained by the…
A renormalization group flow equation with a scale-dependent transformation of field variables gives a unified description of fundamental and composite degrees of freedom. In the context of the effective average action, we study the…
We study the problem of the boundary conditions in the numerical simulation of closed and open quantum systems, described by a Schr\"odinger equation. On one hand, we show that a closed quantum system is defined by local boundary…
We review our recent results on the on-shell description of sine-Gordon model with integrable boundary conditions. We determined the spectrum of boundary states together with their reflection factors by closing the boundary bootstrap and…
The interest in the properties of edge states in Chern insulators and in $\mathbb{Z}_2$ topological insulator has increased rapidly in recent years. We present calculations on how to influence the transport properties of chiral and helical…
We make an attempt to map the integrable boundary conditions for 2 dimensional non-linear O(N) $\sigma$-models. We do it at various levels: classically, by demanding the existence of infinitely many conserved local charges and also by…
The problem of calculating of the mass spectrum of the two-body Bethe-Salpeter equation is studied with no reduction to the three-dimensional ("quasipotential") equation. The method to find the ground state and excited states for a channel…
The bound states of two particles are studied in frames of non-relativistic quantum field model with current $\times$ current type interaction by analyzing the Bethe-Salpeter amplitudes. The Bethe-Salpeter equations are obtained in closed…
We use quantum electrodynamics and the Bethe-Salpeter equation to calculate the bound state energies for a two-particle system comprised of a spin-0 and spin-1/2 particle. We generalize our treatment to include the finite size of the…
In this work we address the reconstruction problem, investigating the construction of field theories from supersymmetric quantum mechanics. The procedure is reviewed, starting from reflectionless potentials that admit one and two bound…
We analyze the Ising model on a random surface with a boundary magnetic field using matrix model techniques. We are able to exactly calculate the disk amplitude, boundary magnetization and bulk magnetization in the presence of a boundary…
It has been established that Matrix Product States can be used to compute the ground state and single-particle excitations and their properties of lattice gauge theories at the continuum limit. However, by construction, in this formalism…
The $\beta$ function for a scalar field theory describes the dependence of the coupling constant on the renormalization mass scale. This dependence is affected by the choice of regularization scheme. I explicitly relate the…
In the framework of relativistic quantum field theory, the solution of homogeneous Bethe-Salpeter equation for two-body bound state can not describe unstable system, so we develop Bethe-Salpeter theory to investigate resonance which is…
We consider a problem whether bound states are made in a scalar theory with a fourth-order derivative term or not. After rewriting the theory to a standard scalar theory with second-order derivative terms, we calculate a correlation…