4,951 research outputs found
A Closed Contour of Integration in Regge Calculus
The analytic structure of the Regge action on a cone in dimensions over a
boundary of arbitrary topology is determined in simplicial minisuperspace. The
minisuperspace is defined by the assignment of a single internal edge length to
all 1-simplices emanating from the cone vertex, and a single boundary edge
length to all 1-simplices lying on the boundary. The Regge action is analyzed
in the space of complex edge lengths, and it is shown that there are three
finite branch points in this complex plane. A closed contour of integration
encircling the branch points is shown to yield a convergent real wave function.
This closed contour can be deformed to a steepest descent contour for all sizes
of the bounding universe. In general, the contour yields an oscillating wave
function for universes of size greater than a critical value which depends on
the topology of the bounding universe. For values less than the critical value
the wave function exhibits exponential behaviour. It is shown that the critical
value is positive for spherical topology in arbitrary dimensions. In three
dimensions we compute the critical value for a boundary universe of arbitrary
genus, while in four and five dimensions we study examples of product manifolds
and connected sums.Comment: 16 pages, Latex, To appear in Gen. Rel. Gra
Approximate Decoherence of Histories and 't Hooft's Deterministic Quantum Theory
This paper explores the possibility that an exactly decoherent set of
histories may be constructed from an approximately decoherent set by small
distortions of the operators characterizing the histories. In particular, for
the case of histories of positions and momenta, this is achieved by doubling
the set of operators and then finding, amongst this enlarged set, new position
and momentum operators which commute, so decohere exactly, and which are
``close'' to the original operators. The enlarged, exactly decoherent, theory
has the same classical dynamics as the original one, and coincides with the
so-called deterministic quantum theories of the type recently studied by 't
Hooft. These results suggest that the comparison of standard and deterministic
quantum theories may provide an alternative method of characterizing emergent
classicality. A side-product is the surprising result that histories of momenta
in the quantum Brownian motion model (for the free particle in the
high-temperature limit) are exactly decoherent.Comment: 41 pages, plain Te
Complex lapse, complex action and path integrals
Imaginary time is often used in quantum tunnelling calculations. This article
advocates a conceptually sounder alternative: complex lapse. In the ``3+1''
action for the Einstein gravitational field minimally coupled to a Klein-Gordon
field, allowing the lapse function to be complex yields a complex action which
generates both the usual Lorentzian theory and its Riemannian analogue, and in
particular allows a change of signature between the two. The action and
variational equations are manifestly well defined in the Hamiltonian
representation, with the momentum fields consequently being complex. The
complex action interpolates between the Lorentzian and Riemannian actions as
they appear formally in the respective path integrals. Thus the complex-lapse
theory provides a unified basis for a path-integral quantum theory of gravity
involving both Lorentzian and Riemannian aspects. A major motivation is the
quantum-tunnelling scenario for the origin of the universe. Taken as an
explanation for the observed quantum tunnelling of particles, the complex-lapse
theory determines that the argument of the lapse for the universe now is
extremely small but negative.Comment: 12 pages, Te
Quantum cosmology with a curvature squared action
The correct quantum description for a curvature squared term in the action
can be obtained by casting the action in the canonical form with the
introduction of a variable which is the negative of the first derivative of the
field variable appearing in the action, only after removing the total
derivative terms from the action. We present the Wheeler-DeWitt equation and
obtain the expression for the probability density and current density from the
equation of continuity. Furthermore, in the weak energy limit we obtain the
classical Einstein equation. Finally we present a solution of the wave
equation.Comment: 8 pages, revte
The exact cosmological solution to the dynamical equations for the Bianchi IX model
Quantum geometrodynamics in extended phase space describes phenomenologically
the integrated system ``a physical object + observation means (a gravitational
vacuum condensate)''. The central place in this version of QGD belongs to the
Schrodinger equation for a wave function of the Universe. An exact solution to
the ``conditionally-classical'' set of equations in extended phase space for
the Bianchi-IX model and the appropriate solution to the Schrodinger equation
are considered. The physical adequacy of the obtained solutions to existing
concepts about possible cosmological scenarios is demonstrated. The
gravitational vacuum condensate is shown to be a cosmological evolution factor.Comment: LaTeX, 14 pages, to be published in Int. J. Mod. Phys.
Global phase time and path integral for string cosmological models
A global phase time is identified for homogeneous and isotropic cosmological
models yielding from the low energy effective action of closed bosonic string
theory. When the Hamiltonian constraint allows for the existence of an
intrinsic time, the quantum transition amplitude is obtained by means of the
usual path integral procedure for gauge systems.Comment: 12 pages, added reference
On the interpretation of time-reparametrization-invariant quantum mechanics
The classical and quantum dynamics of simple time-reparametrization-
invariant models containing two degrees of freedom are studied in detail.
Elimination of one ``clock'' variable through the Hamiltonian constraint leads
to a description of time evolution for the remaining variable which is
essentially equivalent to the standard quantum mechanics of an unconstrained
system. In contrast to a similar proposal of Rovelli, evolution is with respect
to the geometrical proper time, and the Heisenberg equation of motion is exact.
The possibility of a ``test clock'', which would reveal time evolution while
contributing negligibly to the Hamiltonian constraint is examined, and found to
be viable in the semiclassical limit of large quantum numbers.Comment: 13 pages, set in REVTeX. One figure available by FAX from
[email protected]
Chern-Simons functional and the no-boundary proposal in Bianchi IX quantum cosmology
The Chern-Simons functional is an exact solution to the
Ashtekar-Hamilton-Jacobi equation of general relativity with a nonzero
cosmological constant. In this paper we consider in Bianchi type
IX cosmology with spatial surfaces. We show that among the classical
solutions generated by~, there is a two-parameter family of
Euclidean spacetimes that have a regular NUT-type closing. When two of the
three scale factors are equal, these spacetimes reduce to a one-parameter
family within the Euclidean Taub-NUT-de~Sitter metrics. For a nonzero
cosmological constant, therefore provides a semiclassical
estimate to the Bianchi~IX no-boundary wave function in Ashtekar's variables.Comment: 9 pages, REVTeX v3.0. (One reference added.
Consistent Histories in Quantum Cosmology
We illustrate the crucial role played by decoherence (consistency of quantum
histories) in extracting consistent quantum probabilities for alternative
histories in quantum cosmology. Specifically, within a Wheeler-DeWitt
quantization of a flat Friedmann-Robertson-Walker cosmological model sourced
with a free massless scalar field, we calculate the probability that the
univese is singular in the sense that it assumes zero volume. Classical
solutions of this model are a disjoint set of expanding and contracting
singular branches. A naive assessment of the behavior of quantum states which
are superpositions of expanding and contracting universes may suggest that a
"quantum bounce" is possible i.e. that the wave function of the universe may
remain peaked on a non-singular classical solution throughout its history.
However, a more careful consistent histories analysis shows that for arbitrary
states in the physical Hilbert space the probability of this Wheeler-DeWitt
quantum universe encountering the big bang/crunch singularity is equal to
unity. A quantum Wheeler-DeWitt universe is inevitably singular, and a "quantum
bounce" is thus not possible in these models.Comment: To appear in Foundations of Physics special issue on quantum
foundation
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