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Your search keyword '"Mathematics"' showing total 3 results
3 results on '"Mathematics"'

1. de Sitter Relativity and Quantum Physics.

Author

Aldrovandi, R., Almeida, J. P. Beltrán, Mayor, C. S. O., and Pereira, J. G.

Subjects
*RELATIVITY (Physics), *QUANTUM theory, *PHYSICS, *MECHANICS (Physics), *SPECIAL relativity (Physics), *DIFFERENTIAL geometry, *MATHEMATICS
Abstract

In the presence of a cosmological constant, interpreted as a purely geometric entity, absence of matter is represented by a de Sitter spacetime. As a consequence, ordinary Poincaré special relativity is no longer valid and must be replaced by a de Sitter special relativity. By considering the kinematics of a spinless particle in a de Sitter spacetime, we study the geodesics of this spacetime, the ensuing definitions of canonical momenta, and explore possible implications for quantum mechanics. [ABSTRACT FROM AUTHOR]

Published
2007
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2. The invariant charges of the Nambu–Goto string and canonical quantization.

Author

Bahns, Dorothea

Subjects
*ALGEBRA, *MATHEMATICS, *MATHEMATICAL analysis, *GEOMETRIC quantization, *DIFFERENTIAL geometry, *QUANTUM theory, *MATHEMATICAL physics
Abstract

It is shown that the algebra of diffeomorphism-invariant charges of the Nambu–Goto string cannot be quantized in the framework of canonical quantization. The argument is shown to be independent of the dimension of the underlying Minkowski space. [ABSTRACT FROM AUTHOR]

Published
2004
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3. Stable quantum systems in anti–de Sitter space: Causality, independence, and spectral properties.

Author

Buchholz, Detlev and Summers, Stephen J.

Subjects
*QUANTUM theory, *PHYSICS, *DIFFERENTIAL geometry, *MATHEMATICS, *MATHEMATICAL analysis, *MATHEMATICAL physics
Abstract

If a state is passive for uniformly accelerated observers in n-dimensional (n>=2) anti–de Sitter (Ads) space–time (i.e., cannot be used by them to operate a perpetuum mobile), they will (a) register a universal value of the Unruh temperature, (b) discover a PCT symmetry, and (c) find that observables in complementary wedge-shaped regions necessarily commute with each other in this state. The stability properties of such a passive state induce a “geodesic causal structure” on AdS and concommitant locality relations. It is shown that observables in these complementary wedge-shaped regions fulfill strong additional independence conditions. In two-dimensional AdS these even suffice to enable the derivation of a nontrivial, local, covariant net indexed by bounded space–time regions. All these results are model-independent and hold in any theory which is compatible with a weak notion of space–time localization. Examples are provided of models satisfying the hypotheses of these theorems. [ABSTRACT FROM AUTHOR]

Published
2004
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