8,430 research outputs found
Compatibility of radial, Lorenz and harmonic gauges
We observe that the radial gauge can be consistently imposed \emph{together}
with the Lorenz gauge in Maxwell theory, and with the harmonic traceless gauge
in linearized general relativity. This simple observation has relevance for
some recent developments in quantum gravity where the radial gauge is
implicitly utilized.Comment: 9 pages, minor changes in the bibliograph
The century of the incomplete revolution: searching for general relativistic quantum field theory
In fundamental physics, this has been the century of quantum mechanics and
general relativity. It has also been the century of the long search for a
conceptual framework capable of embracing the astonishing features of the world
that have been revealed by these two ``first pieces of a conceptual
revolution''. I discuss the general requirements on the mathematics and some
specific developments towards the construction of such a framework. Examples of
covariant constructions of (simple) generally relativistic quantum field
theories have been obtained as topological quantum field theories, in
nonperturbative zero-dimensional string theory and its higher dimensional
generalizations, and as spin foam models. A canonical construction of a general
relativistic quantum field theory is provided by loop quantum gravity.
Remarkably, all these diverse approaches have turn out to be related,
suggesting an intriguing general picture of general relativistic quantum
physics.Comment: To appear in the Journal of Mathematical Physics 2000 Special Issu
Quantum Loop Representation for Fermions coupled to Einstein-Maxwell field
Quantization of the system comprising gravitational, fermionic and
electromagnetic fields is developed in the loop representation. As a result we
obtain a natural unified quantum theory. Gravitational field is treated in the
framework of Ashtekar formalism; fermions are described by two Grassmann-valued
fields. We define a -algebra of configurational variables whose
generators are associated with oriented loops and curves; ``open'' states --
curves -- are necessary to embrace the fermionic degrees of freedom. Quantum
representation space is constructed as a space of cylindrical functionals on
the spectrum of this -algebra. Choosing the basis of ``loop'' states we
describe the representation space as the space of oriented loops and curves;
then configurational and momentum loop variables become in this basis the
operators of creation and annihilation of loops and curves. The important
difference of the representation constructed from the loop representation of
pure gravity is that the momentum loop operators act in our case simply by
joining loops in the only compatible with their orientaiton way, while in the
case of pure gravity this action is more complicated.Comment: 28 pages, REVTeX 3.0, 15 uuencoded ps-figures. The construction of
the representation has been changed so that the representation space became
irreducible. One part is removed because it developed into a separate paper;
some corrections adde
Multiple-event probability in general-relativistic quantum mechanics
We discuss the definition of quantum probability in the context of "timeless"
general--relativistic quantum mechanics. In particular, we study the
probability of sequences of events, or multi-event probability. In conventional
quantum mechanics this can be obtained by means of the ``wave function
collapse" algorithm. We first point out certain difficulties of some natural
definitions of multi-event probability, including the conditional probability
widely considered in the literature. We then observe that multi-event
probability can be reduced to single-event probability, by taking into account
the quantum nature of the measuring apparatus. In fact, by exploiting the
von-Neumann freedom of moving the quantum classical boundary, one can always
trade a sequence of non-commuting quantum measurements at different times, with
an ensemble of simultaneous commuting measurements on the joint
system+apparatus system. This observation permits a formulation of quantum
theory based only on single-event probability, where the results of the "wave
function collapse" algorithm can nevertheless be recovered. The discussion
bears also on the nature of the quantum collapse
Ultraviolet behavior in background independent quantum field theory
We describe a background independent quantization of the scalar field that
provides an explicit realization of Fock-like states and associated operators
in a polymer Hilbert space. The vacuum expectation values of the commutator and
anti-commutator of the creation and annihilation operators become energy
dependent, and exhibit a surprising transition to fermionic behavior at high
energy. Furthermore the approach yields a modified dispersion relation with a
leading correction proportional to the momentum cubed. These results suggests a
fundamental change in the ultraviolet properties of quantum fields.Comment: 8 pages, 5 figure
Gauge Transformation Properties of Vector and Tensor Potentials Revisited: a Group Quantization Approach
The possibility of non-trivial representations of the gauge group on
wavefunctionals of a gauge invariant quantum field theory leads to a generation
of mass for intermediate vector and tensor bosons. The mass parameters m show
up as central charges in the algebra of constraints, which then become of
second-class nature. The gauge group coordinates acquire dynamics outside the
null-mass shell and provide the longitudinal field degrees of freedom that
massless bosons need to form massive bosons. This is a `non-Higgs' mechanism
that could provide new clues for the best understanding of the symmetry
breaking mechanism in unified field theories. A unified quantization of
massless and massive non-Abelian Yang-Mills, linear Gravity and Abelian
two-form gauge field theories are fully developed from this new approach, where
a cohomological origin of mass is pointed out.Comment: 22 pages, LaTeX, no figures; final version to appear in Int. J. Mod.
