Farahmand Hasanov | Searcharxiv

arXiv2026

Non-vacuum gravitational effective action

Curvature expansion for the heat kernel trace and the one-loop effective action is built for the wave operator of the theory in the quasi-thermal setup of a nonvacuum quantum state. This setup implies a non-static and non-stationary Euclidean gravitational background with periodic boundary conditions of the period $β=1/T$, where $T$ plays the role of effective global temperature to be locally rescaled by the metric gravitational potential. The results are obtained in the approximation quadratic in metric perturbations on top of flat Euclidean space and covariantized in terms of spacetime curvature. Covariantization includes a special vector field $ξ^μ(x)$ which generalizes the Killing vector of static geometries with time translation isometry to the case of a generic arbitrarily inhomogeneous metric subject to timelike periodicity condition. This vector field is obtained as a covariant metric functional to quadratic order in metric perturbations and gives rise to the local function $T/\sqrt{ξ^2(x)}$, $ξ^2(x)=g_{μν}(x)ξ^μ(x)ξ^ν(x)$, reducing to Tolman temperature $T/\sqrt{g_{00}(\boldsymbol{x})}$ on stationary manifolds with Killing symmetry. High ``temperature'' asymptotic behavior of the nonlocal form factors---operator coefficients of the curvature tensor structures in the heat kernel and effective action---are obtained and possible cosmological applications of these results are discussed.

hep-th↗

arXiv2024

Unperturbation theory: reconstructing Lagrangians from instanton fluctuations

Instantons present a deep insight into non-perturbative effects both in physics and mathematics. While leading instanton effects can be calculated simply as an exponent of the instanton action, the calculation of subleading contributions usually requires the spectrum of fluctuation operator on the instanton background and its Green's function, explicit knowledge of which is rare and a great success. Thus, we propose an inverse problem, namely, the reconstruction of the nonlinear action of the theory admitting instantons from the given fluctuation operator with a known Green's function. We constructively build the solution for this problem and apply it to a wide class of exactly solvable Schrödinger operators, called shape-invariant operators, and its simpler subclass, namely reflectionless Pöschl-Teller operators. In the latter case, we found that for the most values of parameters the reconstructed potentials are naturally defined not on the real line, but on some special multisheet covering of the complex plane, and discuss its physical interpretation. For the wider but less simple class of shape-invariant operators, we derive the set of parameters leading to the new infinite families of analytic potentials.

hep-th↗