160 research outputs found
Description of Friedmann Observables in Quantum Universe
The solution of the problem of describing the Friedmann observables (the
Hubble law, the red shift, etc.) in quantum cosmology is proposed on the basis
of the method of gaugeless Hamiltonian reduction in which the gravitational
part of the energy constraint is considered as a new momentum. We show that the
conjugate variable corresponding to the new momentum plays a role of the
invariant time parameter of evolution of dynamical variables in the sector of
the Dirac observables of the general Hamiltonian approach. Relations between
these Dirac observables and the Friedmann observables of the expanding Universe
are established for the standard Friedmann cosmological model with dust and
radiation. The presented reduction removes an infinite factor from the
functional integral, provides the normalizability of the wave function of the
Universe and distinguishes the conformal frame of reference where the Hubble
law is caused by the alteration of the conformal dust mass.Comment: 10 pages, LaTe
Standing waves in the Lorentz-covariant world
When Einstein formulated his special relativity, he developed his dynamics
for point particles. Of course, many valiant efforts have been made to extend
his relativity to rigid bodies, but this subject is forgotten in history. This
is largely because of the emergence of quantum mechanics with wave-particle
duality. Instead of Lorentz-boosting rigid bodies, we now boost waves and have
to deal with Lorentz transformations of waves. We now have some understanding
of plane waves or running waves in the covariant picture, but we do not yet
have a clear picture of standing waves. In this report, we show that there is
one set of standing waves which can be Lorentz-transformed while being
consistent with all physical principle of quantum mechanics and relativity. It
is possible to construct a representation of the Poincar\'e group using
harmonic oscillator wave functions satisfying space-time boundary conditions.
This set of wave functions is capable of explaining the quantum bound state for
both slow and fast hadrons. In particular it can explain the quark model for
hadrons at rest, and Feynman's parton model hadrons moving with a speed close
to that of light.Comment: LaTex 20 pages, presented at the 2004 meeting of the International
Association of Relativistic Dynamincs, to be published in the proceeding
Algebraic analysis of a model of two-dimensional gravity
An algebraic analysis of the Hamiltonian formulation of the model
two-dimensional gravity is performed. The crucial fact is an exact coincidence
of the Poisson brackets algebra of the secondary constraints of this
Hamiltonian formulation with the SO(2,1)-algebra. The eigenvectors of the
canonical Hamiltonian are obtained and explicitly written in closed
form.Comment: 21 pages, to appear in General Relativity and Gravitatio
On Verification of the Non-Generational Conjectural- Derivation of First Class constraints: HP Monopole's Field case
In [7] we proposed a non-generational conjectural derivation of all first
class constraints (involving, only, variables compatible with canonical Poisson
brackets) for realistic gauge (singular) field theories; and we verified the
conjecture in cases of electromagnetic field, Yang Mills fields interacting
with scalar and spinor fields, and the gravitational field. Here we will
further verify our conjecture for the case of 't Hooft- Polyakov (HP)
monopole's field (i.e. in the Higgs Vacuum); and show that we will reproduce
the results in Ref.[6], which we reached at using Dirac's standard
multi-generational algorithm
Constrained Analysis of Topologically Massive Gravity
We quantize the Einstein gravity in the formalism of weak gravitational
fields by using the constrained Hamiltonian method. Special emphasis is given
to the 2+1 spacetime dimensional case where a (topological) Chern-Simons term
is added to the Lagrangian.Comment: 15 pages, IF-UFRJ-21/9
Stargenfunctions, generally parametrized systems and a causal formulation of phase space quantum mechanics
We address the deformation quantization of generally parametrized systems
displaying a natural time variable. The purpose of this exercise is twofold:
first, to illustrate through a pedagogical example the potential of quantum
phase space methods in the context of constrained systems and particularly of
generally covariant systems. Second, to show that a causal representation for
quantum phase space quasidistributions can be easily achieved through general
parametrization. This result is succinctly discussed.Comment: 19 pages, to appear in J. Math. Phy
Time and Dirac Observables in Friedmann Cosmologies
A cosmological time variable is emerged from the Hamiltonian formulation of
Friedmann model to measure the evolution of dynamical observables in the
theory. A set of observables has been identified for the theory on the null
hypersurfaces that its evolution is with respect to the volume clock introduced
by the cosmological time variable.Comment: 11 page
Darboux coordinates for the Hamiltonian of first order Einstein-Cartan gravity
Based on preliminary analysis of the Hamiltonian formulation of the first
order Einstein-Cartan action (arXiv:0902.0856 [gr-qc] and arXiv:0907.1553
[gr-qc]) we derive the Darboux coordinates, which are a unique and uniform
change of variables preserving equivalence with the original action in all
spacetime dimensions higher than two. Considerable simplification of the
Hamiltonian formulation using the Darboux coordinates, compared with direct
analysis, is explicitly demonstrated. Even an incomplete Hamiltonian analysis
in combination with known symmetries of the Einstein-Cartan action and the
equivalence of Hamiltonian and Lagrangian formulations allows us to
unambiguously conclude that the \textit{unique} \textit{gauge} invariances
generated by the first class constraints of the Einstein-Cartan action and the
corresponding Hamiltonian are \textit{translation and rotation in the tangent
space}. Diffeomorphism invariance, though a manifest invariance of the action,
is not generated by the first class constraints of the theory.Comment: 44 pages, references are added, organization of material is slightly
modified (additional section is introduced), more details of calculation of
the Dirac bracket between translational and rotational constraints are
provide
Abelian Magnetic Monopole Dominance in Quark Confinement
We prove Abelian magnetic monopole dominance in the string tension of QCD.
Abelian and monopole dominance in low energy physics of QCD has been confirmed
for various quantities by recent Monte Carlo simulations of lattice gauge
theory. In order to prove this dominance, we use the reformulation of continuum
Yang-Mills theory in the maximal Abelian gauge as a deformation of a
topological field theory of magnetic monopoles, which was proposed in the
previous article by the author. This reformulation provides an efficient way
for incorporating the magnetic monopole configuration as a topological
non-trivial configuration in the functional integral. We derive a version of
the non-Abelian Stokes theorem and use it to estimate the expectation value of
the Wilson loop. This clearly exhibits the role played by the magnetic monopole
as an origin of the Berry phase in the calculation of the Wilson loop in the
manifestly gauge invariant manner. We show that the string tension derived from
the diagonal (abelian) Wilson loop in the topological field theory (studied in
the previous article) converges to that of the full non-Abelian Wilson loop in
the limit of large Wilson loop. Therefore, within the above reformulation of
QCD, this result (together with the previous result) completes the proof of
quark confinement in QCD based on the criterion of the area law of the full
non-Abelian Wilson loop.Comment: 33 pages, Latex, no figures, version accepted for publication in
Phys. Rev. D (additions of sec. 4.5 and references, and minor changes
Interaction of global and local monopoles
We study the direct interaction between global and local monopoles. While in
two previous papers, the coupling between the two sectors was only indirect
through the coupling to gravity, we here introduce a new term in the potential
that couples the Goldstone field and the Higgs field directly. We investigate
the influence of this term in curved space and compare it to the results
obtained previously.Comment: 9 Revtex pages, 4 ps-figure
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