Mode regularization, time slicing, Weyl ordering, and phase space path integrals for quantum-mechanical nonlinear sigma models

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 58, Issue 4, 1998, Pages

  Bastianelli, Fiorenzo ^a   Schalm, Koenraad ^b   van Nieuwenhuizen, Peter ^b  

^a UNIVERSITY OF MODENA AND REGGIO EMILIA   (Italy)

^b STONY BROOK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0007236644     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.58.044002     Document Type: Article

References (22)

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6. At the one-loop level mode regularization reproduces these results, but the energy cutoff does not; see A. Rebhan and P. van Nieuwenhuizen, Nucl. Phys. B508, 449 (1997).
7. This can be explained by a new quantum principle for field theories with topological vacua; see H. Nastase, A. Rebhan, M. Stephanov, and P. van Nieuwenhuizen, hep-th/9802074.
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22. C. Bernard and A. Duncan, Phys. Rev. D 11, 848 (1975). These authors verify Matthews’ theorem by a path integral approach to second order in the coupling constant. However, they assume that all factors (Formula presented) which appear in their derivation may be set equal to zero. They also study as an example the Lagrangian (Formula presented). Again they can only prove Matthews’ theorem if they set all (Formula presented) terms to zero. It would be satisfying if a path integral proof could be given without assuming that (Formula presented) is zero. Conceivably, careful discretization as well as the new ghosts of 34 are required.