Calculation of Heat-Kernel Coefficients and Usage of Computer Algebra

Abstract

The calculation of heat-kernel coefficients with the classical DeWitt algorithm has been discussed. We present the explicit form of the coefficients up to $h_5$ in the general case and up to $h_7^{min}$ for the minimal parts. The results are compared with the expressions in other papers. A method to optimize the usage of memory for working with large expressions on universal computer algebra systems has been proposed.

12 pages, LaTeX, no figures. Extended version of contribution to AIHENP'95, Pisa, April 3-8, 1995

References in corpus (6)

• Extension of the Chiral Perturbation Theory Meson Lagrangian to Order $P^6$
• The Higher Derivative Expansion of the Effective Action by the String-Inspired Method, Part I
• Heat-Kernel Calculation of Quark Determinant and Computer Algebra
• An Improved Heat Kernel Expansion from Worldline Path Integrals
• An Effective Chiral Meson Lagrangian at $O(P^6)$ from the NJL Model
• Chiral Meson Lagrangians from the QCD Based NJL Model Modified by Nonlocal Effects

Cited by in corpus (15)

• Perturbative Quantum Field Theory in the String-Inspired Formalism
• Index-free Heat Kernel Coefficients
• The Higher Derivative Expansion of the Effective Action by the String Inspired Method. Part II
• The thermal heat kernel expansion and the one-loop effective action of QCD at finite temperature
• Transport Equation Approach to Calculations of Hadamard Green functions and non-coincident DeWitt coefficients
• Massive field contributions to the QCD vacuum tunneling amplitude
• The Polyakov loop and the heat kernel expansion at finite temperature
• Covariant derivative expansion of the heat kernel
• Derivative expansion of the heat kernel in curved space
• Derivative expansion of the heat kernel at finite temperature
• The method of covariant symbols in curved space-time
• Application of the Worldline Path Integral Method to the Calculation of Inverse Mass Expansions
• Higher-derivative gauge theories from noncommutative geometry
• On the number of terms in the Lovelock products
• Application of geometric symbol calculus to computing heat invariants