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Vladimir V. Belokurov

Publications and source records attributed to Vladimir V. Belokurov.

11 recordsLinked to original sources
arXiv2026

Quantum "Twin Peaks" or Path Integrals in the Future Light Cone

By analogy with the Wiener measure on the Euclidean plane that is invariant under the group of rotations and quasi-invariant under the group of diffeomorphisms, we construct the path integrals measure that is invariant under the Lorentz group and quasi-invariant under the group of diffeomorphisms. The correspondence between the paths in the future cone of the Minkowskian plane and the paths in the coverings of the Euclidean plane is established.

math-ph↗
arXiv2024

Perturbation Theory for Path Integrals in Quadratic Gravity

The action $A$ of Quadratic Gravity in FLRW metric is invariant under the group of diffeomorphisms of the time coordinate and can be written in terms of the only dynamical variable $g(τ)\,.$ We construct perturbation theory for calculating path integrals of the form $\int\,F(g)\,\exp\left\{-A (g)\right\}dg\,,$ and find the averaged value of the scale factor in the first nontrivial perturbative order.

hep-th↗
arXiv2022

An Approach to Quantum 2D Gravity

We consider a model of 2D gravity with the action quadratic in curvature and represent path integrals as integrals over the SL(2, R) invariant Gaussian functional measure. We reduce these path integrals to the products of Wiener path integrals and calculate the correlation function of the metric in the first perturbative order.

hep-th↗
arXiv2022

Path Integrals in Quadratic Gravity

Using the invariance of Quadratic Gravity in FLRW metric under the group of diffeomorphisms of the time coordinate, we rewrite the action $A$ of the theory in terms of the invariant dynamical variable $g(τ)\,.$ We propose to consider the path integrals $\int\,F(g)\,\exp\left\{-A \right\}dg$ as the integrals over the functional measure $μ(g)=\exp\left\{-A_{2} \right\}dg\,,\ $ where $A_{2}$ is the part of the action $A$ quadratic in $R\,.$ The rest part of the action stands in the exponent in the integrand as the "interaction" term. We prove the measure $μ(g)$ to be equivalent to the Wiener measure, and, as an example, calculate the averaged scale factor in the first nontrivial perturbative order.

hep-th↗
arXiv2020

Schwarzian functional integrals calculus

We derive the general rules of functional integration in the theories of Schwarzian type, thus completing the elaboration of Schwarzian functional integrals calculus initiated in \cite{(BShExact)}, \cite{(BShCorrel)}. Our approach is mathematically rigorous and does not contain any unproved conjectures. It is based on the analysis of the properties of the measures on the groups of diffeomorphisms, and does not appeal for the experience from other physical models. Its great merit consists in reducing a problem of functional integration to that of the only functional integral (\ref{E}) that is calculated explicitly with the result written in the form of the ordinary integral. We evaluate two-point and four-point correlation functions defined as functional integrals over the groups $Diff^{1}_{+}(\textbf{R}) $ and $Diff^{1}_{+}(S^{1})\,,$ and discuss the difference between the results in the two cases.

hep-th↗
arXiv2019

Polar decomposition of the Wiener measure: Schwarzian theory versus conformal quantum mechanics

We derive the explicit form of the polar decomposition of the Wiener measure, and obtain the equation connecting functional integrals in conformal quantum mechanics to those in the Schwarzian theory. Using this connection we evaluate some nontrivial functional integrals in the Schwarzian theory and also find the fundamental solution of the Schroedinger equation in imaginary time in the model of conformal quantum mechanics.

hep-th↗
arXiv2018

Unusual view of the Schwarzian theory

A decomposition of the Wiener measure based on its quasi-invariance under the group of diffeo- morphisms is proposed. As a result, functional integrals in the Schwarzian theory can be written as the Fourier transform of the integrals in a tahyonic model with the Calogero potential.

hep-th↗
arXiv2017

Evolution of the Universe caused by the averaged potential of the quantum scalar field

We study the quantum theory of the singular scalar field $φ$ minimally coupled to gravity. In our approach, the scalar field is treated as a true quantum variable, while the scale factor $a(t)$ is supposed to be classical. We evaluate the quantum average of the self-interaction potential $V(φ)$ and use it in the modified differential equation for the Hubble parameter.

hep-th↗
arXiv2015

Convergent Perturbation Theory for the lattice $ϕ^4$-model

The standard lattice perturbation theory leads to the asymptotic series because of the incorrect interchange of the summation and integration. However, changing the initial approximation of the perturbation theory, one can generate the convergent series. We study the lattice $ϕ^4$-model and compare the operator $\langleϕ_n^2\rangle$ calculated using the convergent series and obtained by Monte Carlo simulations.

hep-lat↗