17 research outputs found
Background Geometry in Gauge Gravitation Theory
Dirac fermion fields are responsible for spontaneous symmetry breaking in
gauge gravitation theory because the spin structure associated with a tetrad
field is not preserved under general covariant transformations. Two solutions
of this problem can be suggested. (i) There exists the universal spin structure
such that any spin structure associated with a tetrad field
is a subbundle of the bundle . In this model, gravitational fields
correspond to different tetrad (or metric) fields. (ii) A background tetrad
field and the associated spin structure are fixed, while
gravitational fields are identified with additional tensor fields q^\la{}_\m
describing deviations \wt h^\la_a=q^\la{}_\m h^\m_a of . One can think of
\wt h as being effective tetrad fields. We show that there exist gauge
transformations which keep the background tetrad field and act on the
effective fields by the general covariant transformation law. We come to
Logunov's Relativistic Theory of Gravity generalized to dynamic connections and
fermion fields.Comment: 12 pages, LaTeX, no figure
A covariant formalism for Chern-Simons gravity
Chern--Simons type Lagrangians in dimensions are analyzed from the
point of view of their covariance and globality. We use the transgression
formula to find out a new fully covariant and global Lagrangian for
Chern--Simons gravity: the price for establishing globality is hidden in a
bimetric (or biconnection) structure. Such a formulation allows to calculate
from a global and simpler viewpoint the energy-momentum complex and the
superpotential both for Yang--Mills and gravitational examples.Comment: 12 pages,LaTeX, to appear in Journal of Physics