Multivalued Fields in Condensed Matter, Electromagnetism, and Gravitation

Kleinert's work includes flexible manipulation of coordinates that led to his evaluation of the path integral for the Coulomb potential. Here he begins with the basics, explaining such topics as Galilean invariance of Newtonian mechanics and Lorentz invariance of Maxwell equations, quantum mechanics, angular moment and spin, and space-time dependent Lorentz transformations. He explains the action approach, including its relation to Maxwell's equation and Dirac fields, then examines continuous symmetries and conservation laws, magnetostatics, multivalued fields in superfluids and superconductors, magnetic monopoles, electric charge confinement, multivalued mapping from ideal crystals to crystals with defects, defect melting, relativistic mechanics in curvilinear coordinates, torsion and curvature from defects and embedding, multivalued mapping, field equations of gravitation, fields of integer spin, particles with half-integer spins, covariant conservation gravitation of spinning matter as a gauge theory, evanescent properties of torsion in gravity, the teleparallel theory of gravitation embedding, and emerging gravity.