Volume 46, Issue 10, October 2005
 QUANTUM MECHANICS (GENERAL AND NONRELATIVISTIC)


Inequalities for experimental tests of the KochenSpecker theorem
View Description Hide DescriptionWe derive inequalities for partite states under the assumption that the hiddenvariable theoretical joint probability distribution for any pair of commuting observables is equal to the quantum mechanical one. Fine showed that this assumption is connected to the nohiddenvariables theorem of Kochen and Specker (KS theorem). These inequalities give a way to experimentally test the KS theorem. The fidelity to the Bell states which is larger than is sufficient for the experimental confirmation of the KS theorem. Hence, the Werner state is enough to test experimentally the KS theorem. Furthermore, it is possible to test the KS theorem experimentally using uncorrelated states. An partite uncorrelated state violates the partite inequality derived here by an amount that grows exponentially with .

Real trajectories in the semiclassical coherent state propagator
View Description Hide DescriptionThe semiclassical approximation to the coherent state propagator requires complex classical trajectories in order to satisfy the associated boundary conditions, but finding these trajectories in practice is a difficult task that may compromise the applicability of the approximation. In this work several approximations to the coherent state propagator are derived that make use only of real trajectories, which are easier to handle and have a more direct physical interpretation. It is verified in a particular example that these real trajectories approximations may have excellent accuracy.

Teleportation schemes in infinite dimensional Hilbert spaces
View Description Hide DescriptionThe success of quantum mechanics is due to the discovery that nature is described in infinite dimension Hilbert spaces, so that it is desirable to demonstrate the quantum teleportation process in a certain infinite dimensional Hilbert space. We describe the teleportation process in an infinite dimensional Hilbert space by giving simple examples.

Continuity bounds on the quantum relative entropy
View Description Hide DescriptionThe quantum relative entropy is frequently used as a distance, or distinguishability measure between two quantum states. In this article we study the relation between this measure and a number of other measures used for that purpose, including the trace norm distance. More specifically, we derive lower and upper bounds on the relative entropy in terms of various distance measures for the difference of the states based on unitarily invariant norms. The upper bounds can be considered as statements of continuity of the relative entropy distance in the sense of Fannes. We employ methods from optimisationtheory to obtain bounds that are as sharp as possible.

The frequency spectrum of the Casimir effect
View Description Hide DescriptionThe frequency spectrum of the Casimir effect between parallel plates is studied. Calculations are performed for both the massless scalar field and the electromagnetic field cases, first using a spectral weight function, and then via the Fourier transform of the renormalized expectation of the Casimir energymomentum operator. The Casimir force is calculated using the spectrum for two plates which are perfectly transparent in a frequency band. The result of this calculation suggests a way to detect the frequency spectrum of the Casimir effect.

Minimum orbit dimension for local unitary action on qubit pure states
View Description Hide DescriptionThe group of local unitary transformations partitions the space of qubit quantum states into orbits, each of which is a differentiable manifold of some dimension. We prove that all orbits of the qubit quantum state space have dimension greater than or equal to for even and greater than or equal to for odd. This lower bound on orbit dimension is sharp, since qubit states composed of products of singlets achieve these lowest orbit dimensions.

Ground state of the massless Nelson model in a nonFock representation
View Description Hide DescriptionWe consider a model of a particle coupled to a massless scalar field (the massless Nelson model) in a nonFock representation. We prove the existence of a ground state of the system, applying the method of Griesemer, Lieb, and Loss.

Application of pseudoHermitian quantum mechanics to a symmetric Hamiltonian with a continuum of scattering states
View Description Hide DescriptionWe extend the application of the techniques developed within the framework of the pseudoHermitian quantum mechanics to study a unitary quantum system described by an imaginary symmetric potential having a continuous real spectrum. For this potential that has recently been used, in the context of optical potentials, for modeling the propagation of electromagnetic waves traveling in a waveguide half and half filled with gain and absorbing media, we give a perturbative construction of the physical Hilbert space, observables, localized states, and the equivalent Hermitian Hamiltonian. Ignoring terms of order three or higher in the nonHermiticity parameter , we show that the equivalent Hermitian Hamiltonian has the form with vanishing outside an interval that is three times larger than the support of , i.e., in of the physical interaction region the potential vanishes identically. We provide a physical interpretation for this unusual behavior and comment on the classical limit of the system.

