Year: 1997
Type: article
Abstract: 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 $R\ifmmode\times\else\texttimes\fi{}{S}^{3}$. 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 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 a priori either, but only the weaker condition $〈{\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{T}}^{00}〉=0$. We present an explicit example of the quantization and diffeomorphism constraints on $R\ifmmode\times\else\texttimes\fi{}{S}^{3}$ for a free conformal scalar field.
Authors: Ignatios Antoniadis, Pawel O. Mazur, Emil Mottola
Institutions: École Polytechnique, Centre de Physique Théorique
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1997027802