Journal of Mathematical Physics: All Topics

On the Kert[e-acute]sz line: Some rigorous bounds

Jean Ruiz and Marc Wouts
We study the Kertesz line of the q-state Potts model at (inverse) temperature beta in the presence of an external magnetic field h. This line separates the two regions of the phase diagram according to the existence or not of an infinite cluster in the FortuinKasteleyn representation of the model. I ... [J. Math. Phys. 49, 053303 (2008)] published Thu May 15, 2008.

New infinite-dimensional quadruple symmetry groups for the general symplectic gravity model

Ya-Jun Gao
The symmetry structures of the general symplectic gravity model are further studied. By using the so-called extended double (ED)-complex function method, the usual RiemannHilbert (RH) problem is extended to an ED-complex formulation. For any fixed non-negative integer n, two pairs of ED RH transform ... [J. Math. Phys. 49, 053519 (2008)] published Wed May 14, 2008.

Characterization of the sequential product on quantum effects

Stan Gudder and Frederic Latremoliere
We present a characterization of the standard sequential product of quantum effects. The characterization is in terms of algebraic, continuity and duality conditions that can be physically motivated. ... [J. Math. Phys. 49, 052106 (2008)] published Wed May 14, 2008.

A topos foundation for theories of physics: III. The representation of physical quantities with arrows delta-breve[sup o](A):Sigma[underaccent underbar [below] --> [openface R][underaccent underbar [below] [sup [succeeds, curly eq]]

A. Doring and C. J. Isham
This paper is the third in a series whose goal is to develop a fundamentally new way of viewing theories of physics. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. In Pape ... [J. Math. Phys. 49, 053517 (2008)] published Tue May 13, 2008.

A topos foundation for theories of physics: II. Daseinisation and the liberation of quantum theory

A. Doring and C. J. Isham
This paper is the second in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time. Our basic contention is that constructing a t ... [J. Math. Phys. 49, 053516 (2008)] published Tue May 13, 2008.

A topos foundation for theories of physics: IV. Categories of systems

A. Doring and C. J. Isham
This paper is the fourth in a series whose goal is to develop a fundamentally new way of building theories of physics. The motivation comes from a desire to address certain deep issues that arise in the quantum theory of gravity. Our basic contention is that constructing a theory of physics is equiv ... [J. Math. Phys. 49, 053518 (2008)] published Tue May 13, 2008.

A topos foundation for theories of physics: I. Formal languages for physics

A. Doring and C. J. Isham
This paper is the first in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time. Our basic contention is that constructing a th ... [J. Math. Phys. 49, 053515 (2008)] published Tue May 13, 2008.

On Burnett coefficients in periodic media in low contrast regime

C. Conca, J. San Martin, L. Smaranda, and M. Vanninathan
In this work, we consider low contrast periodic media and we study the dependence of the effective or homogenized tensor and the dispersion tensor in terms of the microstructure. We treat both one-dimensional structures and some laminated structures in higher dimension. Interesting properties of the ... [J. Math. Phys. 49, 053514 (2008)] published Mon May 12, 2008.

Correlation function of the Schur process with a fixed final partition

T. Imamura and T. Sasamoto
We consider a generalization of the Schur process in which a partition evolves from the empty partition into an arbitrary fixed final partition. We obtain a double integral representation of the correlation kernel. For a special final partition with only one row, the edge scaling limit is also discu ... [J. Math. Phys. 49, 053302 (2008)] published Mon May 12, 2008.

Representations of the Schr[o-umlaut]dinger--Virasoro algebras

Junbo Li and Yucai Su
In this paper, it is proved that an irreducible weight module with finite-dimensional weight spaces over the SchrodingerVirasoro algebras is a highest/lowest weight module or a uniformly bounded module. Furthermore, indecomposable modules of the intermediate series over these algebras are completely ... [J. Math. Phys. 49, 053512 (2008)] published Fri May 9, 2008.

On global properties of certain homogeneous exact solutions of Einstein field equations

M. Ulanovskii
The aim of this paper is an application of some general results on homogeneous Lorentz manifolds to exact solutions of Einstein field equations. We study the relation < of a chronological sequence of events. We examine a number of known solutions and show that in all but one, the relation < is maxim ... [J. Math. Phys. 49, 052502 (2008)] published Fri May 9, 2008.

