The path integral representation of the transition amplitude for a particle moving in curved space has presented unexpected challenges since the introduction of path integrals by Feynman fifty years ago. In this paper we discuss and review mode regularization of the configuration space path integral, and present a three loop computation of the transition amplitude to test with success the consistency of such a regularization. Key features of the method are the use of the Lee-Yang ghost fields, which guarantee a consistent treatment of the non-trivial path integral measure at higher loops, and an effective potential specific to mode regularization which arises at two loops. We also perform the computation of the transition amplitude using the regularization of the path integral by time discretization, which also makes use of Lee-Yang ghost fields and needs its own specific effective potential. This computation is shown to reproduce the same final result as the one performed in mode regularization.

Mode regularization of the configuration space path integral in curved space / Bastianelli, Fiorenzo; Corradini, Olindo. - In: PHYSICAL REVIEW D. - ISSN 0556-2821. - D60 (1999) 044014:(1999), pp. 1-10. [10.1103/PhysRevD.60.044014]

Mode regularization of the configuration space path integral in curved space

CORRADINI, Olindo
1999

Abstract

The path integral representation of the transition amplitude for a particle moving in curved space has presented unexpected challenges since the introduction of path integrals by Feynman fifty years ago. In this paper we discuss and review mode regularization of the configuration space path integral, and present a three loop computation of the transition amplitude to test with success the consistency of such a regularization. Key features of the method are the use of the Lee-Yang ghost fields, which guarantee a consistent treatment of the non-trivial path integral measure at higher loops, and an effective potential specific to mode regularization which arises at two loops. We also perform the computation of the transition amplitude using the regularization of the path integral by time discretization, which also makes use of Lee-Yang ghost fields and needs its own specific effective potential. This computation is shown to reproduce the same final result as the one performed in mode regularization.
1999
D60 (1999) 044014
1
10
Mode regularization of the configuration space path integral in curved space / Bastianelli, Fiorenzo; Corradini, Olindo. - In: PHYSICAL REVIEW D. - ISSN 0556-2821. - D60 (1999) 044014:(1999), pp. 1-10. [10.1103/PhysRevD.60.044014]
Bastianelli, Fiorenzo; Corradini, Olindo
File in questo prodotto:
File Dimensione Formato  
PRD60.pdf

Accesso riservato

Descrizione: Articolo principale
Tipologia: Versione pubblicata dall'editore
Dimensione 110.05 kB
Formato Adobe PDF
110.05 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
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/11380/1074786
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 29
  • ???jsp.display-item.citation.isi??? 24
social impact