1,879 research outputs found
Spaces with torsion from embedding and the special role of autoparallel trajectories
As a contribution to the ongoing discussion of trajectories of spinless
particles in spaces with torsion we show that the geometry of such spaces can
be induced by embedding their curves in a euclidean space without torsion.
Technically speaking, we define the tangent (velocity) space of the embedded
space imposing non-holonomic constraints upon the tangent space of the
embedding space. Parallel transport in the embedded space is determined as an
induced parallel transport on the surface of constraints. Gauss' principle of
least constraint is used to show that autoparallels realize a constrained
motion that has a minimal deviation from the free, unconstrained motion, this
being a mathematical expression of the principle of inertia.Comment: LaTeX file in src, no figures. Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Paper also at
http://www.physik.fu-berlin.de/~kleinert/kleiner_re259/preprint.htm
Coordinate-free quantization of first-class constrained systems
The coordinate-free formulation of canonical quantization, achieved by a
flat-space Brownian motion regularization of phase-space path integrals, is
extended to a special class of closed first-class constrained systems that is
broad enough to include Yang-Mills type theories with an arbitrary compact
gauge group. Central to this extension are the use of coherent state path
integrals and of Lagrange multiplier integrations that engender projection
operators onto the subspace of gauge invariant states
Phase space structure and the path integral for gauge theories on a cylinder
The physical phase space of gauge field theories on a cylindrical spacetime
with an arbitrary compact simple gauge group is shown to be the quotient a rank of the gauge group, the affine Weyl group.
The PI formula resulting from Dirac's operator method contains a symmetrization
with respect to rather than the integration domain reduction. It gives
a natural solution to Gribov's problem. Some features of fermion quantum
dynamics caused by the nontrivial phase space geometry are briefly discussed.Comment: Saclay-T93/07
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