The Laplacian on homogeneous spaces

Liangzhong Hu
The solution of the eigenvalue problem of the Laplacian on a general homogeneous space G/H is given. Here, G is a compact, semisimple Lie group, H is a closed subgroup of G, and the rank of H is equal to the rank of G. It is shown that the multiplicity of the lowest eigenvalue of the Laplacian on G/ ... [J. Math. Phys. 49, 053513 (2008)] published Fri May 9, 2008.

Relating on-shell and off-shell formalisms in perturbative quantum field theory

Christian Brouder and Michael Dutsch
In the on-shell formalism (mostly used in perturbative quantum field theory), the entries of the time-ordered product T are on-shell fields (i.e., the basic fields satisfy the free field equations). With that, (multi)linearity of T is incompatible with the action Ward identity. This can be circumven ... [J. Math. Phys. 49, 052303 (2008)] published Fri May 9, 2008.

Existence and asymptotic stability for the semilinear wave equation with boundary damping and source term

Jong Yeoul Park and Tae Gab Ha
In this paper, we consider the semilinear wave equation with boundary conditions. This work is devoted to prove the existence of solutions and uniform decay rates of the wave equation with boundary damping and source term. ... [J. Math. Phys. 49, 053511 (2008)] published Thu May 8, 2008.

On a class of damped vibration problems with obstacles and without direct variational structures

Xian Wu
The main purpose of this paper is to study the following damped vibration problems: x-double_dot =q(x)|x-dot |+f(t), with x(0)x(2pi)=x-dot(0)x-dot(2pi)=0, x(t)>=0, [for all]t[is-an-element-of]R and x-dot(t)=x-dot(t), if x(t)=0, where x-dot(t)=lim0 x-dot(t) and x-dot(t)=lim+0 x-dot(t). The variatio ... [J. Math. Phys. 49, 053510 (2008)] published Thu May 8, 2008.

Abelian gauge theories on compact manifolds and the Gribov ambiguity

Gerald Kelnhofer
We study the quantization of Abelian gauge theories of principal torus bundles over compact manifolds with and without boundary. It is shown that these gauge theories suffer from a Gribov ambiguity originating in the nontriviality of the bundle of connections whose geometrical structure will be anal ... [J. Math. Phys. 49, 052302 (2008)] published Thu May 8, 2008.

A new eight vertex model and higher dimensional, multiparameter generalizations

B. Abdesselam and A. Chakrabarti
We study statistical models, specifically transfer matrices corresponding to a multiparameter hierarchy of braid matrices of (2n) x (2n) dimensions with 2n free parameters (n=1,2,3,…). The simplest, 4 x 4 case, is treated in detail. Powerful recursion relations are constructed by explicitly g ... [J. Math. Phys. 49, 053301 (2008)] published Wed May 7, 2008.

The Lorentz extension as consequence of the family symmetry

Hai-Jun Wang
In this paper, we postulate an algebraic model to explain how the symmetry of three lepton species plays its role in the Lorentz extension. Inspired by the two-to-one mapping between the SL(2,C) group and the Lorentz group, we design a mapping between the SL(3,C) group, which displays the family sym ... [J. Math. Phys. 49, 053508 (2008)] published Wed May 7, 2008.

Heisenberg algebra, umbral calculus and orthogonal polynomials

G. Dattoli, D. Levi, and P. Winternitz
Umbral calculus can be viewed as an abstract theory of the Heisenberg commutation relation [P-hat,M-hat]=1. In ordinary quantum mechanics, P-hat is the derivative and M-hat the coordinate operator. Here, we shall realize P-hat as a second order differential operator and M-hat as a first order integr ... [J. Math. Phys. 49, 053509 (2008)] published Wed May 7, 2008.

Solution of the Dirac equation in the rotating Bertotti--Robinson spacetime

A. Al-Badawi and I. Sakalli
The Dirac equation is solved in the rotating BertottiRobinson spacetime. The set of equations representing the Dirac equation in the NewmanPenrose formalism is decoupled into an axial and an angular part. The axial equation, which is independent of mass, is exactly solved in terms of hypergeometric ... [J. Math. Phys. 49, 052501 (2008)] published Wed May 7, 2008.

Central configurations with a quasihomogeneous potential function

Robert T. Jones
For the classical N-body problem, if the masses are paced at rest in the configuration that is central, then the masses will tend to the origin and result in a simultaneous collision [A. Winter, The Analytical Foundations of Celestial Mechanics, 1st ed. (Princeton University Press, Princeton, 1941)] ... [J. Math. Phys. 49, 052901 (2008)] published Wed May 7, 2008.

