Interdisciplinary mathematics. Volume XIX. Yang-Mills, Kaluza-Klein, and the Einstein program

Book · Sun Jan 01 04:00:00 UTC 1978

OSTI ID:6575886

Hermann, R

Topics in the quantum theory of fields are considered. The following subjects are addressed: Yang-Mills, Kaluza-Klein and Riemannian submersions with totally geodesic fibers; the geometry of the Dirac magnetic monopoles, fiber bundles and connections; the differential-geometric theory of quantum mechanics - local and global quantization. Several appendixes deal with the following topics: cohomology and gauge invariance and the calculus of variations for particle and field theories; a coordinate-free description of the local calculus of variations theory and its associated gauge and cohomology theory; local gauge-invariant Lagrange variational problems; Maxwell and Yang-Mills equations in terms of differential forms and the variational formalism; similarity solutions of differential equations defined by symmetry groups; general field theories described by means of differential forms - field theoretic symplectic structures, instantons and solitons; the zero-energy Yang-Mills states considered from the point of view of global differential geometry. 80 references. (RWR)

• OSTI ID: 6575886
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIFFERENTIAL EQUATIONS
DIFFERENTIAL TOPOLOGY
ELEMENTARY PARTICLES
EQUATIONS
FIELD THEORIES
GAUGE INVARIANCE
INSTANTONS
INVARIANCE PRINCIPLES
MAGNETIC MONOPOLES
MATHEMATICAL SPACE
MATHEMATICS
MAXWELL EQUATIONS
MONOPOLES
PARTIAL DIFFERENTIAL EQUATIONS
POSTULATED PARTICLES
QUANTUM FIELD THEORY
QUASI PARTICLES
RIEMANN SPACE
SOLITONS
SPACE
TOPOLOGY
VARIATIONAL METHODS
YANG-MILLS THEORY