Heat Content Asymptotics for Operators of Laplace Type with Spectral Boundary Conditions

Gilkey, Peter Β.; Kirsten, Klaus; Jh, Park

doi:10.1023/b:math.0000043236.80871.34

Cited by 6 publications

(3 citation statements)

References 26 publications

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“…The coefficient a 3 can be found in [242]. Some string theory applications suggest [406,414] that spectral boundary conditions can be defined directly for a second order differential operator.…”

Section: Spectral or Atiyah-patodi-singer (Aps) Boundary Conditionsmentioning

confidence: 99%

Heat kernel expansion: user's manual

2003

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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).Comment: 113 pp, to be submitted to Phys.Repts, v2: added references and corrected typo

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Section: Spectral or Atiyah-patodi-singer (Aps) Boundary Conditionsmentioning

confidence: 99%

Heat kernel expansion: user's manual

2003

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“…For example, it has been proved that, in the so-called covariant perturbation theory, one can resum all the derivatives acting on contributions to second [15][16][17] and third order in the curvatures [18][19][20][21] (see also rederivations and physical consequences in [22,23]). Other studied scenarios include resummations in abelian bundles [24], QED [25], symmetric spaces [26,27] and powers of the curvature [28,29]; see [30] for additional considerations and [31,32] for a related computation by Wigner. In the above-mentioned developments, much more attention has been given to the case of manifolds without boundaries, being the study of HKs in manifolds with boundaries much less developed; a not exhaustive list of works which deal with the latter problem include [14,[33][34][35][36][37][38] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Resummed heat-kernel and form factors for surface contributions: Dirichlet semitransparent boundary conditions

Franchino-Viñas

2023

J. Phys. A: Math. Theor.

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In this article we consider resummed expressions for the heat-kernel's trace of a Laplace operator, the latter including a potential and imposing Dirichlet semitransparent boundary conditions on a surface of codimension one in flat space. We obtain resummed expressions that correspond to the first and second order expansion of the heat-kernel in powers of the potential. We show how to apply these results to obtain the bulk and surface form factors of a scalar quantum field theory in $d=4$ with a Yukawa coupling to a background. Additionally, we discuss a connection between heat-kernels for Dirichlet semitransparent, Dirichlet and Robin boundary conditions.

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“…, we recall the basic notions of Laplace type operators in Section 1 of [15]. Let V be a vector bundle on M .…”

Section: A Kastler-kalau-walze Type Theorem For Conformal Perturbatio...mentioning

confidence: 99%

On K-K-W Type Theorems for Conformal Perturbations of Twisted Dirac Operators

Wang,

Wang

2021

Preprint

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Heat Content Asymptotics for Operators of Laplace Type with Spectral Boundary Conditions

Abstract: Let P be an operator of Dirac type and let D = P 2 be the associated operator of Laplace type. We impose spectral boundary conditions and study the leading heat content coefficients for D.2000 Mathematics Subject Classification. Primary 58J50.

Cited by 6 publications

References 26 publications

Heat kernel expansion: user's manual

Heat kernel expansion: user's manual

Resummed heat-kernel and form factors for surface contributions: Dirichlet semitransparent boundary conditions

On K-K-W Type Theorems for Conformal Perturbations of Twisted Dirac Operators

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