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To analyze linear field equations on a locally homogeneous space–time by means of separation of variables, it is necessary to set up appropriate harmonics according to its symmetry group. In this paper, the harmonics are presented for a spatially compactified Bianchi II cosmological model—the nilgeometric model. Based on the group structure of the Bianchi II group (also known as the Heisenberg group) and the compactified spatial topology, the irreducible differential regular representations and the multiplicity of each irreducible representation, as well as the explicit form of the harmonics are all completely determined. They are also extended to vector harmonics. It is demonstrated that the Klein–Gordon and Maxwell equations actually reduce to systems of ODEs, with an asymptotic solution for a special case. [ABSTRACT FROM AUTHOR]

The Hughston–Jozsa–Wootters theorem shows that any finite ensemble of quantum states can be prepared “at a distance,” and it has been used to demonstrate the insecurity of all bit commitment protocols based on finite quantum systems without superselection rules. In this paper, we prove a generalized HJW theorem for arbitrary ensembles of states on a C*-algebra. We then use this result to demonstrate the insecurity of bit commitment protocols based on infinite quantum systems, and quantum systems with Abelian superselection rules. [ABSTRACT FROM AUTHOR]

If a state is passive for uniformly accelerated observers in n-dimensional (n>=2) anti–de Sitter (Ads) space–time (i.e., cannot be used by them to operate a perpetuum mobile), they will (a) register a universal value of the Unruh temperature, (b) discover a PCT symmetry, and (c) find that observables in complementary wedge-shaped regions necessarily commute with each other in this state. The stability properties of such a passive state induce a “geodesic causal structure” on AdS and concommitant locality relations. It is shown that observables in these complementary wedge-shaped regions fulfill strong additional independence conditions. In two-dimensional AdS these even suffice to enable the derivation of a nontrivial, local, covariant net indexed by bounded space–time regions. All these results are model-independent and hold in any theory which is compatible with a weak notion of space–time localization. Examples are provided of models satisfying the hypotheses of these theorems. [ABSTRACT FROM AUTHOR]

In this paper, we give a realization of crystal bases of the fundamental representations over Uq(Cn(1)) in terms of Young diagrams k introduced by Premat. Further, we give a generalized Lascoux–Leclerc–Thibon algorithm for computing the global bases. [ABSTRACT FROM AUTHOR]

We classify all irreducible, almost commutative geometries whose spectral action is dynamically nondegenerate. Heavy use is made of Krajewski’s diagrammatic language. The motivation for our definition of dynamical nondegeneracy stems from particle physics where the fermion masses are nondegenerate. [ABSTRACT FROM AUTHOR]

In this paper, we give a realization of crystal bases of the fundamental representations over Uq(Cn(1)) in terms of Young diagrams k introduced by Premat. Further, we give a generalized Lascoux–Leclerc–Thibon algorithm for computing the global bases. [ABSTRACT FROM AUTHOR]

One of the simplest pseudo-Hermitian models with real spectrum (viz., square-well on a real interval I of coordinates) is re-examined. A PT-symmetric complex deformation C of I is introduced and shown tractable via an innovated approach to matching conditions. The result is surprising: An arbitrarily small deformation I→C implies a sudden collapse (i.e., the spontaneous PT-symmetry breaking) of virtually all the spectrum (i.e., up to its low-energy part). [ABSTRACT FROM AUTHOR]

The known link of the division algebras to 10-dimensional spacetime and one leptoquark family is extended to encompass three leptoquark families. [ABSTRACT FROM AUTHOR]