Hyperbolic Hubbard--Stratonovich transformation made rigorous

Y. V. Fyodorov, Y. Wei, and M. R. Zirnbauer
We revisit a long standing issue in the theory of disordered electron systems and their effective description by a nonlinear sigma model: the hyperbolic HubbardStratonovich (HS) transformation in the bosonic sector. For time-reversal invariant systems without spin, this sector is known to have a non ... [J. Math. Phys. 49, 053507 (2008)] published Wed May 7, 2008.

Applications of continuity and discontinuity of a fractional derivative of the wave functions to fractional quantum mechanics

Jianping Dong and Mingyu Xu
The space fractional Schrodinger equation with a finite square potential, periodic potential, and delta-function potential is studied in this paper. We find that the continuity or discontinuity condition of a fractional derivative of the wave functions should be considered to solve the fractional Sc ... [J. Math. Phys. 49, 052105 (2008)] published Tue May 6, 2008.

Dynamic phase transitions for ferromagnetic systems

Tian Ma and Shouhong Wang
This article presents a phenomenological dynamic phase transition theory for ferromagnetism, leading to a precise description of the dynamic transitions and to a physical prediction on the spontaneous magnetization. The analysis also suggests asymmetry of fluctuations in both the ferromagnetism and ... [J. Math. Phys. 49, 053506 (2008)] published Tue May 6, 2008.

Optimal covariant measurement of momentum on a half line in quantum mechanics

Yutaka Shikano and Akio Hosoya
We cannot perform the projective measurement of a momentum on a half line since it is not an observable. Nevertheless, we would like to obtain some physical information of the momentum on a half line. We define an optimality for measurement as minimizing the variance between an inferred outcome of t ... [J. Math. Phys. 49, 052104 (2008)] published Tue May 6, 2008.

Atomistic and orthoatomistic effect algebras

Josef Tkadlec
We characterize atomistic effect algebras, prove that a weakly orthocomplete Archimedean atomic effect algebra is orthoatomistic and present an example of an orthoatomistic orthomodular poset that is not weakly orthocomplete. ... [J. Math. Phys. 49, 053505 (2008)] published Tue May 6, 2008.

Decoherence rates for Galilean covariant dynamics

Jeremy Clark
We introduce a measure of decoherence for a class of density operators. For Gaussian density operators in dimension one, it coincides with an index used by Morikawa [Quantum decoherence and classical correlation in quantum mechanics, Phys. Rev. D 42, 29292931 (1990)]. Spatial decoherence rates are d ... [J. Math. Phys. 49, 052103 (2008)] published Tue May 6, 2008.

On models of certain p,q-algebra representations: The p,q-oscillator algebra

Vivek Sahai and Sarasvati Yadav
We construct one and two variable models of the p,q-oscillator algebra in terms of ladder operators. By using two p,q-analogs of the exponential function mapping, we show that matrix elements of these operators can be represented in terms of p,q-special functions. Further, we exhibit that these matr ... [J. Math. Phys. 49, 053504 (2008)] published Mon May 5, 2008.

Orthogonal polynomials from Hermitian matrices

Satoru Odake and Ryu Sasaki
A unified theory of orthogonal polynomials of a discrete variable is presented through the eigenvalue problem of Hermitian matrices of finite or infinite dimensions. It can be considered as a matrix version of exactly solvable Schrodinger equations. The Hermitian matrices (factorizable Hamiltonians) ... [J. Math. Phys. 49, 053503 (2008)] published Fri May 2, 2008.

Erratum: ``Classification of marginally trapped Lagrangian surfaces in Lorentzian complex space form'' [J. Math. Phys. [bold 48], 013509 (2007)]

Bang-Yen Chen and Franki Dillen
... [J. Math. Phys. 49, 059901 (2008)] published Fri May 2, 2008.

The role of von Neumann and L[u-umlaut]ders postulates in the Einstein, Podolsky, and Rosen considerations: Comparing measurements with degenerate and nondegenerate spectra

Andrei Khrennikov
We show that the projection postulate plays a crucial role in the discussion on the so-called quantum nonlocality, in particular, in the Einstein, Podolsky, and Rosen argument. We stress that the original von Neumann projection postulate was crucially modified by extending it to observables with deg ... [J. Math. Phys. 49, 052102 (2008)] published Fri May 2, 2008.

