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HEISENBERG REPRESENTATION IN CLASSICAL GENERAL RELATIVITY

Journal Article · · Nuovo Cimento (Italy) Divided into Nuovo Cimento A and Nuovo Cimento B
DOI:https://doi.org/10.1007/BF02733364· OSTI ID:4019877
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A classical Heisenberg representation which excludes Hamilton-Jacobi- like canonical transformations is defined. The freedom of co-ordinate transformations in general relativity allows many extra canonical transformations not found in conventional Lorentz covariant theory. This wider class of canonical formalisms possess all the properties usually associated with the Heisenberg picture in that in each formalism the measurable quantities, g mu nu (t), are obtained from knowledge of the canonical variables at the same time without any explicit co-ordinate dependence. Further, the Hamiltonian is a constsnt of motion. Only in Heisenberg frames is the Hamiltonian to be associated with the energy of the system. In spite of the additional freedom of canonical transformations, it is shown that the Hamiltonian is numerically the same for a fixed state of the gravitational field in any Heisenberg representation. The energy is then a uniquely definable quantity in the theory. In the process, it is estublished that two Heisenberg frames can differ by co- ordinate transformations that depend only on the canonical variables and not explicitly on the coordinates. These transformations must also preserve the property that at spatial infinity the metric become Lorentz so that the physical boundary conditions be unaltered. (auth)
Research Organization:
Syracuse Univ., N.Y.; and Brandeis Univ., Waltham, Mass.
Sponsoring Organization:
USDOE
NSA Number:
NSA-15-017727
OSTI ID:
4019877
Journal Information:
Nuovo Cimento (Italy) Divided into Nuovo Cimento A and Nuovo Cimento B, Journal Name: Nuovo Cimento (Italy) Divided into Nuovo Cimento A and Nuovo Cimento B Vol. Vol: (10), 19; ISSN NUCIA
Country of Publication:
Country unknown/Code not available
Language:
English

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Related Subjects

CANONICAL ENSEMBLE
DIFFERENTIAL EQUATIONS
ENERGY
HAMILTON- JACOBI EQUATIONS
HAMILTONIAN
HEISENBERG REPRESENTATION
LORENTZ TRANSFORMATIONS
PHYSICS
QUANTUM MECHANICS
RELATIVITY THEORY