A bijective map r: X2→X2, where X={x1,…,xn} is a finite set, is called a set-theoretic solution of the Yang–Baxter equation (YBE) if the braid relation r12r23r12=r23r12r23 holds in X3. A nondegenerate involutive solution (X,r) satisfying r(xx)=xx, for all x∈X, is called square-free solution. There exist close relations between the square-free set-theoretic solutions of YBE, the semigroups of I-type, the semigroups of skew polynomial type, and the Bieberbach groups, as it was first shown in a joint paper with Michel Van den Bergh. In this paper we continue the study of square-free solutions (X,r) and the associated Yang–Baxter algebraic structures—the semigroup S(X,r), the group G(X,r) and the k-algebra A(k,X,r) over a field k, generated by X and with quadratic defining relations naturally arising and uniquely determined by r. We study the properties of the associated Yang–Baxter structures, and prove a conjecture of the present author that the three notions: a square-free solution of (set-theoretic) YBE, a semigroup of I type, and a semigroup of skew-polynomial-type, are equivalent. This implies that the Yang–Baxter algebra A(k,X,r) is a Poincaré–Birkhoff–Witt-type algebra, with respect to some appropriate ordering of X. We conjecture that every square-free solution of YBE is retractable, in the sense of Etingof–Schedler–Solovyev. [ABSTRACT FROM AUTHOR]

According to a theorem by Treves [Duke Math. J.DUMJAO 108, 251 (2001) ], the conserved functionals of the KdV equation vanish on each formal Laurent series 1/x2+u0+∑k=2+∞ukxk. We propose a new, very simple geometrical proof for this statement. [ABSTRACT FROM AUTHOR]

The article studies the high energy asymptotics of the spectral shill function (SSF) for the three-dimensional Schrodinger operator with constant magnetic field, perturbed by an electric potential which decays fast enough at infinity. The article also introduces the concepts of index of a Fredholm pair of orthogonal projections, and index for a pair of self-adjoint operators, and describe some basic properties related to these concepts which will be often used in the sequel. As far as the authors are informed, the high energy asymptotics of the SSF for three-dimensional Schrodinger operators with constant magnetic fields is investigated for the first time in the present note.

Robertson intelligent states which minimize the Schrödinger–Robertson uncertainty relation are constructed as eigenstates of a linear combination of Weyl generators of the su(3) algebra. The construction is based on the analytic representations of su(3) coherent states. New classes of coherent and squeezed states are explicitly derived. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence of a global periodic attractor for a strongly damped nonlinear wave equation with time-periodic driving force under homogeneous Dirichlet boundary condition. It is proved that in certain parameter region, for arbitrary time-periodic driving force, the system has a unique periodic solution attracting any bounded set exponentially. This implies that the system behaves exactly as a one-dimensional system. We mention, in particular, that the obtained result can be used to prove the existence of global periodic attractor of the usual damped and driven wave equations. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the existence and uniqueness of the local strong solutions to the initial boundary problem for a one-dimensional shallow-water equation (Camassa–Holm equation) on the half-space {x>0} with initial data uo∈H2(R+)∩H01(R+). The solution is obtained as a limit of the solutions for a class of approximation problems. We also establish the global result of the corresponding solution, provided that the initial data u0 satisfies certain positivity condition. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A number of problems in mechanics and mathematical physics involve evaluation of two- dimensional phase-modulated lattice sums of the form where G is a lattice vector. Problems of interest come from various fields, including electrostatics, superconductivity, fluid turbulence; and vortex dynamics. This sum is slowly and conditionally convergent, and numerous formulations have been presented to facilitate its rapid computation. When the lattice defined by G is square or rectangular, the evaluation of these sums can be very elegantly using an identity derived by M.L. Glasser.

