Bastianelli, F.; Corradini, O.; van Nieuwenhuizen, P. Dimensional regularization of nonlinear sigma models on a finite time interval. (English) Zbl 1058.81600 Phys. Lett., B 494, No. 1-2, 161-167 (2000). Summary: We extend dimensional regularization to the case of compact spaces. Contrary to previous regularization schemes employed for nonlinear sigma models on a finite time interval (“quantum mechanical path integrals in curved space”) dimensional regularization requires only a covariant finite two-loop counterterm. This counterterm is nonvanishing and given by 1/8\(\hslash^2\)R. Cited in 1 Document MSC: 81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory 81T18 Feynman diagrams Keywords:dimensional regularization; nonlinear sigma models; finite time interval; compact spaces; regularization schemes; covariant two-loop counterterm; finite two-loop counterterm PDFBibTeX XMLCite \textit{F. Bastianelli} et al., Phys. Lett., B 494, No. 1--2, 161--167 (2000; Zbl 1058.81600) Full Text: DOI References: [1] Dewitt, B. S.: Supermanifols. (1992) [2] Misrahi, M.: J. math. Phys.. 16, 2201 (1975) [3] Gervais, J. L.; Jevicki, A.: Nucl. phys. B. 110, 93 (1976) [4] Tomboulis, E.: Phys. rev. D. 12, 1678 (1975) [5] Schwinger, J.: Phys. rev.. 130, 402 (1963) [6] Christ, N. H.; Lee, T. D.: Phys. rev. D. 22, 939 (1980) [7] Abers, E. S.; Lee, B. W.: Phys. rep.. 9, 63 (1973) [8] Bastianelli, F.: Nucl. phys. B. 376, 113 (1992) [9] Bastianelli, F.; Van Nieuwenhuizen, P.: Nucl. phys. B. 389, 53 (1993) [10] De Boer, J.; Peeters, B.; Skenderis, K.; Van Nieuwenhuizen, P.: Nucl. phys. B. 459, 631 (1996) [11] Schalm, K.; Van Nieuwenhuizen, P.: Phys. lett. B. 446, 247 (1998) [12] Bastianelli, F.; Schalm, K.; Van Nieuwenhuizen, P.: Phys. rev. D. 58, 044002 (1998) [13] Bastianelli, F.; Corradini, O.: Phys. rev. D. 60, 044014 (1999) [14] Peeters, K.; Waldron, A.: Jhep. 9902, 024 (1999) [15] Kleinert, H.; Chervyakov, A.: [16] Bastianelli, F.; Corradini, O.; Van Nieuwenhuizen, P.: Phys. lett. B. 490, 154 (2000) [17] Hooft, G. ’t; Veltman, M.: Nucl. phys. B. 44, 189 (1972) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.