1,168 research outputs found
Inequivalent Quantizations and Holonomy Factor from the Path-Integral Approach
A path-integral quantization on a homogeneous space G/H is proposed based on
the guiding principle `first lift to G and then project to G/H'. It is then
shown that this principle gives a simple procedure to obtain the inequivalent
quantizations (superselection sectors) along with the holonomy factor (induced
gauge field) found earlier by algebraic approaches. We also prove that the
resulting matrix-valued path-integral is physically equivalent to the
scalar-valued path-integral derived in the Dirac approach, and thereby present
a unified viewpoint to discuss the basic features of quantizing on
obtained in various approaches so far.Comment: 21 pages, uses Plain Te
Conserved currents for general teleparallel models
The obstruction for the existence of an energy momentum tensor for the
gravitational field is connected with differential-geometric features of the
Riemannian manifold. It has not to be valid for alternative geometrical
structures. In this article a general 3-parameter class of teleparallel models
is considered. The field equation turns out to have a form completely similar
to the Maxwell field equation d*\F^a=\T^a. By applying the Noether procedure,
the source 3-form \T^a is shown to be connected with the diffeomorphism
invariance of the Lagrangian. Thus the source of the coframe field is
interpreted as the total conserved energy-momentum current of the system. A
reduction of the conserved current to the Noether current and the Noether
charge for the coframe field is provided. An energy-momentum tensor for the
coframe field is defined in a diffeomorphism invariant and a translational
covariant way. The total energy-momentum current of a system is conserved. Thus
a redistribution of the energy-momentum current between material and coframe
(gravity) field is possible in principle, unlike as in GR. The energy-momentum
tensor is calculated for various teleparallel models: the pure Yang-Mills type
model, the anti-Yang-Mills type model and the generalized teleparallel
equivalent of GR. The latter case can serve as a very close alternative to the
GR description of gravity.Comment: 22 pages, 3 figure
Nonholonomic constraints in -symplectic Classical Field Theories
A -symplectic framework for classical field theories subject to
nonholonomic constraints is presented. If the constrained problem is regular
one can construct a projection operator such that the solutions of the
constrained problem are obtained by projecting the solutions of the free
problem. Symmetries for the nonholonomic system are introduced and we show that
for every such symmetry, there exist a nonholonomic momentum equation. The
proposed formalism permits to introduce in a simple way many tools of
nonholonomic mechanics to nonholonomic field theories.Comment: 27 page
Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk
We study higher form Proca equations on Einstein manifolds with boundary data
along conformal infinity. We solve these Laplace-type boundary problems
formally, and to all orders, by constructing an operator which projects
arbitrary forms to solutions. We also develop a product formula for solving
these asymptotic problems in general. The central tools of our approach are (i)
the conformal geometry of differential forms and the associated exterior
tractor calculus, and (ii) a generalised notion of scale which encodes the
connection between the underlying geometry and its boundary. The latter also
controls the breaking of conformal invariance in a very strict way by coupling
conformally invariant equations to the scale tractor associated with the
generalised scale. From this, we obtain a map from existing solutions to new
ones that exchanges Dirichlet and Neumann boundary conditions. Together, the
scale tractor and exterior structure extend the solution generating algebra of
[31] to a conformally invariant, Poincare--Einstein calculus on (tractor)
differential forms. This calculus leads to explicit holographic formulae for
all the higher order conformal operators on weighted differential forms,
differential complexes, and Q-operators of [9]. This complements the results of
Aubry and Guillarmou [3] where associated conformal harmonic spaces parametrise
smooth solutions.Comment: 85 pages, LaTeX, typos corrected, references added, to appear in
Memoirs of the AM
Holographic Reconstruction and Renormalization in Asymptotically Ricci-flat Spacetimes
In this work we elaborate on an extension of the AdS/CFT framework to a
subclass of gravitational theories with vanishing cosmological constant. By
building on earlier ideas, we construct a correspondence between Ricci-flat
spacetimes admitting asymptotically hyperbolic hypersurfaces and a family of
conformal field theories on a codimension two manifold at null infinity. By
truncating the gravity theory to the pure gravitational sector, we find the
most general spacetime asymptotics, renormalize the gravitational action,
reproduce the holographic stress tensors and Ward identities of the family of
CFTs and show how the asymptotics is mapped to and reconstructed from conformal
field theory data. In even dimensions, the holographic Weyl anomalies identify
the bulk time coordinate with the spectrum of central charges with
characteristic length the bulk Planck length. Consistency with locality in the
bulk time direction requires a notion of locality in this spectrum.Comment: 44 pages, 4 figures. v2: minor changes in section
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