Abstract
The conformal anomaly and a contribution to the one-loop effective action associated with the product \(\otimes _p \mathcal{L}_p \) of the Laplace operators \(\mathcal{L}_p \), p=1,2 acting in irreducible rank 1 symmetric spaces are calculated. The explicit form of the zeta functions and the conformal anomaly of the stress-energy momentum tensor is derived.
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References
M. Wodzicki, “Non-commutative residue,” in Lecture Notes in Mathematics, Vol. 1289, edited by Yu. I. Manin, Springer-Verlag, Berlin (1987), pp. 320 ff.
M. Kontsevich and S. Vishik, Preprint MPI/94-30 (1994).
M. Kontsevich and S. Vishik, http://xxx.lanl.gov/abs/hep-th/9406140.
A. Connes, Commun. Math. Phys. 117, 673 (1988).
D. Kastler, Commun. Math. Phys. 166, 633 (1995).
A. Connes and J. Lott, Nucl. Phys. B 18, 29 (1990).
A. Connes, Non-Commutative Geometry, Academic Press, New York, 1994.
A. Connes, http://xxx.lanl.gov/abs/hep-th/9603053.
A. H. Chamseddine and A. Connes, http://xxx.lanl.gov/abs/hep-th/9606001.
A. H. Chamseddine and A. Connes, http://xxx.lanl.gov/abs/hep-th/9606056.
C. P. Martin, J. M. Garcia-Bondia, and J. C. Varilly, http://xxx.lanl.gov/abs/hep-th/9605001.
W. Kalau and M. Walze, J. Geom. Phys. 16, 327 (1995).
T. Ackermann, http://xxx.lanl.gov/abs/funct-an/9506006.
T. Ackermann and J. Tolksdorf, http://xxx.lanl.gov/abs/hep-th/9503152.
N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space, Cambridge University Press, Cambridge, 1982.
I. L. Buchbinder, S. D. Odintsov, and I. L. Shapiro, Effective Action in Quantum Gravity, A. Hilger, Bristol, 1992.
K. Benson, J. Bernstein, and S. Dodelson, Phys. Rev. D 44, 2480 (1991).
E. Elizalde, L. Vanzo, and S. Zerbini, http://xxx.lanl.gov/abs/hep-th/9701060.
S. Deser and A. Schwimmer, Phys. Lett. B 309, 279 (1993).
E. Copeland and D. Toms, Class. Quantum Grav. 3, 431 (1986).
V. P. Dergalev and S. D. Odintsov, Effective Action of Conformally-Invariant Theories in Multidimensional Space, In Gravity and Fundamental Interactions, Moscow 1988.
A. A. Bytsenko, E. Elizalde, and S. D. Odintsov, J. Math. Phys. 36, 5084 (1995).
E. Elizalde, S. D. Odintsov, A. Romeo et al., Zeta Regularization Techniques with Applications, World Scientific, Singapore, 1994.
A. A. Bytsenko, G. Cognola, L. Vanzo, and S. Zerbini, Phys. Rep. 266, 1 (1996).
S. Helgason, Differential Geometry and Symmetric Spaces, Pure and Applied Math. Ser. 12, Academic Press, 1962.
A. A. Bytsenko and F. L. Williams, http://xxx.lanl.gov/abs/hep-th/9706120.
F. L. Williams, J. Math. Phys. 38, 796 (1997).
R. Camporesi, Commun. Math. Phys. 148, 283 (1992).
R. Camporesi and A. Higuchi, Phys. Rev. D 47, 3339 (1993).
R. Camporesi and A. Higuchi, J. Math. Phys. 35, 4217 (1994).
S. Nojiri and S. D. Odintsov, http://xxx.lanl.gov/abs/hep-th/9706009.
S. Nojiri and S. D. Odintsov, http://xxx.lanl.gov/abs/hep-th/9706143.
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Pis’ma Zh. Éksp. Teor. Fiz. 67, No. 3, 166–171 (10 February 1998)
Published in English in the original Russian journal. Edited by Steve Torstveit.
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Bytsenko, A.A., Goncalves, A.E. & Williams, F.L. The conformal anomaly associated with an operator product acting in rank 1 symmetric spaces. Jetp Lett. 67, 176–181 (1998). https://doi.org/10.1134/1.567647
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DOI: https://doi.org/10.1134/1.567647