Lagrangian dynamics on higher-dimensional spaces with applications to Kaluza--Klein theories
We review and apply the method of Lagrangian dynamics to particle motion in higher-dimensional spaces. We discuss in detail the case of a Kaluza--Klein theory with coset spaces as fiber. While the total metric we use in general need not allow for Killing vectors, we require that the restriction to the fiber does. We find that for general Jordan--Thiry scalar fields, the geodesic motion in total space is not describable in terms of particle motion in the base manifold with the usual internal charges. The cases when this is possible are discussed. We also consider the geodesic motion in the Sorkin--Gross--Perry Kaluza--Klein monopoles. We find all the conserved quantities and the equations can be integrated by quadrature.
- Research Organization:
- Institute of Physics, Academia Sinica, Taipei, Taiwan, Republic of China
- OSTI ID:
- 6054634
- Journal Information:
- J. Math. Phys. (N.Y.); (United States), Vol. 26:5
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
KALUZA-KLEIN THEORY
DYNAMICS
MAGNETIC MONOPOLES
EQUATIONS OF MOTION
PARTICLES
CONSERVATION LAWS
ELECTROMAGNETISM
GENERAL RELATIVITY THEORY
GEODESICS
GRAVITATION
INTEGRALS
LAGRANGIAN FUNCTION
LIE GROUPS
MATHEMATICAL MANIFOLDS
METRICS
QUADRATURES
SCALAR FIELDS
SPACE-TIME
TOPOLOGY
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
EQUATIONS
FIELD THEORIES
FUNCTIONS
MAGNETISM
MATHEMATICS
MECHANICS
MONOPOLES
PARTIAL DIFFERENTIAL EQUATIONS
POSTULATED PARTICLES
SYMMETRY GROUPS
UNIFIED-FIELD THEORIES
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645201 - High Energy Physics- Particle Interactions & Properties-Theoretical- General & Scattering Theory