7,167 research outputs found
Clebsch-Gordan Coefficients for the Extended Quantum-Mechanical Poincar\'e Group and Angular Correlations of Decay Products
This paper describes Clebsch-Gordan coefficients (CGCs) for unitary
irreducible representations (UIRs) of the extended quantum mechanical
Poincar\'e group \pt. `Extended' refers to the extension of the 10 parameter
Lie group that is the Poincar\'e group by the discrete symmetries , , and
; `quantum mechanical' refers to the fact that we consider projective
representations of the group. The particular set of CGCs presented here are
applicable to the problem of the reduction of the direct product of two
massive, unitary irreducible representations (UIRs) of \pt with positive
energy to irreducible components. Of the sixteen inequivalent representations
of the discrete symmetries, the two standard representations with are considered. Also included in the analysis are additive internal
quantum numbers specifying the superselection sector. As an example, these CGCs
are applied to the decay process of the meson.Comment: 26 pages, double spaced. Version 2: typos corrected, introduction
change
On the preservation of unitarity during black hole evolution and information extraction from its interior
For more than 30 years the discovery that black holes radiate like black
bodies of specific temperature has triggered a multitude of puzzling questions
concerning their nature and the fate of information that goes down the black
hole during its lifetime. The most tricky issue in what is known as information
loss paradox is the apparent violation of unitarity during the
formation/evaporation process of black holes. A new idea is proposed based on
the combination of our knowledge on Hawking radiation as well as the
Einstein-Podolsky-Rosen phenomenon, that could resolve the paradox and spare
physicists from the unpalatable idea that unitarity can ultimately be violated
even under special conditions.Comment: 8 pages, no figure
Classical solution of the wave equation
The classical limit of wave quantum mechanics is analyzed. It is shown that
the general requirements of continuity and finiteness to the solution
, where and
is the reduced classical action of the physical system, result in the
asymptote of the exact solution and general quantization condition for ,
which yields the exact eigenvalues of the system.Comment: 8 Pages, 10 Refs, LaTe
The Causal Interpretation of Quantum Mechanics and The Singularity Problem in Quantum Cosmology
We apply the causal interpretation of quantum mechanics to homogeneous
quantum cosmology and show that the quantum theory is independent of any
time-gauge choice and there is no issue of time. We exemplify this result by
studying a particular minisuperspace model where the quantum potential driven
by a prescribed quantum state prevents the formation of the classical
singularity, independently on the choice of the lapse function. This means that
the fast-slow-time gauge conjecture is irrelevant within the framework of the
causal interpretation of quantum cosmology.Comment: 18 pages, LaTe
Typicality vs. probability in trajectory-based formulations of quantum mechanics
Bohmian mechanics represents the universe as a set of paths with a
probability measure defined on it. The way in which a mathematical model of
this kind can explain the observed phenomena of the universe is examined in
general. It is shown that the explanation does not make use of the full
probability measure, but rather of a suitable set function deriving from it,
which defines relative typicality between single-time cylinder sets. Such a set
function can also be derived directly from the standard quantum formalism,
without the need of an underlying probability measure. The key concept for this
derivation is the {\it quantum typicality rule}, which can be considered as a
generalization of the Born rule. The result is a new formulation of quantum
mechanics, in which particles follow definite trajectories, but which is only
based on the standard formalism of quantum mechanics.Comment: 24 pages, no figures. To appear in Foundation of Physic
The free energy in a class of quantum spin systems and interchange processes
We study a class of quantum spin systems in the mean-field setting of the
complete graph. For spin the model is the Heisenberg ferromagnet,
for general spin it has a probabilistic representation
as a cycle-weighted interchange process. We determine the free energy and the
critical temperature (recovering results by T\'oth and by Penrose when
). The critical temperature is shown to coincide (as a function of
) with that of the state classical Potts model, and the phase
transition is discontinuous when .Comment: 22 page
Classical mechanics without determinism
Classical statistical particle mechanics in the configuration space can be
represented by a nonlinear Schrodinger equation. Even without assuming the
existence of deterministic particle trajectories, the resulting quantum-like
statistical interpretation is sufficient to predict all measurable results of
classical mechanics. In the classical case, the wave function that satisfies a
linear equation is positive, which is the main source of the fundamental
difference between classical and quantum mechanics.Comment: 11 pages, revised, to appear in Found. Phys. Let
Relating the Lorentzian and exponential: Fermi's approximation,the Fourier transform and causality
The Fourier transform is often used to connect the Lorentzian energy
distribution for resonance scattering to the exponential time dependence for
decaying states. However, to apply the Fourier transform, one has to bend the
rules of standard quantum mechanics; the Lorentzian energy distribution must be
extended to the full real axis instead of being bounded from
below (``Fermi's approximation''). Then the Fourier transform
of the extended Lorentzian becomes the exponential, but only for times , a time asymmetry which is in conflict with the unitary group time evolution
of standard quantum mechanics. Extending the Fourier transform from
distributions to generalized vectors, we are led to Gamow kets, which possess a
Lorentzian energy distribution with and have exponential
time evolution for only. This leads to probability predictions
that do not violate causality.Comment: 23 pages, no figures, accepted by Phys. Rev.
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