On the semigroup decomposition of the time evolution of quantum mechanical resonances
View Description Hide DescriptionA way of utilizing LaxPhillips type semigroups for the description of time evolution of resonances for scattering problems involving Hamiltonians with a semibounded spectrum was recently introduced by Strauss. In the proposed framework the evolution is decomposed into a background term and an exponentially decaying resonance term evolving according to a semigroup law given by a LaxPhillipstype semigroup; this is called the semigroup decomposition. However, the proposed framework assumes that the matrix in the energy representation is the boundary value on the positive real axis of a bounded analytic function in the upper halfplane. This condition puts strong restrictions on possible applications of this formalism. In this paper it is shown that there is a simple way of weakening the assumptions on the matrix analyticity while still obtaining the semigroup decomposition of the evolution of a resonance.
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 RELATIVISTIC QUANTUM MECHANICS, FIELD THEORY, BRANE THEORY (INCLUDING STRINGS)


Geometry of flat connections, coarse graining and the continuum limit
View Description Hide DescriptionA notion of effective gauge fields which does not involve a background metric is introduced. The role of scale is played by cellular decompositions of the base manifold. Once a cellular decomposition is chosen, the corresponding space of effective gauge fields is the space of flat connections with singularities on its codimension two skeleton, . If cellular decomposition is finer than cellular decomposition, there is a coarse graining map . We prove that the triple is a principal fiber bundle with a preferred global section given by the natural inclusion map . Since the spaces are partially ordered (by inclusion) and this order is directed in the direction of refinement, we can define a continuum limit, . We prove that, in an appropriate sense, . We also define a construction of measures in as the continuum limit (not a projective limit) of effective measures.

Function group approach to unconstrained Hamiltonian Yang–Mills theory
View Description Hide DescriptionStarting from the temporal gauge Hamiltonian for classical pure Yang–Mills theory with the gauge group SU(2) a canonical transformation is initiated by parametrizing the Gauss law generators with three new canonical variables. The construction of the remaining variables of the new set proceeds through a number of intermediate variables in several steps, which are suggested by the Poisson bracket relations and the gauge transformation properties of these variables. The unconstrained Hamiltonian is obtained from the original one by expressing it in the new variables and then setting the Gauss law generators to zero. This Hamiltonian turns out to be local and it decomposes into a finite Laurent series in powers of the coupling constant.

A note on BRST quantization of SU(2) YangMills mechanics
View Description Hide DescriptionThe quantization of SU(2) YangMillstheory reduced to spacetime dimensions is performed in the BRST framework. We show that in the unitary gauge the BRST procedure has difficulties which can be solved by introduction of additional singlet ghost variables. In the Lorenz gauge one has additional unphysical degrees of freedom, but the BRST quantization is free of the problems of the unitary gauge.

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Coset methods are used to construct the action describing the dynamics of the (massive) NambuGoldstone scalar degree of freedom associated with the spontaneous breaking of the isometry group of space to that of an subspace. The resulting action is an invariant AdS generalization of the NambuGoto action. The vector fieldtheory equivalent action is also determined.

