Balachandran, AP and de Queiroz, AR and Vaidya, S (2015) Non-Abelian gauge redundancy and entropic ambiguities. In: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 12 (6).
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The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. Therefore one reaches the remarkable possibility that there may be many entropies for a given state. We show that this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This ambiguity in entropy, which can occur at zero temperature, can often be traced to a gauge symmetry emergent from the non-trivial topological character of the configuration space of the underlying system. We also establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix. After demonstrating this entropy ambiguity for the simple example of the algebra of 2 x 2 matrices, we argue that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. We work out the simplest situation with such non-Abelian symmetry, that of an ethylene molecule.
| Item Type: | Journal Article |
|---|---|
| Publication: | INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS |
| Publisher: | WORLD SCIENTIFIC PUBL CO PTE LTD |
| Additional Information: | Copy right for this article belongs to the WORLD SCIENTIFIC PUBL CO PTE LTD, 5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE |
| Keywords: | Non-Abelian gauge symmetry; von Neumann entropy; GNS construction |
| Department/Centre: | Division of Physical & Mathematical Sciences > Centre for High Energy Physics |
| Date Deposited: | 31 Jul 2015 10:46 |
| Last Modified: | 31 Jul 2015 10:46 |
| URI: | http://eprints.iisc.ac.in/id/eprint/51945 |
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