10,053 research outputs found
Symmetry Representations in the Rigged Hilbert Space Formulation of Quantum Mechanics
We discuss some basic properties of Lie group representations in rigged
Hilbert spaces. In particular, we show that a differentiable representation in
a rigged Hilbert space may be obtained as the projective limit of a family of
continuous representations in a nested scale of Hilbert spaces. We also
construct a couple of examples illustrative of the key features of group
representations in rigged Hilbert spaces. Finally, we establish a simple
criterion for the integrability of an operator Lie algebra in a rigged Hilbert
space
Solutions of Quantum Gravity Coupled to the Scalar Field
We consider the Wheeler-De Witt equation for canonical quantum gravity
coupled to massless scalar field. After regularizing and renormalizing this
equation, we find a one-parameter class of its solutions.Comment: 8 pages, LaTe
Black Hole Solution of Quantum Gravity
We present a spherically symmetric and static exact solution of Quantum
Einstein Equations. This solution is asymptotically (for large ) identical
with the black hole solution on the anti--De Sitter background and, for some
range of values of the mass possesses two horizons. We investigate
thermodynamical properties of this solution.Comment: Plain Latex, 10 page
Irreversible Quantum Mechanics in the Neutral K-System
The neutral Kaon system is used to test the quantum theory of resonance
scattering and decay phenomena. The two dimensional Lee-Oehme-Yang theory with
complex Hamiltonian is obtained by truncating the complex basis vector
expansion of the exact theory in Rigged Hilbert space. This can be done for K_1
and K_2 as well as for K_S and K_L, depending upon whether one chooses the
(self-adjoint, semi-bounded) Hamiltonian as commuting or non-commuting with CP.
As an unexpected curiosity one can show that the exact theory (without
truncation) predicts long-time 2 pion decays of the neutral Kaon system even if
the Hamiltonian conserves CP.Comment: 36 pages, 1 PostScript figure include
Topological Black Holes in Quantum Gravity
We derive the black hole solutions with horizons of non-trivial topology and
investigate their properties in the framework of an approach to quantum gravity
being an extension of Bohm's formulation of quantum mechanics. The solutions we
found tend asymptotically (for large ) to topological black holes. We also
analyze the thermodynamics of these space-times.Comment: 4pages, no figures, plain LaTe
Relativistic Partial Wave Analysis Using the Velocity Basis of the Poincare Group
The velocity basis of the Poincare group is used in the direct product space
of two irreducible unitary representations of the Poincare group. The velocity
basis with total angular momentum j will be used for the definition of
relativistic Gamow vectors.Comment: 14 pages; revte
The density matrix in the de Broglie-Bohm approach
If the density matrix is treated as an objective description of individual
systems, it may become possible to attribute the same objective significance to
statistical mechanical properties, such as entropy or temperature, as to
properties such as mass or energy. It is shown that the de Broglie-Bohm
interpretation of quantum theory can be consistently applied to density
matrices as a description of individual systems. The resultant trajectories are
examined for the case of the delayed choice interferometer, for which Bell
appears to suggest that such an interpretation is not possible. Bell's argument
is shown to be based upon a different understanding of the density matrix to
that proposed here.Comment: 15 pages, 4 figure
Hypersurface Bohm-Dirac models
We define a class of Lorentz invariant Bohmian quantum models for N entangled
but noninteracting Dirac particles. Lorentz invariance is achieved for these
models through the incorporation of an additional dynamical space-time
structure provided by a foliation of space-time. These models can be regarded
as the extension of Bohm's model for N Dirac particles, corresponding to the
foliation into the equal-time hyperplanes for a distinguished Lorentz frame, to
more general foliations. As with Bohm's model, there exists for these models an
equivariant measure on the leaves of the foliation. This makes possible a
simple statistical analysis of position correlations analogous to the
equilibrium analysis for (the nonrelativistic) Bohmian mechanics.Comment: 17 pages, 3 figures, RevTex. Completely revised versio
Semiclassical approximation with zero velocity trajectories
We present a new semiclassical method that yields an approximation to the
quantum mechanical wavefunction at a fixed, predetermined position. In the
approach, a hierarchy of ODEs are solved along a trajectory with zero velocity.
The new approximation is local, both literally and from a quantum mechanical
point of view, in the sense that neighboring trajectories do not communicate
with each other. The approach is readily extended to imaginary time propagation
and is particularly useful for the calculation of quantities where only local
information is required. We present two applications: the calculation of
tunneling probabilities and the calculation of low energy eigenvalues. In both
applications we obtain excellent agrement with the exact quantum mechanics,
with a single trajectory propagation.Comment: 16 pages, 7 figure
Resonances, Unstable Systems and Irreversibility: Matter Meets Mind
The fundamental time-reversal invariance of dynamical systems can be broken
in various ways. One way is based on the presence of resonances and their
interactions giving rise to unstable dynamical systems, leading to well-defined
time arrows. Associated with these time arrows are semigroups bearing time
orientations. Usually, when time symmetry is broken, two time-oriented
semigroups result, one directed toward the future and one directed toward the
past. If time-reversed states and evolutions are excluded due to resonances,
then the status of these states and their associated backwards-in-time oriented
semigroups is open to question. One possible role for these latter states and
semigroups is as an abstract representation of mental systems as opposed to
material systems. The beginnings of this interpretation will be sketched.Comment: 9 pages. Presented at the CFIF Workshop on TimeAsymmetric Quantum
Theory: The Theory of Resonances, 23-26 July 2003, Instituto Superior
Tecnico, Lisbon, Portugal; and at the Quantum Structures Association Meeting,
7-22 July 2004, University of Denver. Accepted for publication in the
Internation Journal of Theoretical Physic
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