General Relativity without Paradigm of Space-time Covariance:
 Sensible Quantum Gravity and Resolution of the “Problem of Time”

 

Prof Hoi-lai Yu
Academia Sinica
 

18 July 2014 (Friday)
2:00 pm
IAS4042, 4/F, Lo Ka Chung Building, Lee Shau Kee Campus, HKUST

Abstract:

Covariance of space and time in General Relativity (GR) entails a number of technical and con- ceptual difficulties. Remarkably, these can be resolved by a paradigm shift from full 4-dimensional general coordinate invariance to invariance only with respect to spatial diffeomorphisms. The frame- work for a theory of gravity with this paradigm shift, from quantum to classical regimes, is presented; GR is contained as a special case. Appositely formulated as a master constraint, the Hamiltonian constraint now determines only dynamics; and is relieved of its dual role of generating symme- try transformations, and the consequent baggage of multi-fingered evolution with arbitrary lapse functions is now absent. The Dirac algebra, in which 4-dimensional diffeomorphism symmetry is only realized on-shell, is replaced by the master constraint algebra which possesses only spatial diffeomorphism gauge symmetry, both on- and off-shell. Decomposition of the spatial metric into unimodular and determinant, q, factors results in mutually commuting pairs of canonical variables. The classical content of GR can be captured with a Hamiltonian constraint linear in the trace of the momentum. This implies a theory of quantum gravity can be described by a Schrodinger equation first order in intrinsic time lnq accompanied with positive semi- definite probability density. The semi-classical Hamilton-Jacobi equation is also first order in intrinsic time, with the implication of being complete; and gauge-invariant physical observables can be constructed from integration constants of its complete integral solution.

 

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The seminar is free and open to the public. No registration is required. Seating is on a first-come first-served basis.

HKUST Jockey Club Institute for Advanced Study
URL: http://ias.ust.hk
Enquiries: ias@ust.hk / 2358 5912

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