4,012 research outputs found
Do Naked Singularities Form?
A naked singularity is formed by the collapse of a Sine-Gordon soliton in 1+1
dimensional dilaton gravity with a negative cosmological constant. We examine
the quantum stress tensor resulting from the formation of the singularity.
Consistent boundary conditions require that the incoming soliton is accompanied
by a flux of incoming radiation across past null infinity, but neglecting the
back reaction of the spacetime leads to the absurd conclusion that the total
energy entering the system by the time the observer is able to receive
information from the singularity is infinite. We conclude that the back
reaction must prevent the formation of the naked singularity.Comment: 7 pages (21 Kb), PHYZZX. Revised version to appear in Class. & Quant.
Grav. Letts. A discussion of the consistency of the Sine-Gordon model is
include
Affine group representation formalism for four dimensional, Lorentzian, quantum gravity
Within the context of the Ashtekar variables, the Hamiltonian constraint of
four-dimensional pure General Relativity with cosmological constant, ,
is reexpressed as an affine algebra with the commutator of the imaginary part
of the Chern-Simons functional, , and the positive-definite volume element.
This demonstrates that the affine algebra quantization program of Klauder can
indeed be applicable to the full Lorentzian signature theory of quantum gravity
with non-vanishing cosmological constant; and it facilitates the construction
of solutions to all of the constraints. Unitary, irreducible representations of
the affine group exhibit a natural Hilbert space structure, and coherent states
and other physical states can be generated from a fiducial state. It is also
intriguing that formulation of the Hamiltonian constraint or Wheeler-DeWitt
equation as an affine algebra requires a non-vanishing cosmological constant;
and a fundamental uncertainty relation of the form
(wherein
is the total volume) may apply to all physical states of quantum gravity.Comment: 13 pages. Revised versio
Electric Dipole Moment of a BPS Monopole
Monopole ``superpartner'' solutions are constructed by acting with finite,
broken supersymmetry transformations on a bosonic N=2 BPS monopole. The terms
beyond first order in this construction represent the backreaction of the the
fermionic zero-mode state on the other fields. Because of the quantum nature of
the fermionic zero-modes, the superpartner solution is necessarily operator
valued. We extract the electric dipole moment operator and show that it is
proportional to the fermion zero-mode angular momentum operator with a
gyroelectric ratio g=2. The magnetic quadrupole operator is shown to vanish
identically on all states. We comment on the usefulness of the monopole
superpartner solution for a study of the long-range spin dependent dynamics of
BPS monopoles.Comment: 8 pages, references and note adde
Three-geometry and reformulation of the Wheeler-DeWitt equation
A reformulation of the Wheeler-DeWitt equation which highlights the role of
gauge-invariant three-geometry elements is presented. It is noted that the
classical super-Hamiltonian of four-dimensional gravity as simplified by
Ashtekar through the use of gauge potential and densitized triad variables can
furthermore be succinctly expressed as a vanishing Poisson bracket involving
three-geometry elements. This is discussed in the general setting of the
Barbero extension of the theory with arbitrary non-vanishing value of the
Immirzi parameter, and when a cosmological constant is also present. A proposed
quantum constraint of density weight two which is polynomial in the basic
conjugate variables is also demonstrated to correspond to a precise simple
ordering of the operators, and may thus help to resolve the factor ordering
ambiguity in the extrapolation from classical to quantum gravity. Alternative
expression of a density weight one quantum constraint which may be more useful
in the spin network context is also discussed, but this constraint is
non-polynomial and is not motivated by factor ordering. The article also
highlights the fact that while the volume operator has become a preeminient
object in the current manifestation of loop quantum gravity, the volume element
and the Chern-Simons functional can be of equal significance, and need not be
mutually exclusive. Both these fundamental objects appear explicitly in the
reformulation of the Wheeler-DeWitt constraint.Comment: 10 pages, LaTeX fil
Basis States for Relativistic, Dynamically-Entangled Particles
In several recent papers on entanglement in relativistic quantum systems and
relativistic Bell's inequalities, relativistic Bell-type two-particle states
have been constructed in analogy to non-relativistic states. These
constructions do not have the form suggested by relativistic invariance of the
dynamics. Two relativistic formulations of Bell-type states are shown for
massive particles, one using the standard Wigner spin basis and one using the
helicity basis. The construction hinges on the use of Clebsch-Gordan
coefficients of the Poincar\'e group to reduce the direct product of two
unitary irreducible representations (UIRs) into a direct sum of UIRs.Comment: 19 pages, three tables, revte
The linearization of the Kodama state
We study the question of whether the linearization of the Kodama state around
classical deSitter spacetime is normalizable in the inner product of the theory
of linearized gravitons on deSitter spacetime. We find the answer is no in the
Lorentzian theory. However, in the Euclidean theory the corresponding
linearized Kodama state is delta-functional normalizable. We discuss whether
this result invalidates the conjecture that the full Kodama state is a good
physical state for quantum gravity with positive cosmological constant.Comment: 14 pages, statement on the corresponding Yang-Mills case correcte
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