Comment on ``Dirac equation in the background of the Nutku helicoid metric'' [J. Math. Phys. 48, 092301 (2007)]

T. Birkandan and M. Hortacsu
The Dirac equation written on the boundary of the Nutku helicoid space consists of a system of ordinary differential equations. We tried to analyze this system and we found that it has a higher singularity than those of the Heun equations which give the solutions of the Dirac equation in the bulk. W ... [J. Math. Phys. 49, 054101 (2008)] published Fri May 2, 2008.

Comments on ``Gazeau--Klauder coherent states for trigonometric Rosen--Morse potential'' [J. Math. Phys. [bold 49], 022104 (2008)]

H. Fakhri and A. Dehghani
In a recently published paper in this journal [A. Cheaghlou and O. Faizy, J. Math. Phys. 49, 022104 (2008)], the authors introduce the GazeauKlauder coherent states for the trigonometric RosenMorse potential as an infinite superposition of the wavefunctions. It is shown that their proposed measure ... [J. Math. Phys. 49, 052101 (2008)] published Fri May 2, 2008.

Representation theory of C-algebras for a higher-order class of spheres and tori

Joakim Arnlind
We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated with a matrix, the representation theory can be understood in terms of loop and string representations, which are closely related to the dynamics ... [J. Math. Phys. 49, 053502 (2008)] published Thu May 1, 2008.

Lotka--Volterra systems integrable in quadratures

Oleg Bogoyavlenskij, Yoshiaki Itoh, and Tetsuyuki Yukawa
Hamiltonian n-dimensional LotkaVolterra systems are introduced that have n1 conserved quantities. The explicit integrability in quadratures is demonstrated. ... [J. Math. Phys. 49, 053501 (2008)] published Thu May 1, 2008.

Reflection positivity and monotonicity

Arthur Jaffe and Gordon Ritter
We prove general reflection positivity results on Riemannian manifolds for both scalar fields and Dirac fields, and comment on applications to quantum field theory. As another application, we prove the inequality C<=C between Dirichlet and Neumann covariance operators on a manifold with a reflection ... [J. Math. Phys. 49, 052301 (2008)] published Thu May 1, 2008.

Genericity of black hole formation in the gravitational collapse of homogeneous self-interacting scalar fields

Roberto Giambo, Fabio Giannoni, and Giulio Magli
The gravitational collapse of a wide class of self-interacting homogeneous scalar fields models is analyzed. The class is characterized by certain general conditions on the scalar field potential, which, in particular, include both asymptotically polynomial and exponential behaviors. Within this cla ... [J. Math. Phys. 49, 042504 (2008)] published Wed Apr 30, 2008.

Nonassociativity, supersymmetry, and hidden variables

Vladimir Dzhunushaliev
It is shown that the supersymmetric quantum mechanics has an octonionic generalization. The generalization is based on the inclusion of quaternions into octonions. The elements from the coset octonions/quaternions are unobservables because they cannot be considered as quantum operators as a conseque ... [J. Math. Phys. 49, 042108 (2008)] published Tue Apr 29, 2008.

On the rest state stability of an objective fractional derivative viscoelastic fluid model

Arnaud Heibig and Liviu Iulian Palade
The one-dimensional fractional derivative Maxwell model has been found very useful in modeling the linear viscoelastic response in the glass transition and alpha-relaxation regions. That motivated further work on generalizations to nonlinear viscoelastic fractional constitutive equations. In the wor ... [J. Math. Phys. 49, 043101 (2008)] published Mon Apr 28, 2008.

Quantum-inspired maximizer

Michail Zak
The objective of this paper is to create a new kind of dynamical systemsa quantum-classical hybridthat would preserve superposition and entanglement of random solutions while allowing one to measure their state variables by using classical methods. Such an optimal combination of characteristics is a ... [J. Math. Phys. 49, 042702 (2008)] published Mon Apr 28, 2008.

Gravitational and harmonic oscillator potentials on surfaces of revolution

Manuele Santoprete
In this paper, we consider the motion of a particle on a surface of revolution under the influence of a central force field. We prove that there are at most two analytic central potentials for which all the bounded, nonsingular orbits are closed and that there are exactly two on some surfaces with c ... [J. Math. Phys. 49, 042903 (2008)] published Fri Apr 25, 2008.

Incompressible and compressible limits of two-component Gross--Pitaevskii equations with rotating fields and trap potentials

Chiun-Chang Lee and Tai-Chia Lin
The relaxation of turbulence is crucial for the formation of vortex lattices and vortex sheets separated by an interface in rapidly rotating two-component BoseEinstein condensates (BECs) depicted by two-component systems of GrossPitaevskii equations (GPEs). To see the relaxation, we study the incomp ... [J. Math. Phys. 49, 043517 (2008)] published Wed Apr 23, 2008.

