Related papers: A numerical approach to harmonic non-commutative s…
We present a simple and consistent way to compute correlation functions in interacting theories with non-trivial phase diagram. As an example we show how to consistently compute the four-point function in three dimensional…
The survey is devoted to numerical solution of the fractional equation $A^\alpha u=f$, $0 < \alpha <1$, where $A$ is a symmetric positive definite operator corresponding to a second order elliptic boundary value problem in a bounded domain…
We derive and analyze the perturbation series for the classical effective action in quantum statistical mechanics, treated as a toy model for the dimensionally reduced effective action in quantum field theory at finite temperature. The…
We describe a general technique to study Dirac operators on noncommutative spaces under some additional assumptions. The main idea is to capture the compact resolvent condition in a combinatorial set up. Using this, we then prove that for a…
We discuss a formulation of harmonic superspace approach for noncommuative N=2 supersymmetric field theories paying main attention on new features arising because of noncommutativity. We begin with the known notions of the harmonic…
Scalar field cosmologies with a generalized harmonic potential are investigated in flat and negatively curved Friedmann-Lema\^itre-Robertson-Walker and Bianchi I metrics. An interaction between the scalar field and matter is considered.…
This paper introduces a mathematical approach that allows one to numerically solve the nonclassical transport equation in a deterministic fashion using classical numerical procedures. The nonclassical transport equation describes particle…
We derive the exact form of the spectral interaction of two strings mediated by a constant scalar field using methods derived from noncommutative geometry. This is achieved by considering a non-product modification of the Connes-Lott model…
Many modern statistical applications ask for the estimation of a covariance (or precision) matrix in settings where the number of variables is larger than the number of observations. There exists a broad class of ridge-type estimators that…
The noncommutative scalar theory with harmonic term (on the Moyal space) has a vanishing beta function. In this paper, we prove the renormalizability of the commutative scalar field theory with harmonic term to all orders by using…
We study "circular net" (discrete orthogonal net) equations for angular data generalized by external spectral parameters. A criterion defining physical regimes of these Hamiltonian equations is the reality of Lagrangian density. There are…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
This work introduces the causal bootstrap, a framework for bounding smeared spectral observables from finite non-perturbative Euclidean data. The method optimizes over the convex set of positive spectral densities compatible with the data…
The new perturbation theory for the problem of nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zero order approximation the exact wave function of harmonic oscillator with variable frequency…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…
We review the noncommutative spectral geometry, a gravitational model that combines noncommutative geometry with the spectral action principle, in an attempt to unify General Relativity and the Standard Model of electroweak and strong…
It is well known that quantum-mechanical perturbation theory often give rise to divergent series that require proper resummation. Here I discuss simple ways in which these divergences can be avoided in the first place. Using the elementary…
The effective action for the interacting massive scalar field in curved space-time is derived using the heat-kernel method. Starting from this effective action, we establish a smooth quadratic form of the low-energy decoupling for the…
High-temperature resummed perturbation theory is plagued by poor convergence properties. The problem appears for theories with bosonic field content such as QCD, QED or scalar theories. We calculate the pressure as well as other…
A new version of the delta expansion is presented, which, unlike the conventional delta expansion, can be used to do nonperturbative calculations in a self-interacting scalar quantum field theory having broken symmetry. We calculate the…