Classical Variational Theory of the Cosmological Constant and Its Consistency with Quantum Prescription
The manifestly-covariant Hamiltonian structure of classical General Relativity is shown to be associated with a path-integral synchronous Hamilton variational principle for the Einstein field equations. A realization of the same variational principle in both unconstrained and constrained forms is pr...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-04-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/12/4/633 |
| Summary: | The manifestly-covariant Hamiltonian structure of classical General Relativity is shown to be associated with a path-integral synchronous Hamilton variational principle for the Einstein field equations. A realization of the same variational principle in both unconstrained and constrained forms is provided. As a consequence, the cosmological constant is found to be identified with a Lagrange multiplier associated with the normalization constraint for the extremal metric tensor. In particular, it is proved that the same Lagrange multiplier identifies a 4-scalar gauge function generally dependent on an invariant proper-time parameter <i>s</i>. Such a result is shown to be consistent with the prediction of the cosmological constant based on the theory of manifestly-covariant quantum gravity. |
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| ISSN: | 2073-8994 |