The symmetries of five-dimensional minimal supergravity reduced to three dimensions

Gerard Clement
The 14 Killing vectors of the target space for five-dimensional minimal supergravity reduced to three dimensions are explicitly constructed in terms of the original field variables. These vectors generate the Lie algebra of G. We also construct a symmetrical 7 x 7 matrix representative of the coset ... [J. Math. Phys. 49, 042503 (2008)] published Wed Apr 23, 2008.

Eightfold way from dynamical first principles in strongly coupled lattice quantum chromodynamics

Paulo A. Faria da Veiga and Michael O'Carroll
We obtain from first principles, i.e., from the quark-gluon dynamics, the Gell'Mann-Ne'eman baryonic eightfold way energy momentum spectrum exactly in an imaginary-time functional integral formulation of strongly coupled lattice quantum chromodynamics in 3+1 dimensions, with local SU(3) gauge and gl ... [J. Math. Phys. 49, 042303 (2008)] published Wed Apr 23, 2008.

On the mode stability of a self-similar wave map

Roland Donninger and Peter C. Aichelburg
We study linear perturbations of a self-similar wave map from Minkowski space to the three-sphere which is conjectured to be linearly stable. By considering analytic mode solutions of the evolution equation for the perturbations, we prove that there are no real unstable eigenvalues apart from the we ... [J. Math. Phys. 49, 043515 (2008)] published Tue Apr 22, 2008.

Dirac--Sobolev inequalities and estimates for the zero modes of massless Dirac operators

A. Balinsky, W. D. Evans, and Y. Saito
The paper analyzes the decay of any zero modes that might exist for a massless Dirac operator H:=alpha(1/i)[del]+Q, where Q is 4 x 4 matrix valued and of order O(|x|) at infinity. The approach is based on inversion with respect to the unit sphere in [openface R] and establishing embedding theorems f ... [J. Math. Phys. 49, 043514 (2008)] published Tue Apr 22, 2008.

Semidensities, second-class constraints, and conversion in anti-Poisson geometry

K. Bering
We consider Khudaverdian's geometric version of a BatalinVilkovisky (BV) operator Delta in the case of a degenerate anti-Poisson manifold. The characteristic feature of such an operator (aside from being a Grassmann-odd, nilpotent, second-order differential operator) is that it sends semidensities t ... [J. Math. Phys. 49, 043516 (2008)] published Tue Apr 22, 2008.

Noncommutative fields and actions of twisted Poincar[e-acute] algebra

M. Chaichian, P. P. Kulish, A. Tureanu, R. B. Zhang, and Xiao Zhang
Within the context of the twisted Poincare algebra, there exists no noncommutative analog of the Minkowski space interpreted as the homogeneous space of the Poincare group quotiented by the Lorentz group. The usual definition of commutative classical fields as sections of associated vector bundles o ... [J. Math. Phys. 49, 042302 (2008)] published Tue Apr 22, 2008.

Relativistic diffusions: A unifying approach

C. Chevalier and F. Debbasch
A new, wide class of relativistic stochastic processes is introduced. All relativistic processes considered so far in the literature are members of this class. For each process, the stochastic equations of motion are obtained in an arbitrary Lorentz frame. The associated Kolmogorov equation is also ... [J. Math. Phys. 49, 043303 (2008)] published Thu Apr 17, 2008.

Nonideal unilateral constraints in impulsive mechanics: A geometric approach

Stefano Pasquero
We use the differential geometric framework of the first jet bundle of the classical space-time bundle to study the impulsive behavior of a mechanical system with a finite number of degrees of freedom subject to nonideal unilateral constraints. We show that this framework allows deeper insights on t ... [J. Math. Phys. 49, 042902 (2008)] published Thu Apr 17, 2008.

Time-dependent Pauli equation in the presence of the Aharonov--Bohm effect

Y. Bouguerra, A. Bounames, M. Maamache, and Y. Saadi
We use the LewisRiesenfeld theory to determine the exact form of the wavefunctions of a two-dimensional Pauli equation of a charged spin 1/2 particle with time-dependent mass and frequency in the presence of the AharonovBohm effect and a two-dimensional time-dependent harmonic oscillator. We find th ... [J. Math. Phys. 49, 042107 (2008)] published Thu Apr 17, 2008.