Rigorous dynamics and radiation theory for a PauliFierz model in the ultraviolet limit
View Description Hide DescriptionThe present paper is devoted to the detailed study of quantization and evolution of the point limit of the PauliFierz model for a charged oscillatorinteracting with the electromagnetic field in dipole approximation. In particular, a well defined dynamics is constructed for the classical model, which is subsequently quantized according to the Segal scheme. To this end, the classical model in the point limit, already obtained by Noja and Posilicano [Ann. I.H.P. Phys. Theor.71, 425 (1999)], is reformulated as a second order abstract wave equation, and a consistent quantum evolution is given. This allows a study of the behavior of the survival and transition amplitudes for the process of decay of the excited states of the charged particle, and the emission of photons in the decay process. In particular, for the survival amplitude the exact time behavior is found. This is completely determined by the resonances of the systems plus a tail term prevailing in the asymptotic, long time regime. Moreover, the survival amplitude exhibits in a fairly clear way the Lamb shift correction to the unperturbed frequencies of the oscillator.

Solutions of the massive Yang–Mills equations by harmonic maps
View Description Hide DescriptionWe consider classical static solutions of the pure massive Yang–Mills field equations in dimensional space–time. By applying harmonic map ansatz, constructed from the harmonic maps , we construct some bounded spherically symmetric solutions having finite energies for , 3, and 4 cases.

Ground state energy of the polaron in the relativistic quantum electrodynamics
View Description Hide DescriptionWe consider the polaronmodel in the relativistic quantum electrodynamics. We prove that the ground state energy of the model is finite for all values of the finestructure constant and the ultraviolet cutoff . Moreover we give an upper bound and a lower bound of the ground state energy.
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 GENERAL RELATIVITY AND GRAVITATION


Induced matter: Curved manifolds encapsulated in Riemannflat dimensional space
View Description Hide DescriptionLiko and Wesson have recently introduced a new fivedimensional induced matter solution of the Einstein equations, a negative curvature RobertsonWalker space embedded in a Riemannflat fivedimensional manifold. We show that this solution is a special case of a more general theorem prescribing the structure of certain dimensional Riemannflat spaces which are all solutions of the Einstein equations. These solutions encapsulate dimensional curved manifolds. Such spaces are said to “induce matter” in the submanifolds by virtue of their geometric structure alone. We prove that the manifold can be any maximally symmetric space.

Tetrads in geometrodynamics
View Description Hide DescriptionA new tetrad is introduced within the framework of geometrodynamics for nonnull electromagnetic fields. This tetrad diagonalizes the electromagnetic stressenergy tensor and allows for maximum simplification of the expression of the electromagnetic field. The EinsteinMaxwell equations will also be simplified.

Analytic structure of radiation boundary kernels for blackhole perturbations
View Description Hide DescriptionExact outer boundary conditions for gravitational perturbations of the Schwarzschild metric feature integral convolution between a timedomain boundary kernel and each radiative mode of the perturbation. For both axial (Regge–Wheeler) and polar (Zerilli) perturbations, we study the Laplace transform of such kernels as an analytic function of (dimensionless) Laplace frequency. We present numerical evidence indicating that each such frequencydomain boundary kernel admits a “sumofpoles” representation. Our work has been inspired by Alpert, Greengard, and Hagstrom’s analysis of nonreflecting boundary conditions for the ordinary scalar wave equation.

Fields of accelerated sources: Born in de Sitter
View Description Hide DescriptionThis paper deals thoroughly with the scalar and electromagnetic fields of uniformly accelerated charges in de Sitter space–time. It gives details and makes various extensions of our Physical Review Letter from 2002. The basic properties of the classical Born solutions representing two uniformly accelerated charges in flat space–time are first summarized. The worldlines of uniformly accelerated particles in de Sitter universe are defined and described in a number of coordinate frames, some of them being of cosmological significance, the others are tied naturally to the particles. The scalar and electromagnetic fields due to the accelerated charges are constructed by using conformal relations between Minkowski and de Sitter space. The properties of the generalized “cosmological” Born solutions are analyzed and elucidated in various coordinate systems. In particular, a limiting procedure is demonstrated which brings the cosmological Born fields in de Sitter space back to the classical Born solutions in Minkowski space. In an extensive Appendix, which can be used independently of the main text, nine families of coordinate systems in de Sitter space–time are described analytically and illustrated graphically in a number of conformal diagrams.
