Heat kernel expansion: user's manual

By D. Vassilevich. 2003

1,197 citations recorded by the source corpus.

Abstract The heat kernel expansion is a very convenient tool for studying one-loop divergences, anomalies and various asymptotics of the effective action. The aim of this report is to collect useful information on the heat kernel coefficients scattered in mathematical and physical literature. We present explicit expressions for these coefficients on manifolds with and without boundaries, subject to local and non-local boundary conditions, in the presence of various types of singularities (e.g., domain walls). In each case the heat kernel coefficients are given in terms of several geometric invariants. These invariants are derived for scalar and spinor theories with various interactions, Yang–Mills fields, gravity, and open bosonic strings. We discuss the relations between the heat kernel coefficients and quantum anomalies, corresponding anomalous actions, and covariant perturbation expansions of the effective action (both “low-” and “high-energy” ones).

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d0e508509771a9f338394f4d865e303fd173d534

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Central charges for BCFTs and holography (2012, methodology): “∆ij is a second order differential operator on M and one can consider the heat kernel K̂ij(x, y; s) of the operator (we will closely follow [36]) ∆ijK̂jl(x, y; s) = ∂ ∂s K̂il(x, y; s).”
A Tower Weak Gravity Conjecture from Infrared Consistency (2018, methodology): “his appendix, we show how to compute the one-loop eective action of gravity and N gauge elds using the heat kernel expansion. Our discussion of the general method follows closely the review articles [64,65]. C.1 Scalars Let us begin with a brief review of the heat kernel approach. As a simple exampl”
Asymptotic Implied Volatility at the Second Order with Application to the SABR Model (2009, neutral): “At short time the solution of equation (7) with initial condition p(X, 0) = δ(X−X0) is asymptotically given by the heat kernel expansion [DeW65] (see [Vas03] for a review)3”
Logarithmic corrections to extremal black hole entropy from quantum entropy function (2010, background): “then the heat kernel K(x, x; s) of the scalar Laplacian is defined as (see [87,88] and references therein) K(x, x; s) = ∑”
Quantum oscillations and black hole ringing (2009, background): “[33] for a review, that the only terms that survive the large mass expansion of such a determinant are given by integrals of local curvatures of the background metric and Maxwell fields.”
Entanglement Entropy of Black Holes (2011, methodology): “The form of the regular coefficients (69) in the heat kernel expansion has been well studied in physics and mathematics literature (for a review see [219]).”
Boundary conformal field theory and a boundary central charge (2017, background): “15 There are two possible choices of boundary conditions, generalizing the “absolute” and “relative” boundary conditions of the Maxwell field Fμν [57].”
Logarithmic corrections to rotating extremal black hole entropy in four and five dimensions (2011, background): “77]forcomputing K0(y) which works under special circumstances. It can be argued on general grounds that the small sexpansion of K(y;s) contains even (odd) powers of sin even (odd) dimensions (see e.g.[76] for a recent review). As a result K0(y), which is the coeﬃcient of the s0 term in the small sex”
Functional determinants in quantum field theory (2007, background): “Then an inverse mass expansion follows (after renormalization) from the small s asymptotic expansion of the heat kernel operator [16] (d is the manifold’s dimension)”