Premium
Fermion Fields in Theories of Gravitation
Author(s) -
Kasper U.
Publication year - 1976
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19764880207
Subject(s) - tetrad , physics , minkowski space , mathematical physics , christoffel symbols , theoretical physics , covariant transformation , gravitation , lorentz transformation , classical mechanics , pure mathematics , mathematics
After an introduction to the formalism used throughout the paper there follows a concise presentation of the theory of fermion fields in one‐tetrad gravitational theories. That presentation gives a hint to the construction of a bi‐tetrad theory, the two tetrad fields being denoted by h A k and h̄ A k . The tetrad field h A k . gives the Riemannian metric g kl while the tetrad field h̄ h A k is orthonormalized with respect to the flat metric a kl . Specializing h̄ A k in such a way that they have the form δ A k in the preferred coordinates of Minkowski space and using a matter Lagrangian which contains these h̄ A k only by the anholonomic components of the metric Christoffel symbols, we obtain a dynamical energy momentum tensor which is equal to the canonical one. Then we consider the relations of the bi‐tetrad theory to other theories which are only covariant with respect to global Lorentz transformations from the beginning. As an example we formulate the main relations of the two‐component neutrino theory.