249,284 research outputs found
Fermions in three-dimensional spinfoam quantum gravity
We study the coupling of massive fermions to the quantum mechanical dynamics
of spacetime emerging from the spinfoam approach in three dimensions. We first
recall the classical theory before constructing a spinfoam model of quantum
gravity coupled to spinors. The technique used is based on a finite expansion
in inverse fermion masses leading to the computation of the vacuum to vacuum
transition amplitude of the theory. The path integral is derived as a sum over
closed fermionic loops wrapping around the spinfoam. The effects of quantum
torsion are realised as a modification of the intertwining operators assigned
to the edges of the two-complex, in accordance with loop quantum gravity. The
creation of non-trivial curvature is modelled by a modification of the pure
gravity vertex amplitudes. The appendix contains a review of the geometrical
and algebraic structures underlying the classical coupling of fermions to three
dimensional gravity.Comment: 40 pages, 3 figures, version accepted for publication in GER
On the Relations between Gravity and BF Theories
We review, in the light of recent developments, the existing relations
between gravity and topological BF theories at the classical level. We include
the Plebanski action in both self-dual and non-chiral formulations, their
generalizations, and the MacDowell-Mansouri action.Comment: v3: journal typeset versio
Hadamard states from null infinity
Free field theories on a four dimensional, globally hyperbolic spacetime,
whose dynamics is ruled by a Green hyperbolic partial differential operator,
can be quantized following the algebraic approach. It consists of a two-step
procedure: In the first part one identifies the observables of the underlying
physical system collecting them in a *-algebra which encodes their relational
and structural properties. In the second step one must identify a quantum
state, that is a positive, normalized linear functional on the *-algebra out of
which one recovers the interpretation proper of quantum mechanical theories via
the so-called Gelfand-Naimark-Segal theorem. In between the plethora of
possible states, only few of them are considered physically acceptable and they
are all characterized by the so-called Hadamard condition, a constraint on the
singular structure of the associated two-point function. Goal of this paper is
to outline a construction scheme for these states which can be applied whenever
the underlying background possesses a null (conformal) boundary. We discuss in
particular the examples of a real, massless conformally coupled scalar field
and of linearized gravity on a globally hyperbolic and asymptotically flat
spacetime.Comment: 23 pages, submitted to the Proceedings of the conference "Quantum
Mathematical Physics", held in Regensburg from the 29th of September to the
02nd of October 201
The Physical Role of Gravitational and Gauge Degrees of Freedom in General Relativity - II: Dirac versus Bergmann observables and the Objectivity of Space-Time
(abridged)The achievements of the present work include: a) A clarification of
the multiple definition given by Bergmann of the concept of {\it (Bergmann)
observable. This clarification leads to the proposal of a {\it main conjecture}
asserting the existence of i) special Dirac's observables which are also
Bergmann's observables, ii) gauge variables that are coordinate independent
(namely they behave like the tetradic scalar fields of the Newman-Penrose
formalism). b) The analysis of the so-called {\it Hole} phenomenology in strict
connection with the Hamiltonian treatment of the initial value problem in
metric gravity for the class of Christoudoulou -Klainermann space-times, in
which the temporal evolution is ruled by the {\it weak} ADM energy. It is
crucial the re-interpretation of {\it active} diffeomorphisms as {\it passive
and metric-dependent} dynamical symmetries of Einstein's equations, a
re-interpretation which enables to disclose their (nearly unknown) connection
to gauge transformations on-shell; this is expounded in the first paper
(gr-qc/0403081). The use of the Bergmann-Komar {\it intrinsic
pseudo-coordinates} allows to construct a {\it physical atlas} of 4-coordinate
systems for the 4-dimensional {\it mathematical} manifold, in terms of the
highly non-local degrees of freedom of the gravitational field (its four
independent {\it Dirac observables}), and to realize the {\it physical
individuation} of the points of space-time as {\it point-events} as a
gauge-fixing problem, also associating a non-commutative structure to each
4-coordinate system.Comment: 41 pages, Revtex
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