Index of content:
Volume 47, Issue 1, January 2006
 QUANTUM MECHANICS (GENERAL AND NONRELATIVISTIC)


NonHermitian interactions between harmonic oscillators, with applications to stable, Lorentzviolating quantum electrodynamics
View Description Hide DescriptionWe examine a new application of the HolsteinPrimakoff realization of the simple harmonic oscillator Hamiltonian. This involves the use of infinitedimensional representations of the Lie algebra su(2). The representations contain nonstandard raising and lowering operators, which are nonlinearly related to the standard and . The new operators also give rise to a natural family of twooscillator couplings. These nonlinear couplings are not generally selfadjoint, but their lowenergy limits are selfadjoint, exactly solvable, and stable. We discuss the structure of a theory involving these couplings. Such a theory might have as its ultralowenergy limit a Lorentzviolating Abelian gauge theory, and we discuss the extremely strong astrophysical constraints on such a model.

A bound on the mutual information, and properties of entropy reduction, for quantum channels with inefficient measurements
View Description Hide DescriptionThe Holevo bound is a bound on the mutual information for a given quantum encoding. In 1996 Schumacher, Westmoreland, and Wootters [Phys. Rev. Lett.76, 3452 (1996)] derived a bound that reduces to the Holevo bound for complete measurements, but that is tighter for incomplete measurements. The most general quantum operations may be both incomplete and inefficient. Here we show that the bound derived by SWW can be further extended to obtain one that is yet again tighter for inefficient measurements. This allows us, in addition, to obtain a generalization of a bound derived by Hall, and to show that the average reduction in the von Neumann entropy during a quantum operation is concave in the initial state, for all quantum operations. This is a quantum version of the concavity of the mutual information. We also show that both this average entropy reduction and the mutual information for pure state ensembles, are Schur concave for unitarily covariant measurements; that is, for these measurements,information gain increases with initial uncertainty.

Entanglement monotones for multiqubit states based on geometric invariant theory
View Description Hide DescriptionWe construct entanglement monotones for multiqubit states based on Plücker coordinate equations of Grassmann variety, which are a central notion in geometric invariant theory. As an illustrative example, we in detail investigate entanglement monotones of a threequbit state.

Inequivalent quantizations of the Calogero model with scale and mirror symmetry
View Description Hide DescriptionWe study the inequivalent quantizations of the Calogero model by separation of variables, in which the model decomposes into the angular and the radial parts. Our inequivalent quantizations respect the “mirror” invariance (which realizes the symmetry under the cyclic permutations of the particles) and the scale invariance in the limit of vanishing harmonic potential. We find a twoparameter family of novel quantizations in the angular part and classify the eigenstates in terms of the irreducible representations of the group. The scale invariance restricts the quantization in the radial part uniquely, except for the eigenstates coupled to the lowest two angular levels for which two types of boundary conditions are allowed independently from all upper levels. It is also found that the eigenvalues corresponding to the singlet representations of the are universal (parameterindependent) in the family, whereas those corresponding to the doublets of the are dependent on one of the parameters. These properties are shown to be a consequence of the spectral preserving (or its subgroup ) transformations allowed in the family of inequivalent quantizations.

 RELATIVISTIC QUANTUM MECHANICS, FIELD THEORY, BRANE THEORY (INCLUDING STRINGS)


Scalar field theory at finite temperature in
View Description Hide DescriptionWe discuss the theory defined in dimensional spacetime and assume that the system is in equilibrium with a thermal bath at temperature. We use the expansion and the method of the composite operator (Cornwall, Jackiw, and Tomboulis) for summing a large set of Feynman graphs. We demonstrate explicitly the ColemanMerminWagner theorem at finite temperature.

The Euclidean scalar Green function in the fivedimensional KaluzaKlein magnetic monopole spacetime
View Description Hide DescriptionIn this paper we present, in a integral form, the Euclidean Green function associated with a massless scalar field in the fivedimensional KaluzaKlein magnetic monopole superposed to a global monopole, admitting a nontrivial coupling between the field with the geometry. This Green function is expressed as the sum of two contributions: the first one related with uncharged component of the field, is similar to the Green function associated with a scalar field in a fourdimensional global monopole spacetime. The second contains the information of all the other components. Using this Green function it is possible to study the vacuum polarization effects on this spacetime. Explicitly we calculate the renormalized vacuum expectation value , which by its turn is also expressed as the sum of two contributions.

