Energy-momentum tensor improvements in two dimensions

International Journal of Modern Physics B

Volumn 10, Issue 13-14, 1996, Pages 1499-1506

  Deser, S ^a   Jackiw, R ^b  

^a BRANDEIS UNIVERSITY   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2842539206     PISSN: 02179792     EISSN: None     Source Type: Journal    
DOI: 10.1142/s021797929600060x     Document Type: Article

References (22)

1. For a review, see for example D. Friedan, E. Martinec and S. Shenker, Nucl. Phys. B271, 93 (1986); F. Bastianelli, Phys. Lett. B227, 464 (1992); F. Bastianelli and U. Lindström, Nucl. Phys. B416, 227 (1994).
2. For a review, see for example D. Friedan, E. Martinec and S. Shenker, Nucl. Phys. B271, 93 (1986); F. Bastianelli, Phys. Lett. B227, 464 (1992); F. Bastianelli and U. Lindström, Nucl. Phys. B416, 227 (1994).
3. For a review, see for example D. Friedan, E. Martinec and S. Shenker, Nucl. Phys. B271, 93 (1986); F. Bastianelli, Phys. Lett. B227, 464 (1992); F. Bastianelli and U. Lindström, Nucl. Phys. B416, 227 (1994).
4. A. Polyakov, Mod. Phys. Lett A2, 893 (1987); Gauge Fields and Strings (Harwood, New York, NY, 1987); see also M. Duff. Nucl. Phys. B125, 334 (1977).
5. A. Polyakov, Mod. Phys. Lett A2, 893 (1987); Gauge Fields and Strings (Harwood, New York, NY, 1987); see also M. Duff. Nucl. Phys. B125, 334 (1977).
6. A. Polyakov, Mod. Phys. Lett A2, 893 (1987); Gauge Fields and Strings (Harwood, New York, NY, 1987); see also M. Duff. Nucl. Phys. B125, 334 (1977).
7. μv was given by M. Bos, Phys. Rev. D 34, 3750 (1986).
8. μ fμ = 0, are maintained. With this approach, the energy-momentum tensor remains traceless, but its divergence becomes equation presented a formula whose structure is in fact dictated by the restricted diffeomorphism symmetry. "Physical" results, like two-dimensional Hawking radiation, remain unaffected. For details see: D. Karakhanyan, R. Manvelyan and R. Mkrtchyan, Phys. Lett. B329, 185 (1994); G. Amelino-Camelia, D. Bak and D. Seminara, Phys. Lett. B354, 213 (1995); J. Navarro-Salas, M. Navarro and C. Talavera, Phys. Lett. B356, 217 (1995); G. Amelino-Camelia, L. Griguolo and D. Seminara, Phys. Lett. B371, 41 (1996); and G. Amelino-Camelia and D. Seminara, MIT preprint MIT-CTP-2443.
9. μ fμ = 0, are maintained. With this approach, the energy-momentum tensor remains traceless, but its divergence becomes equation presented a formula whose structure is in fact dictated by the restricted diffeomorphism symmetry. "Physical" results, like two-dimensional Hawking radiation, remain unaffected. For details see: D. Karakhanyan, R. Manvelyan and R. Mkrtchyan, Phys. Lett. B329, 185 (1994); G. Amelino-Camelia, D. Bak and D. Seminara, Phys. Lett. B354, 213 (1995); J. Navarro-Salas, M. Navarro and C. Talavera, Phys. Lett. B356, 217 (1995); G. Amelino-Camelia, L. Griguolo and D. Seminara, Phys. Lett. B371, 41 (1996); and G. Amelino-Camelia and D. Seminara, MIT preprint MIT-CTP-2443.
10. μ fμ = 0, are maintained. With this approach, the energy-momentum tensor remains traceless, but its divergence becomes equation presented a formula whose structure is in fact dictated by the restricted diffeomorphism symmetry. "Physical" results, like two-dimensional Hawking radiation, remain unaffected. For details see: D. Karakhanyan, R. Manvelyan and R. Mkrtchyan, Phys. Lett. B329, 185 (1994); G. Amelino-Camelia, D. Bak and D. Seminara, Phys. Lett. B354, 213 (1995); J. Navarro-Salas, M. Navarro and C. Talavera, Phys. Lett. B356, 217 (1995); G. Amelino-Camelia, L. Griguolo and D. Seminara, Phys. Lett. B371, 41 (1996); and G. Amelino-Camelia and D. Seminara, MIT preprint MIT-CTP-2443.
