Multi-dimensional Virasoro algebra and quantum gravity
arXiv:0709.2539
Abstract
I review the multi-dimensional generalizations of the Virasoro algebra, i.e. the non-central Lie algebra extensions of the algebra vect(N) of general vector fields in N dimensions, and its Fock representations. Being the Noether symmetry of background independent theories such as N-dimensional general relativity, this algebra is expected to be relevant to the quantization of gravity. To this end, more complicated modules which depend on dynamics in the form of Euler-Lagrange equations are described. These modules can apparently only be interpreted as quantum fields if spacetime has four dimensions and both bosons and fermions are present.
In: Mathematical physics research at the leading edge, ed: Charles V. Benton, pp 91-111, 2004 Nova Science Publishers Inc. ISBN 1-59033-905-3
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Cited by in corpus (6)
- Manifestly covariant canonical quantization of gravity and diffeomorphism anomalies in four dimensions
- The physical observer I: Absolute and relative fields
- The physical observer II: Gauge and diff anomalies
- QJT as a Regularization: Origin of the New Gauge Anomalies
- Three Principles for Quantum Gravity
- Quantum Jet Theory, Observer Dependence, and Multi-dimensional Virasoro algebra