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Related papers: Heat kernel coefficients for massive gravity

200 papers

Among the available perturbative approaches in quantum field theory, heat kernel techniques provide a powerful and geometrically transparent framework for computing effective actions in nontrivial backgrounds. In this work, resummation…

High Energy Physics - Theory · Physics 2025-11-06 S. A. Franchino-Viñas , C. García-Pérez , F. D. Mazzitelli , S. Pla , V. Vitagliano

We suggest a systematic calculational scheme for heat kernels of covariant nonminimal operators in causal theories whose characteristic surfaces are null with respect to a generic metric. The calculational formalism is based on a…

High Energy Physics - Theory · Physics 2025-12-05 Andrei O. Barvinsky , Alexey E. Kalugin , Władysław Wachowski

We establish two-sided Gaussian bounds on the heat kernel of divergence-form parabolic equation with singular time-inhomogeneous vector field satisfying some minimal assumptions.

Analysis of PDEs · Mathematics 2023-11-22 Damir Kinzebulatov , Yuliy A. Semenov

Using our recently proposed covariant algebraic approach the heat kernel for a Laplace-like differential operator in low-energy approximation is studied. Neglecting all the covariant derivatives of the gauge field strength (Yang-Mills…

High Energy Physics - Theory · Physics 2009-10-28 I. G. Avramidi

We present a very quick and powerful method for the calculation of heat-kernel coefficients. It makes use of rather common ideas, as integral representations of the spectral sum, Mellin transforms, non-trivial commutation of series and…

High Energy Physics - Theory · Physics 2016-09-06 M. Bordag , E. Elizalde , K. Kirsten

We present a formalism for computing arbitrary multi-loop Feynman graphs in curved spacetime using the heat kernel approach. To this end, we compute the off-diagonal components of the heat kernel in Riemann normal coordinates up to second…

High Energy Physics - Theory · Physics 2024-08-09 Igor Carneiro , Gero von Gersdorff

In this note we apply heat kernels to derive some localization formula in sympletcic geometry, to study moduli spaces of flat connections on a Riemann surface, to obtain the push-forward measures for certain maps between Lie groups and to…

Differential Geometry · Mathematics 2007-05-23 Kefeng Liu

We obtain heat kernel estimates for a class of fourth order non-uniformly elliptic operators in two dimensions. Contrary to existing results, the operators considered have symbols that are not strongly convex. This rises certain…

Analysis of PDEs · Mathematics 2022-11-22 Gerassimos Barbatis , Panagiotis Branikas

We derive the first six coefficients of the heat kernel expansion for the electromagnetic field in a cavity by relating it to the expansion for the Laplace operator acting on forms. As an application we verify that the electromagnetic…

Mathematical Physics · Physics 2015-06-26 F. Bernasconi , G. M. Graf , D. Hasler

We introduce a class of non-commutative Heisenberg like infinite dimensional Lie groups based on an abstract Wiener space. The Ricci curvature tensor for these groups is computed and shown to be bounded. Brownian motion and the…

Probability · Mathematics 2008-05-13 Bruce Driver , Maria Gordina

In this paper we shall study vacuum fluctuations of a single scalar field with Dirichlet boundary conditions in a finite but very long line. The spectral heat kernel, the heat partition function and the spectral zeta function are calculated…

Mathematical Physics · Physics 2009-07-27 J. Mateos Guilarte , J. M. Munoz-Castaneda , M. J. Senosiain

We consider certain results for the heat kernel of nonminimal operators. The general expressions provided by Gusynin and Kornyak resulting from symbolic computation programmes for n dimensions are evaluated for 4 dimensions which are…

High Energy Physics - Theory · Physics 2008-11-26 B. Ananthanarayan

We compute the first four heat-kernel coefficients required for the renormalization of Linearized Massive Gravity. We focus on the Fierz-Pauli theory in a curved spacetime, describing the propagation of a massive spin $2$ field in a…

High Energy Physics - Theory · Physics 2025-03-17 Leonardo Farolfi , Filippo Fecit

The aim of this paper is threefold. First, we obtain the precise bounds for the heat kernel on isotropic Heisenberg groups by using well-known results in the three dimensional case. Second, we study the asymptotic estimates at infinity for…

Analysis of PDEs · Mathematics 2018-09-25 Hong-Quan Li , Ye Zhang

We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are H\"older continuous locally in space and time. This is done via local…

Differential Geometry · Mathematics 2018-07-23 Lashi Bandara , Paul Bryan

We report the calculation of the fourth coefficient in an expansion of the heat kernel of a non-minimal, non-abelian kinetic operator in an arbitrary background gauge in arbitrary space-time dimension. The fourth coefficient is shown to…

High Energy Physics - Theory · Physics 2009-10-28 E. I. Guendelman , A. V. Leonidov , V. A. Nechitailo , D. A. Owen

The local momentum space expansion for the real vector field is considered. Using Riemann normal coordinates we obtain an expansion of the Feynman Green function up and including terms that are quadratic in the curvature. The results are…

High Energy Physics - Theory · Physics 2015-06-22 David J. Toms

We obtain Sobolev inequalities for the Schrodinger operator -\Delta-V, where V has critical behaviour V(x)=((N-2)/2)^2|x|^{-2} near the origin. We apply these inequalities to obtain pointwise estimates on the associated heat kernel,…

Analysis of PDEs · Mathematics 2007-05-23 G. Barbatis , S. Filippas , A. Tertikas

The heat kernel coefficients $H_k$ to the Schr\"odinger operator with a matrix potential are investigated. We present algorithms and explicit expressions for the Taylor coefficients of the $H_k$. Special terms are discussed, and for the…

High Energy Physics - Theory · Physics 2009-10-28 I. G. Avramidi , R. Schimming

We numerically compute the heat kernel on a square lattice torus equipped with the measure corresponding to Liouville quantum gravity (LQG). From the on-diagonal heat kernel we verify that the spectral dimension of LQG is 2. Furthermore,…

Mathematical Physics · Physics 2014-11-07 Grigory Bonik , Joe P. Chen , Alexander Teplyaev