Tensor analysis and curvature in quantum space-time
Introducing quantum space-time into physics by means of the transformation language of noncommuting coordinates gives a simple scheme of generalizing the tensor analysis. The general covariance principle for the quantum space-time case is discussed, within which one can obtain the covariant structure of basic tensor quantities and the motion equation for a particle in a gravitational field. Definitions of covariant derivatives and curvature are also generalized in the give case. It turns out that the covariant structure of the Riemann-Christoffel curvature tensor is not preserved in quantum space-time. However, if the curvature tensor R/sub ..mu.. nu lambda chi/(z) is redetermined up to the value of the L/sup 2/ term, then its covariant structure is achieved, and it, in turn, allows them to reconstruct the Einstein equation in quantum space-time.
- Research Organization:
- Institute of Physics and Technology, Ulat-Bator, Mongolia
- OSTI ID:
- 6169906
- Journal Information:
- Int. J. Theor. Phys.; (United States), Journal Name: Int. J. Theor. Phys.; (United States) Vol. 26:3; ISSN IJTPB
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
657003 -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COORDINATES
CURVILINEAR COORDINATES
DIFFERENTIAL EQUATIONS
EINSTEIN FIELD EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
FIELD EQUATIONS
FIELD THEORIES
FUNCTIONS
GENERAL RELATIVITY THEORY
GRAVITATIONAL FIELDS
INVARIANCE PRINCIPLES
JACOBIAN FUNCTION
MATHEMATICAL MANIFOLDS
MATHEMATICAL MODELS
MATHEMATICAL SPACE
MECHANICS
METRICS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
QUANTIZATION
QUANTUM MECHANICS
RELATIVITY THEORY
RIEMANN SPACE
SPACE
SPACE-TIME
TENSORS
TRAJECTORIES
TRANSFORMATIONS