# Two Function Families and Their Application to Hankel Transform of Heat Kernel

@inproceedings{Ivanov2021TwoFF, title={Two Function Families and Their Application to Hankel Transform of Heat Kernel}, author={A V Ivanov and N. V. Kharuk}, year={2021} }

In this paper, we study an asymptotic expansion of the heat kernel for a Laplace operator on a smooth Riemannian manifold without a boundary at enough small values of the proper time. The Seeley–DeWitt coefficients of this decomposition satisfy a set of recurrence relations, which we use to construct two function families of a special kind. Using these functions, we find the expansion of a heat kernel for the inverse Laplace operator for an arbitrary dimension of space. We show that the new…

## References

SHOWING 1-10 OF 21 REFERENCES

Heat kernel expansion: user's manual

- Physics, Mathematics
- 2003

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…

Heat Kernels and Dirac Operators

- Mathematics
- 1992

The past few years have seen the emergence of new insights into the Atiyah-Singer Index Theorem for Dirac operators. In this book, elementary proofs of this theorem, and some of its more recent…

Asymptotic Formulae in Spectral Geometry

- Mathematics
- 2003

A great deal of progress has been made recently in the field of asymptotic formulas that arise in the theory of Dirac and Laplace type operators. Asymptotic Formulae in Spectral Geometry collects…

Asymptotic behaviors of the heat kernel in covariant perturbation theory

- Physics, Mathematics
- 1994

The trace of the heat kernel is expanded in a basis of nonlocal curvature invariants of nth order. The coefficients of this expansion (the nonlocal form factors) are calculated to third order in the…

Soliton fermionic number from the heat kernel expansion

- Physics, MathematicsThe European Physical Journal C
- 2019

We consider different methods of calculating the (fractional) fermion number of solitons based on the heat kernel expansion. We derive a formula for the localized $$\eta $$η function that provides a…

Nonperturbative late time asymptotics for the heat kernel in gravity theory

- Physics
- 2003

Recently proposed nonlocal and nonperturbative late time behavior of the heat kernel is generalized to curved spacetimes. Heat kernel trace asymptotics is dominated by two terms one of which…

Diagram Technique for the Heat Kernel of the Covariant Laplace Operator

- Physics, MathematicsTheoretical and Mathematical Physics
- 2019

We present a diagram technique used to calculate the Seeley–DeWitt coefficients for a covariant Laplace operator. We use the combinatorial properties of the coefficients to construct a matrix…

The Generalized Schwinger-Dewitt Technique in Gauge Theories and Quantum Gravity

- Physics
- 1985

Abstract The article contains a systematic presentation of the covariant diagrammatic technique for the effective action in gauge theories. The Schwinger-DeWitt technique is generalized and converted…

New nonlocal effective action

- Physics
- 2002

We suggest a new method for the calculation of the nonlocal part of the effective action. It is based on the resummation of the perturbation series for the heat kernel and its functional trace at…

Tables of Integral Transforms

- Mathematics
- 2012

In this chapter, we provide a set of short tables of integral transforms of the functions that are either cited in the text or are in most common use in mathematical, physical, and engineering…