Partition functions of supersymmetric gauge theories in noncommutative and their unified perspective
View Description Hide DescriptionWe investigate cohomological gauge theories in noncommutative . We show that vacuum expectation values of the theories do not depend on noncommutative parameters, and the large noncommutative parameter limit is equivalent to the dimensional reduction. As a result of these facts, we show that a partition function of a cohomological theory defined in noncommutative and a partition function of a cohomological field theory in are equivalent if they are connected through dimensional reduction. Therefore, we find several partition functions of supersymmetric gauge theories in various dimensions are equivalent. Using this technique, we determine the partition function of the U(1) gauge theory in noncommutative , where its action does not include a topological term. The result is common among (8dim, ), (6dim, ), (2dim, ) and the IKKT matrix model given by their dimensional reduction to 0dim.

Gauged Wess–Zumino model in noncommutative Minkowski superspace
View Description Hide DescriptionWe develop a gauged Wess–Zumino model in noncommutative Minkowski superspace. This is the natural extension of the work of Carlson and Nazaryan, which extended supersymmetry written over deformed Euclidean superspace to Minkowski superspace. We investigate the coupling of the vector and chiral superfields. Noncommutativity is implemented by replacing products with star products. Although, in general, our star product is nonassociative, we prove that it is associative to the first order in the deformation parameter . We show that our model reproduces the theory in the appropriate limit, namely when the deformation parameters . Essentially, we find the theory and a conjugate copy. As in the theory, a reparametrization of the gauge parameter, vector superfield, and chiral superfield are necessary to write standard independent gauge theory. However, our choice of parametrization differs from that used in the supersymmetry, which leads to some unexpected new terms.

Magnetic monopole in the loop representation
View Description Hide DescriptionWe quantize, within the Loop Representation formalism, the electromagnetic field in the presence of a static magnetic pole. It is found that the loopdependent physical wave functionals of the quantum Maxwell theory become multivalued, through a topological phase factor depending on the solid angle subtended at the monopole by a surface bounded by the loop. It is discussed how this fact generalizes what occurs in ordinary quantum mechanics in multiply connected spaces.

Quiver gauge theory of nonAbelian vortices and noncommutative instantons in higher dimensions
View Description Hide DescriptionWe construct explicit Bogomolnyi, Prasad, Sommerfeld (BPS) and nonBPS solutions of the YangMillsequations on the noncommutative space which have manifest spherical symmetry. Using SU(2)equivariant dimensional reduction techniques, we show that the solutions imply an equivalence between instantons on and nonAbelian vortices on , which can be interpreted as a blowingup of a chain of branes on into a chain of spherical branes on . The lowenergy dynamics of these configurations is described by a quiver gauge theory which can be formulated in terms of new geometrical objects generalizing superconnections. This formalism enables the explicit assignment of brane charges in equivariant theory to the instanton solutions.

 GENERAL RELATIVITY AND GRAVITATION


Fractional boundaries for fluid spheres
View Description Hide DescriptionA single Israel layer can be created when two metrics adjoin with no continuous metric derivative across the boundary. The properties of the layer depend only on the two metrics it separates. By using a fractional derivative match, a family of Israel layers can be created between the same two metrics. The family is indexed by the order of the fractional derivative. The method is applied to Tolman IV and V interiors and a Schwarzschild vacuum exterior. The method creates new ranges of modeling parameters for fluid spheres. A thin shell analysis clarifies pressure/tension in the family of boundary layers.

Colliding wave solutions from fivedimensional black holes and black branes
View Description Hide DescriptionWe consider both the fivedimensional MyersPerry and ReissnerNordstrom black holes (BHs) and black branes in dimensions. By employing the isometry with the colliding plane waves (CPWs) we generate CauchyHorizon (CH) forming CPW solutions. From the fivedimensional vacuum solution through the KaluzaKlein reduction the corresponding EinsteinMaxwelldilaton solution is obtained. This CH forming cross polarized solution with the dilaton turns out to be a rather complicated nontype metric. Since we restrict ourselves to the fivedimensional BHs we obtain exact solutions for colliding 2 and 3form fields in dimensions for . By dualizing these forms we can obtain also colliding  and forms which are important processes in the low energy limit of the string theory. All solutions obtained are CH forming, implying that an analytic extension beyond is possible.

