704 research outputs found
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
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
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
String/M-branes for Relativists
These notes present an introduction to branes in ten and eleven dimensional supergravity and string/M-theory which is geared to an audience of traditional relativists, especially graduate students and others with little background in supergravity. They are designed as a tutorial and not as a thorough review of the subject; as a result, many topics of current interest are not addressed. However, a guide to further reading is included. The presentation begins with eleven dimensional supergravity, stressing its relation to 3+1 Einstein-Maxwell theory. The notion of Kaluza-Klein compactification is then introduced, and is used to relate the eleven dimensional discussion to supergravity in 9+1 dimensions and to string theory. The focus is on type IIA supergravity, but the type IIB theory is also addressed, as is the T-duality symmetry that relates them. Branes in both 10+1 and 9+1 dimensions are included. Finally, although the details are not discussed, a few comments are provided on the relation between supergravity and string perturbation theory and on black hole entropy. The goal is to provide traditional relativists with a kernel of knowledge from which to grow their understanding of branes and strings
Quantum constraints, Dirac observables and evolution: group averaging versus Schroedinger picture in LQC
A general quantum constraint of the form (realized in particular in Loop Quantum Cosmology models) is
studied. Group Averaging is applied to define the Hilbert space of solutions
and the relational Dirac observables. Two cases are considered. In the first
case, the spectrum of the operator is assumed to be
discrete. The quantum theory defined by the constraint takes the form of a
Schroedinger-like quantum mechanics with a generalized Hamiltonian
. In the second case, the spectrum is absolutely continuous
and some peculiar asymptotic properties of the eigenfunctions are assumed. The
resulting Hilbert space and the dynamics are characterized by a continuous
family of the Schroedinger-like quantum theories. However, the relational
observables mix different members of the family. Our assumptions are motivated
by new Loop Quantum Cosmology models of quantum FRW spacetime. The two cases
considered in the paper correspond to the negative and, respectively, positive
cosmological constant. Our results should be also applicable in many other
general relativistic contexts.Comment: RevTex4, 32 page
Kinematical Hilbert Spaces for Fermionic and Higgs Quantum Field Theories
We extend the recently developed kinematical framework for diffeomorphism
invariant theories of connections for compact gauge groups to the case of a
diffeomorphism invariant quantum field theory which includes besides
connections also fermions and Higgs fields. This framework is appropriate for
coupling matter to quantum gravity. The presence of diffeomorphism invariance
forces us to choose a representation which is a rather non-Fock-like one : the
elementary excitations of the connection are along open or closed strings while
those of the fermions or Higgs fields are at the end points of the string.
Nevertheless we are able to promote the classical reality conditions to quantum
adjointness relations which in turn uniquely fixes the gauge and diffeomorphism
invariant probability measure that underlies the Hilbert space. Most of the
fermionic part of this work is independent of the recent preprint by Baez and
Krasnov and earlier work by Rovelli and Morales-Tec\'otl because we use new
canonical fermionic variables, so-called Grassman-valued half-densities, which
enable us to to solve the difficult fermionic adjointness relations.Comment: 26p, LATE
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