Abstract
In a previous paper, we discussed simple examples like particle on a circle and molecules to argue that mixed states can arise from anomalous symmetries. This idea was applied to the breakdown (anomaly) of color SU(3) in the presence of non-abelian monopoles. Such mixed states create entropy as well.
In this article, we extend these ideas to the topological geons of Friedman and Sorkin in quantum gravity. The “large diffeos” or mapping class groups can become anomalous in their quantum theory as we show. One way to eliminate these anomalies is to use mixed states, thereby creating entropy. These ideas may have something to do with black hole entropy as we speculate.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. Álvarez-Gaumé and E. Witten, Gravitational Anomalies, Nucl. Phys. B 234 (1984) 269 [INSPIRE].
E. Witten, Global gravitational anomalies, Commun. Math. Phys. 100 (1985) 197 [INSPIRE].
S. Surya and S. Vaidya, Global anomalies in canonical gravity, Nucl. Phys. B 523 (1998) 391 [hep-th/9709170] [INSPIRE].
E. Witten, An SU(2) Anomaly, Phys. Lett. B 117 (1982) 324 [INSPIRE].
A. Balachandran and S. Vaidya, Emergent chiral symmetry: parity and time reversal doubles, Int. J. Mod. Phys. A 12 (1997) 5325 [hep-th/9612053] [INSPIRE].
A. Balachandran and S. Vaidya, Parity doubles in quark physics, Phys. Rev. Lett. 78 (1997) 13 [hep-ph/9606283] [INSPIRE].
A. Balachandran and S. Vaidya, Skyrmions, spectral flow and parity doubles, Int. J. Mod. Phys. A 14 (1999) 445 [hep-th/9803125] [INSPIRE].
J. Friedman and R. Sorkin, Spin 1/2 from gravity, Phys. Rev. Lett. 44 (1980) 1100 [INSPIRE].
J. Friedman and R. Sorkin, Spin 1/2 from gravity, Phys. Rev. Lett. 45 (1980) 148.
C. Aneziris et al., Aspects of spin and statistics in generally covariant theories, Int. J. Mod. Phys. A 4 (1989) 5459 [INSPIRE].
J. Esteve, Anomalies in conservation laws in the hamiltonian formalism, Phys. Rev. D 34 (1986) 674 [INSPIRE].
M. Aguado, M. Asorey and J. Esteve, Vacuum nodes and anomalies in quantum theories, Commun. Math. Phys. 218 (2001) 233 [hep-th/0010227] [INSPIRE].
A. Balachandran and A.R. de Queiroz, Mixed states from anomalies, arXiv:1108.3898 [INSPIRE].
E. Witten, A simple proof of the positive energy theorem, Commun. Math. Phys. 80 (1981) 381 [INSPIRE].
G. Gibbons, S. Hawking, G.T. Horowitz and M.J. Perry, Positive mass theorems for black holes, Commun. Math. Phys. 88 (1983) 295 [INSPIRE].
A. Balachandran, Bringing up a quantum baby, quant-ph/9702055 [INSPIRE].
A.P. Balachandran, G. Marmo, B.S. Skagerstam and A. Stern, Classical topology and quantum states, World Scientific, Singapore (1991).
M.F. Atiyah, V.K. Patodi and I.M. Singer, Spectral asymmetry and riemannian geometry — I, Math. Proc. Camb. Phil. Soc. 77 (1975) 43.
M.F. Atiyah, V.K. Patodi and I.M. Singer, Spectral asymmetry and riemannian geometry — II, Math. Proc. Camb. Phil. Soc. 78 (1975) 405.
M.F. Atiyah, V.K. Patodi and I.M. Singer, Spectral asymmetry and riemannian geometry — III, Math. Proc. Camb. Phil. Soc. 79 (1976) 71.
I. Gelfand and M. Naimark, On the inclusion of a normed ring into the ring of operators in a Hilbert space, Matem. Sbornik 12 (1943) 197.
A. Balachandran, G. Bimonte, G. Marmo and A. Simoni, Topology change and quantum physics, Nucl. Phys. B 446 (1995) 299 [gr-qc/9503046] [INSPIRE].
J. Birman, Braids, links, and mapping class groups, Princeton University Press, Princeton U.S.A. (1974).
A. Balachandran et al., Monopole topology and the problem of color, Phys. Rev. Lett. 50 (1983) 1553 [INSPIRE].
A. Balachandran et al., Nonabelian monopoles break color. 1. Classical mechanics, Phys. Rev. D 29 (1984) 2919 [INSPIRE].
A. Balachandran et al., Nonabelian monopoles break color. 2. Field theory and quantum mechanics, Phys. Rev. D 29 (1984) 2936 [INSPIRE].
J.L. Friedman, K. Schleich and D.M. Witt, Topological censorship, Phys. Rev. Lett. 71 (1993) 1486 [Erratum ibid. 75 (1995) 1872] [gr-qc/9305017] [INSPIRE].
D. Gannon, Singularities in nonsimply connected space-times, J. Math. Phys. 16 (1975) 2364.
D. Gannon, On the topology of spacelike hypersurfaces, singularities, and black holes, Gen. Rel. Grav. 7 (1976) 219.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1109.5290
Rights and permissions
About this article
Cite this article
Balachandran, A.P., de Queiroz, A.R. Quantum gravity: mixed states from diffeomorphism anomalies. J. High Energ. Phys. 2011, 126 (2011). https://doi.org/10.1007/JHEP11(2011)126
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2011)126