11. μ fμ = 0, are maintained. With this approach, the energy-momentum tensor remains traceless, but its divergence becomes equation presented a formula whose structure is in fact dictated by the restricted diffeomorphism symmetry. "Physical" results, like two-dimensional Hawking radiation, remain unaffected. For details see: D. Karakhanyan, R. Manvelyan and R. Mkrtchyan, Phys. Lett. B329, 185 (1994); G. Amelino-Camelia, D. Bak and D. Seminara, Phys. Lett. B354, 213 (1995); J. Navarro-Salas, M. Navarro and C. Talavera, Phys. Lett. B356, 217 (1995); G. Amelino-Camelia, L. Griguolo and D. Seminara, Phys. Lett. B371, 41 (1996); and G. Amelino-Camelia and D. Seminara, MIT preprint MIT-CTP-2443.
12. μ fμ = 0, are maintained. With this approach, the energy-momentum tensor remains traceless, but its divergence becomes equation presented a formula whose structure is in fact dictated by the restricted diffeomorphism symmetry. "Physical" results, like two-dimensional Hawking radiation, remain unaffected. For details see: D. Karakhanyan, R. Manvelyan and R. Mkrtchyan, Phys. Lett. B329, 185 (1994); G. Amelino-Camelia, D. Bak and D. Seminara, Phys. Lett. B354, 213 (1995); J. Navarro-Salas, M. Navarro and C. Talavera, Phys. Lett. B356, 217 (1995); G. Amelino-Camelia, L. Griguolo and D. Seminara, Phys. Lett. B371, 41 (1996); and G. Amelino-Camelia and D. Seminara, MIT preprint MIT-CTP-2443.
13. S. Deser and A. Schwimmer, in preparation.
14. D. Boulware and S. Deser, J. Math. Phys. 8, 1468 (1967).
15. In the two-dimensional case, these are finite and were calculated long ago by S. Fubini, A. Hanson and R. Jackiw, Phys. Rev. D 7, 1732 (1972) as well as by S. Ferrara, R. Gatto and A. Grillo, Nuovo Cim. 12A, 959 (1972).
16. In the two-dimensional case, these are finite and were calculated long ago by S. Fubini, A. Hanson and R. Jackiw, Phys. Rev. D 7, 1732 (1972) as well as by S. Ferrara, R. Gatto and A. Grillo, Nuovo Cim. 12A, 959 (1972).
17. That the improved energy-momentum tensor possess a canonical triple-derivative Schwinger term in its equal time commutator algebra was noted by C. Callan, S. Coleman and R. Jackiw, Ann. Phys. (New York) 59, 42 (1970).
18. The improvement does modify the dilation and special conformal generators in dimensions higher than two, and for the Liouville theory in two dimensions. In these instances, the unimproved energy-momentum tensor is not traceless, so that dilation and special conformal generators cannot be given by moments of this energy-momentum tensor, see e.g. Ref. 8 and Jackiw in Progress in Quantum Field Theory, eds. H. Ezawa and S. Kamefuchi (North-Holland, Amsterdam, 1986).
19. R. Jackiw, C. Teitelboim in Quantum Theory of Gravity, ed. S. Christensen (Adam Hilger, Bristol, 1984).
20. μ now no longer depends solely on the metric, but involves the Zweibein in an essential way, since the connection is equation presented. The first term is metric, but the second one clearly depends on the essentially non-metric part of the Zweibein.
21. a; see Jackiw in S. Treiman, R. Jackiw, B. Zumino and E. Witten, Current Algebra and Anomalies, (Princeton University Press/World Scientific, Princeton, NJ/Singapore, 1985).
22. We thank V. P. Nair for pointing this out.