750 research outputs found
Group Averaging and Refined Algebraic Quantization
We review the framework of Refined Algebraic Quantization and the method of
Group Averaging for quantizing systems with first-class constraints. Aspects
and results concerning the generality, limitations, and uniqueness of these
methods are discussed.Comment: 4 pages, LaTeX 2.09 using espcrc2.sty. To appear in the proceedings
of the third "Meeting on Constrained Dynamics and Quantum Gravity", Nucl.
Phys. B (Proc. Suppl.
On Group Averaging for SO(n,1)
The technique known as group averaging provides powerful machinery for the
study of constrained systems. However, it is likely to be well defined only in
a limited set of cases. Here, we investigate the possibility of using a
`renormalized' group averaging in certain models. The results of our study may
indicate a general connection between superselection sectors and the rate of
divergence of the group averaging integral.Comment: Minor corrections, 17 pages,RevTe
On the Generality of Refined Algebraic Quantization
The Dirac quantization `procedure' for constrained systems is well known to
have many subtleties and ambiguities. Within this ill-defined framework, we
explore the generality of a particular interpretation of the Dirac procedure
known as refined algebraic quantization. We find technical conditions under
which refined algebraic quantization can reproduce the general implementation
of the Dirac scheme for systems whose constraints form a Lie algebra with
structure constants. The main result is that, under appropriate conditions, the
choice of an inner product on the physical states is equivalent to the choice
of a ``rigging map'' in refined algebraic quantization.Comment: 12 pages, no figures, ReVTeX, some changes in presentation, some
references adde
Group Averaging for de Sitter free fields
Perturbative gravity about global de Sitter space is subject to
linearization-stability constraints. Such constraints imply that quantum states
of matter fields couple consistently to gravity {\it only} if the matter state
has vanishing de Sitter charges; i.e., only if the state is invariant under the
symmetries of de Sitter space. As noted by Higuchi, the usual Fock spaces for
matter fields contain no de Sitter-invariant states except the vacuum, though a
new Hilbert space of de Sitter invariant states can be constructed via
so-called group-averaging techniques. We study this construction for free
scalar fields of arbitrary positive mass in any dimension, and for linear
vector and tensor gauge fields in any dimension. Our main result is to show in
each case that group averaging converges for states containing a sufficient
number of particles. We consider general -particle states with smooth
wavefunctions, though we obtain somewhat stronger results when the
wavefunctions are finite linear combinations of de Sitter harmonics. Along the
way we obtain explicit expressions for general boost matrix elements in a
familiar basis.Comment: 33 pages, 2 figure
Comparison between various notions of conserved charges in asymptotically AdS-spacetimes
We derive hamiltionian generators of asymptotic symmetries for general
relativity with asymptotic AdS boundary conditions using the ``covariant phase
space'' method of Wald et al. We then compare our results with other
definitions that have been proposed in the literature. We find that our
definition agrees with that proposed by Ashtekar et al, with the spinor
definition, and with the background dependent definition of Henneaux and
Teitelboim. Our definition disagrees with the one obtained from the
``counterterm subtraction method,'' but the difference is found to consist only
of a ``constant offset'' that is determined entirely in terms of the boundary
metric. We finally discuss and justify our boundary conditions by a linear
perturbation analysis, and we comment on generalizations of our boundary
conditions, as well as inclusion of matter fields.Comment: 64p, Latex, no figures, v2: references added, typos corrected, v3:
some equations correcte
Dirac Action on M5 and M2 Branes with Bulk Fluxes
We derive an explicit form of the quadratic in fermions Dirac action on the
M5 brane for an arbitrary on-shell background of 11D supergravity with
non-vanishing fluxes and in presence of a chiral 2-form on M5. This action may
be used to generalize the conditions for which the non-perturbative
superpotential can be generated in M/string theory. We also derive the Dirac
action with bulk fluxes on the M2 brane.Comment: 12 pages References adde
Comparing Formulations of Generalized Quantum Mechanics for Reparametrization-Invariant Systems
A class of decoherence schemes is described for implementing the principles
of generalized quantum theory in reparametrization-invariant `hyperbolic'
models such as minisuperspace quantum cosmology. The connection with
sum-over-histories constructions is exhibited and the physical equivalence or
inequivalence of different such schemes is analyzed. The discussion focuses on
comparing constructions based on the Klein-Gordon product with those based on
the induced (a.k.a. Rieffel, Refined Algebraic, Group Averaging, or Spectral
Analysis) inner product. It is shown that the Klein-Gordon and induced products
can be simply related for the models of interest. This fact is then used to
establish isomorphisms between certain decoherence schemes based on these
products.Comment: 21 pages ReVTe
Recommended from our members
Refined algebraic quantization: systems with a single constraint
This paper explores in some detail a recent proposal (the Rieffel induction/refined algebraic quantization scheme) for the quantization of constrained gauge systems. Below, the focus is on systems with a single constraint and, in this context, on the uniqueness of the construction. While in general the results depend heavily on the choices made for certain auxiliary structures, an additional physical argument leads to a unique result for typical cases. We also discuss the `superselection laws' that result from this scheme and how their existence also depends on the choice of auxiliary structures. Again, when these structures are chosen in a physically motivated way, the resulting superselection laws are physically reasonable
- …