Phys.
Counting surface states in the loop quantum gravity
We adopt the point of view that (Riemannian) classical and (loop-based)
quantum descriptions of geometry are macro- and micro-descriptions in the usual
statistical mechanical sense. This gives rise to the notion of geometrical
entropy, which is defined as the logarithm of the number of different quantum
states which correspond to one and the same classical geometry configuration
(macro-state). We apply this idea to gravitational degrees of freedom induced
on an arbitrarily chosen in space 2-dimensional surface. Considering an
`ensemble' of particularly simple quantum states, we show that the geometrical
entropy corresponding to a macro-state specified by a total area of
the surface is proportional to the area , with being
approximately equal to . The result holds both for case of open
and closed surfaces. We discuss briefly physical motivations for our choice of
the ensemble of quantum states.Comment: This paper is a substantially modified version of the paper `The
Bekenstein bound and non-perturbative quantum gravity'. Although the main
result (i.e. the result of calculation of the number of quantum states that
correspond to one and the same area of 2-d surface) remains unchanged, it is
presented now from a different point of view. The new version contains a
discussion both of the case of open and closed surfaces, and a discussion of
a possibility to generalize the result obtained considering arbitrary surface
quantum states. LaTeX, 21 pages, 6 figures adde
The physical hamiltonian in nonperturbative quantum gravity
A quantum hamiltonian which evolves the gravitational field according to time
as measured by constant surfaces of a scalar field is defined through a
regularization procedure based on the loop representation, and is shown to be
finite and diffeomorphism invariant. The problem of constructing this
hamiltonian is reduced to a combinatorial and algebraic problem which involves
the rearrangements of lines through the vertices of arbitrary graphs. This
procedure also provides a construction of the hamiltonian constraint as a
finite operator on the space of diffeomorphism invariant states as well as a
construction of the operator corresponding to the spatial volume of the
universe.Comment: Latex, 11 pages, no figures, CGPG/93/
Polymer Parametrised Field Theory
Free scalar field theory on 2 dimensional flat spacetime, cast in
diffeomorphism invariant guise by treating the inertial coordinates of the
spacetime as dynamical variables, is quantized using LQG type `polymer'
representations for the matter field and the inertial variables. The quantum
constraints are solved via group averaging techniques and, analogous to the
case of spatial geometry in LQG, the smooth (flat) spacetime geometry is
replaced by a discrete quantum structure. An overcomplete set of Dirac
observables, consisting of (a) (exponentials of) the standard free scalar field
creation- annihilation modes and (b) canonical transformations corresponding to
conformal isometries, are represented as operators on the physical Hilbert
space. None of these constructions suffer from any of the `triangulation'
dependent choices which arise in treatments of LQG. In contrast to the standard
Fock quantization, the non- Fock nature of the representation ensures that the
algebra of conformal isometries as well as that of spacetime diffeomorphisms
are represented in an anomaly free manner. Semiclassical states can be analysed
at the gauge invariant level. It is shown that `physical weaves' necessarily
underly such states and that such states display semiclassicality with respect
to, at most, a countable subset of the (uncountably large) set of observables
of type (a). The model thus offers a fertile testing ground for proposed
definitions of quantum dynamics as well as semiclassical states in LQG.Comment: 44 pages, no figure
2+1 Gravity without dynamics
A three dimensional generally covariant theory is described that has a 2+1
canonical decomposition in which the Hamiltonian constraint, which generates
the dynamics, is absent. Physical observables for the theory are described and
the classical and quantum theories are compared with ordinary 2+1 gravity.Comment: 9 page
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