 DYNAMICAL SYSTEMS


Explicit solutions of the classical Calogero and Sutherland systems for any root system
View Description Hide DescriptionExplicit solutions of the classical Calogero (rational with/without harmonic confining potential) and Sutherland (trigonometric potential) systems is obtained by diagonalization of certain matrices of simple time evolution. The method works for Calogero & Sutherland systems based on any root system. It generalizes the wellknown results by Olshanetsky and Perelomov for the type root systems. Explicit solutions of the (rational and trigonometric) higher Hamiltonian flows of the integrable hierarchy can be readily obtained in a similar way for those based on the classical root systems.

Fractional Lindstedt series
View Description Hide DescriptionThe parametric equations of the surfaces on which highly resonant quasiperiodic motions develop (lowerdimensional tori) cannot be analytically continued, in general, in the perturbation parameter , i.e., they are not analytic functions of . However rather generally quasiperiodic motions whose frequencies satisfy only one rational relation (“resonances of order 1”) admit formal perturbation expansions in terms of a fractional power of depending on the degeneration of the resonance. We find conditions for this to happen, and in such a case we prove that the formal expansion is convergent after suitable resummation.

 CLASSICAL MECHANICS AND CLASSICAL FIELDS


Covariant irreducible parametrization of electromagnetic fields in arbitrary spacetime
View Description Hide DescriptionWe present a new unified covariant description of electromagnetic field properties for an arbitrary spacetime. We derive a complete set of irreducible components describing a sixdimensional electromagnetic field from the Maxwell and metric tensors using the symmetry group SL(2,C). For the special case of a flat spacetime metric the components are shown to correspond to the scalar invariants of the electromagnetic field, the energymomentumstress tensor and in addition, three new tensors expressing physical observables of rank two and four, respectively. We make a physical interpretation of one of the new rank two tensor as describing a classical intrinsic spin of the electromagnetic field.

Some mathematical properties of Maxwell’s equations for macroscopic dielectrics
View Description Hide DescriptionWe consider a number of mathematical properties of Maxwell’sequations for linear dispersive and absorptive dielectric media using the auxiliary field method developed earlier by the author [A. Tip, Phys. Rev. A57, 4818 (1998)]. Here the fields are interpreted as square integrable functions of . In case the susceptibility is piecewise constant in , we show rigorously that a decomposition into independent equations for longitudinal and transverse fields can be made. We point out its relevance for the study of spectral properties of photonic crystals. Again, for the piecewise constant case we discuss the usual boundary conditions at interfaces and discuss the different nature of those for the longitudinal and transverse fields. Then we consider energy conservation for dispersive, nonabsorptive, media. We show that additional contributions to the free field energy density, as given in the literature, are associated with the energy stored in the auxiliary field modes. Finally, we show that also for nonlinear dielectrics it is possible to obtain a conserved energy by introducing auxiliary fields.

 STATISTICAL PHYSICS


Auger effect in the generalized kinetic theory of electrons and holes
View Description Hide DescriptionIn this paper we propose a model for a proper kinetic description of the Auger effect as a generation/recombination mechanism for electrons and holes in a bipolar device. Boltzmanntype equations for the twospecies population in a phonon background are presented, and equilibria and their stability are investigated. Particles and quasiparticles are allowed to obey generalized statistics, in order to possibly include nonstandard or nonextensive effects. The macroscopic recombination/generation rate is recovered as hydrodynamic limit.

Determinant representation of correlation functions for the free Fermion model
View Description Hide DescriptionWith the help of the factorizing matrix, the scalar products of the free fermion model are represented by determinants. By means of these results, we obtain the determinant representations of correlation functions of the model.

 METHODS OF MATHEMATICAL PHYSICS


The equivalence problem for fourth order differential equations under fiber preserving diffeomorphisms
View Description Hide DescriptionIn the present work we use the method of equivalence to determine necessary and sufficient conditions for a general fourth order ordinary differential equation to be equivalent to the flat model under a fiber preserving transformation. As a result, explicit and simple conditions are obtained.

Possible quantum kinematics
View Description Hide DescriptionThe quantum group and space theory is reformulated from the standard skewsymmetric basis to an arbitrary one. The dimensional quantum Cayley–Klein spaces are described in Cartesian basis and the quantum analogs of dimensional constant curvature spaces are introduced. Part of the fourdimensional constant curvature spaces are interpreted as the noncommutative analogs of spacetime models. As a result the quantum (anti) de Sitter, Minkowski, Newton, Galilei, Carroll kinematics with the fundamental length and the fundamental time are suggested.
