16,511 research outputs found
A Hamiltonian functional for the linearized Einstein vacuum field equations
By considering the Einstein vacuum field equations linearized about the
Minkowski metric, the evolution equations for the gauge-invariant quantities
characterizing the gravitational field are written in a Hamiltonian form by
using a conserved functional as Hamiltonian; this Hamiltonian is not the analog
of the energy of the field. A Poisson bracket between functionals of the field,
compatible with the constraints satisfied by the field variables, is obtained.
The generator of spatial translations associated with such bracket is also
obtained.Comment: 5 pages, accepted in J. Phys.: Conf. Serie
Local continuity laws on the phase space of Einstein equations with sources
Local continuity equations involving background fields and variantions of the
fields, are obtained for a restricted class of solutions of the
Einstein-Maxwell and Einstein-Weyl theories using a new approach based on the
concept of the adjoint of a differential operator. Such covariant conservation
laws are generated by means of decoupled equations and their adjoints in such a
way that the corresponding covariantly conserved currents possess some
gauge-invariant properties and are expressed in terms of Debye potentials.
These continuity laws lead to both a covariant description of bilinear forms on
the phase space and the existence of conserved quantities. Differences and
similarities with other approaches and extensions of our results are discussed.Comment: LaTeX, 13 page
Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty
We analyze the quantum dynamics of the non-relativistic two-dimensional
isotropic harmonic oscillator in Heisenberg's picture. Such a system is taken
as toy model to analyze some of the various quantum theories that can be built
from the application of Dirac's quantization rule to the various symplectic
structures recently reported for this classical system. It is pointed out that
that these quantum theories are inequivalent in the sense that the mean values
for the operators (observables) associated with the same physical classical
observable do not agree with each other. The inequivalence does not arise from
ambiguities in the ordering of operators but from the fact of having several
symplectic structures defined with respect to the same set of coordinates. It
is also shown that the uncertainty relations between the fundamental
observables depend on the particular quantum theory chosen. It is important to
emphasize that these (somehow paradoxical) results emerge from the combination
of two paradigms: Dirac's quantization rule and the usual Copenhagen
interpretation of quantum mechanics.Comment: 8 pages, LaTex file, no figures. Accepted for publication in Phys.
Rev.
Rotational symmetry and degeneracy: a cotangent-perturbed rigid rotator of unperturbed level multiplicity
We predict level degeneracy of the rotational type in diatomic molecules
described by means of a cotangent-hindered rigid rotator. The problem is shown
to be exactly solvable in terms of non-classical Romanovski polynomials. The
energies of such a system are linear combinations of t(t+1) and 1/[t(t+1)+1/4]
terms with the non-negative integer principal quantum number t=n+|/bar{m}|
being the sum of the degree n of the polynomials and the absolute value,
|/bar{m}|, of the square root of the separation constant between the polar and
azimuthal motions. The latter obeys, with respect to t, the same branching
rule, |/bar{m}|=0,1,..., t, as does the magnetic quantum number with respect to
the angular momentum, l, and, in this fashion, the t quantum number presents
itself indistinguishable from l. In effect, the spectrum of the hindered
rotator has the same (2t+1)-fold level multiplicity as the unperturbed one. For
small t values, the wave functions and excitation energies of the perturbed
rotator differ from the ordinary spherical harmonics, and the l(l+1) law,
respectively, while approaching them asymptotically with increasing t. In this
fashion the breaking of the rotational symmetry at the level of the
representation functions is opaqued by the level degeneracy. The model provides
a tool for the description of rotational bands with anomalously large gaps
between the ground state and its first excitation.Comment: 10 pages, 6 figures; Molecular Physics 201
Time reparametrization invariance in arbitrary range p-spin models: symmetric versus non-symmetric dynamics
We explore the existence of time reparametrization symmetry in p-spin models.
Using the Martin-Siggia-Rose generating functional, we analytically probe the
long-time dynamics. We perform a renormalization group analysis where we
systematically integrate over short timescale fluctuations. We find three
families of stable fixed points and study the symmetry of those fixed points
with respect to time reparametrizations. One of those families is composed
entirely of symmetric fixed points, which are associated with the low
temperature dynamics. The other two families are composed entirely of
non-symmetric fixed points. One of these two non-symmetric families corresponds
to the high temperature dynamics.
Time reparametrization symmetry is a continuous symmetry that is
spontaneously broken in the glass state and we argue that this gives rise to
the presence of Goldstone modes. We expect the Goldstone modes to determine the
properties of fluctuations in the glass state, in particular predicting the
presence of dynamical heterogeneity.Comment: v2: Extensively modified to discuss both high temperature
(non-symmetric) and low temperature (symmetric) renormalization group fixed
points. Now 16 pages with 1 figure. v1: 13 page
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