Quantum Diffeomorphisms and Conformal Symmetry

Details Quantum Diffeomorphisms and Conformal Symmetry Quantum Diffeomorphisms and Conformal Symmetry

1995-09-28

arxiv.org/abs/hep-th/9509168v1

Phys.Rev. D55 (1997) 4756-4769

Physics

High Energy Physics

High Energy Physics - Theory

PlainTeX File, 37 pages

Scientific paper

10.1103/PhysRevD.55.4756

We analyze the constraints of general coordinate invariance for quantum theories possessing conformal symmetry in four dimensions. The character of these constraints simplifies enormously on the Einstein universe $R \times S^3$. The $SO(4,2)$ global conformal symmetry algebra of this space determines uniquely a finite shift in the Hamiltonian constraint from its classical value. In other words, the global Wheeler-De Witt equation is {\it modified} at the quantum level in a well-defined way in this case. We argue that the higher moments of $T^{00}$ should not be imposed on the physical states {\it a priori} either, but only the weaker condition $\langle \dot T^{00} \rangle = 0$. We present an explicit example of the quantization and diffeomorphism constraints on $R \times S^3$ for a free conformal scalar field.

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