The worldline formalism has in recent years emerged as a powerful tool for the computation of effective actions and heat kernels. However, implementing nontrivial boundary conditions in this formalism has turned out to be a difficult problem. Recently, such a generalization was developed for the case of a scalar field on the half-space R_+ x R^D-1, based on an extension of the associated worldline path integral to the full R^D using image charges. We present here an improved version of this formalism which allows us to write down non-recursive master formulas for the n-point contribution to the heat kernel trace of a scalar field on the half-space with Dirichlet or Neumann boundary conditions. These master formulas are suitable to computerization. We demonstrate the efficiency of the formalism by a calculation of two new heat-kernel coefficients for the half-space, a_4 and a_9/2.

Scalar heat kernel with boundary in the worldline formalism / Bastianelli, Fiorenzo; Corradini, Olindo; Pisani, Pablo A. G; Schubert, Christian. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2008:10(2008), pp. 0-20. [10.1088/1126-6708/2008/10/095]

Scalar heat kernel with boundary in the worldline formalism

CORRADINI, Olindo;
2008

Abstract

The worldline formalism has in recent years emerged as a powerful tool for the computation of effective actions and heat kernels. However, implementing nontrivial boundary conditions in this formalism has turned out to be a difficult problem. Recently, such a generalization was developed for the case of a scalar field on the half-space R_+ x R^D-1, based on an extension of the associated worldline path integral to the full R^D using image charges. We present here an improved version of this formalism which allows us to write down non-recursive master formulas for the n-point contribution to the heat kernel trace of a scalar field on the half-space with Dirichlet or Neumann boundary conditions. These master formulas are suitable to computerization. We demonstrate the efficiency of the formalism by a calculation of two new heat-kernel coefficients for the half-space, a_4 and a_9/2.
2008
2008
10
0
20
Scalar heat kernel with boundary in the worldline formalism / Bastianelli, Fiorenzo; Corradini, Olindo; Pisani, Pablo A. G; Schubert, Christian. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2008:10(2008), pp. 0-20. [10.1088/1126-6708/2008/10/095]
Bastianelli, Fiorenzo; Corradini, Olindo; Pisani, Pablo A. G; Schubert, Christian
File in questo prodotto:
File Dimensione Formato  
jhep0810.pdf

Open access

Descrizione: Articolo principale
Tipologia: Versione pubblicata dall'editore
Dimensione 282 kB
Formato Adobe PDF
282 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1074542
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 22
  • ???jsp.display-item.citation.isi??? 23
social impact