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We study the invariants of spin networks embedded in a three-dimensional manifold which are based on the path integral for SU(2) BF-Theory. These invariants appear naturally in Loop Quantum Gravity, and have been defined as spin-foam state…
A perturbation theory for Massive Thirring Model (MTM) in radial quantization approach is developed. Investigation of the twisted sector in this theory allows us to calculate the vacuum expectation values of exponential fields $ exp iaphi…
The quantum theory of cosmological perturbations in single field inflation is formulated in terms of a path integral. Starting from a canonical formulation, we show how the free propagators can be obtained from the well known…
We study the infra-red limit of non-abelian Chern-Simons gauge theory perturbed by a non-topological, albeit gauge invariant, mass term. It is shown that, in this limit, we may construct an infinite class of integrable quantum mechanical…
Infrared divergences in QED and other theories with massless particles show that in such theories the $S$ matrix cannot be defined in the usual way. Typically, this is not viewed as a big problem since one is interested in cross sections,…
In some versions of the theory of inflation, it is assumed that before inflation began the universe was in a Friedmann-Robertson-Walker (FRW) stage, with the energy density dominated by massless particles. The origin of the nearly…
We consider the two-dimensional quantum field theory of a scalar field self-interacting via two periodic terms of frequencies $\alpha$ and $\beta$. Looking at the theory as a perturbed Sine-Gordon model, we use Form Factor Perturbation…
In this work, the linear and gauge-invariant theory of cosmological perturbations in a class of anisotropic and shear-free spacetimes is developed. After constructing an explicit set of complete eigenfunctions in terms of which…
We derive a simple classification of quantum spin Chern-Simons theories with gauge group T=U(1)^N. While the classical Chern-Simons theories are classified by an integral lattice the quantum theories are classified differently. Two quantum…
The Chern-Simons functionals built from various connections determined by the initial data $h_{\mu\nu}$, $\chi_{\mu\nu}$ on a 3-manifold $\Sigma$ are investigated. First it is shown that for asymptotically flat data sets the logarithmic…
A general model independent approach using the `off-shell Bethe Ansatz' is presented to obtain an integral representation of generalized form factors. The general techniques are applied to the quantum sine-Gordon model alias the massive…
Higher orders in perturbation theory require the calculation of Feynman integrals at multiple loops. We report on an approach to systematically solve Feynman integrals by means of symbolic summation and discuss the underlying algorithms.…
We consider a version of the symmetric Anderson impurity model (compactified) which has a non-Fermi liquid weak coupling regime. We find that in the Majorana fermion representation, perturbation theory can be conveniently developed in terms…
We present an approach for the calculation of the $\mathbb{Z}_2$ topological invariant in non-crystalline two-dimensional quantum spin Hall insulators. While topological invariants were originally mathematically introduced for crystalline…
The unitary transformation of path-integral differential measure is described. The main properties of perturbation theory in the phase space of action-angle, energy-time variables are investigated. The measure in cylindrical coordinates is…
This review deals with strongly disordered topological insulators and covers some recent applications of a well established analytic theory based on the methods of Non-Commutative Geometry (NCG) and developed for the Integer Quantum…
In five spacetime dimensions, instantons are finite energy, solitonic particles. We describe the dynamics of these objects in the presence of a Chern-Simons interaction. For U(N) instantons, we show that the 5d Chern-Simons term induces a…
A previously proposed non-canonical coupled-perturbed Kohn-Sham density functional theory (KS-DFT)/Hartree-Fock (HF) treatment for spin-orbit coupling is here generalized to infinite periodic systems. The scalar-relativistic periodic…
In this article, we propose the realization of conformal manifolds, which are smooth manifolds of scale-conformal invariant interacting Hamiltonians in two-dimensional quantum many-body systems. Such phenomena can occur in various…
We consider the $2+1$ dimensional Yang-Mills theory with gauge group $\text{SU}(N)$ on a flat 2-torus under twisted boundary conditions. We study the possibility of phase transitions (tachyonic instabilities) when $N$ and the volume vary…