A first analysis regarding matter-dynamical diffeomorphism coupling
Authors: Aldaya V.; Jaramillo J.L.
Source: Classical and Quantum Gravity, Volume 17, Number 23, 2000 , pp. 4877-4894(18)
Publisher: Institute of Physics Publishing
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Abstract:
A first attempt at adding matter degrees of freedom to the two-dimensional `vacuum' gravity model presented in Aldaya and Jaramillo ( [A article="0264-9381/17/7/306"] 2000 Class.?Quantum Grav.?171649 [/A] ) is analysed in this paper. Just as in the previous pure gravity case, quantum diffeomorphism operators (constructed from a Virasoro algebra) possess a dynamical content; their gauge nature is recovered only after the classical limit. Emphasis is placed on the new physical modes modelled on an [iopmath latex="$SU(1, 1)$"] SU(1,1) [/iopmath] -Kac-Moody algebra. The non-trivial coupling to `gravity' is a consequence of the natural semi-direct structure of the entire extended algebra. A representation associated with the discrete series of the rigid [iopmath latex="$SU(1, 1)$"] SU(1,1) [/iopmath] algebra is revisited in the light of previously neglected crucial global features which imply the appearance of an [iopmath latex="$SU(1, 1)$"] SU(1,1) [/iopmath] -Kac-Moody fusion rule, determining the rather entangled quantum structure of the physical system. In the classical limit, an action which explicitly couples gravity and matter modes governs the dynamics.
Language: English
Document Type: Miscellaneous
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