The classical MICZ-Kepler problem is shown to be reducible to an isotropic two-dimensional system of linear harmonic oscillators and a conservation law in terms of new variables related to the Ermanno–Bernoulli constants and the components of the Poincaré vector. An algorithmic route to linearization is shown based on Lie symmetry analysis and the reduction method [ Nucci, J. Math. Phys. 37, 1772 (1996) ]. First integrals are also obtained by symmetry analysis and the reduction method [ Marcelli and Nucci,J. Math. Phys. 44, 2111 (2002) ]. [ABSTRACT FROM AUTHOR]

Motivated by existence problems for dissipative systems arising naturally in lattice models from quantum statistical mechanics, we consider the following C*-algebraic setting: A given Hermitian dissipative mapping δ is densely defined in a unital C*-algebra A. The identity element in A is also in the domain of δ. Completely dissipative maps δ are defined by the requirement that the induced maps, (aij)→(δ(aij)), are dissipative on the n-by-n complex matrices over A for all n. We establish the existence of different types of maximal extensions of completely dissipative maps. If the enveloping von Neumann algebra of A is injective, we show the existence of an extension of δ which is the infinitesimal generator of a quantum dynamical semigroup of completely positive maps in the von Neumann algebra. If δ is a given well-behaved *-derivation, then we show that each of the maps ±δ is completely dissipative. [ABSTRACT FROM AUTHOR]

The previous supersymmetric generalization of the unitary Harish-Chandra integral prompted the conjecture that the Harish-Chandra formula should have an extension to superspaces. We prove this conjecture for the unitary orthosymplectic supermanifold UOSp(k1/2k2). To this end, we construct and solve an eigenvalue equation. [ABSTRACT FROM AUTHOR]

The previous supersymmetric generalization of the unitary Harish-Chandra integral prompted the conjecture that the Harish-Chandra formula should have an extension to superspaces. We prove this conjecture for the unitary orthosymplectic supermanifold UOSp(k1/2k2). To this end, we construct and solve an eigenvalue equation. [ABSTRACT FROM AUTHOR]

Riemann’s method is one of the definitive ways of solving Cauchy’s problem for a second order linear hyperbolic partial differential equation in 2 variables. Chaundy’s equation, with 4 parameters, is the most general self-adjoint equation for which the Riemann function is known. Here we show that Chaundy’s equation possesses a two-dimensional vector space of second-order symmetry operators. Hence a new equivalence class of Riemann functions, admitting no first-order symmetries and obtainable only via a higher order symmetry, is found. A new 5 parameter Riemann function is then subsequently derived. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

p-mechanics is a consistent physical theory which describes both classical and quantum mechanics simultaneously through the representation theory of the Heisenberg group. In this paper we describe how nonlinear canonical transformations affect p-mechanical observables and states. Using this we show how canonical transformations change a quantum mechanical system. We seek an operator on the set of p-mechanical observables which corresponds to the classical canonical transformation. In order to do this we derive a set of integral equations which when solved will give us the coherent state expansion of this operator. The motivation for these integral equations comes from the work of Moshinsky and a variety of collaborators. We consider a number of examples and discuss the use of these equations for non-bijective transformations. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Historically Lie algebras of first-order symmetry operators have proven to be a useful method for finding equivalence classes of Riemann functions. Here this idea is extended to higher order symmetries. The approach is to seek self-adjoint linear hyperbolic partial differential equations that separate variables in more than one coordinate system under the action of the group E(1,1). The equations derived admit no nontrivial first-order operators and can only be obtained from second-order symmetry operators. Using this symmetry structure, a new equivalence class of Riemann functions can then be found. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The recently introduced SLE growth processes are based on conformal maps from an open and simply connected subset of the upper half-plane to the half-plane itself. We generalize this by considering a hierarchy of stochastic evolutions mapping open and simply connected subsets of smaller and smaller fractions of the upper half-plane to these fractions themselves. The evolutions are all driven by one-dimensional Brownian motion. Ordinary chordal SLE appears at grade one in the hierarchy. At grade two we find a direct correspondence to conformal field theory through the explicit construction of a level-four null vector in a highest-weight module of the Virasoro algebra. This conformal field theory has central charge c=-22/5 and is associated with the Yang–Lee singularity. Our construction may thus offer a novel description of this statistical model. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In a previous article, an “invariant method” to calculate monomial integrals over the U(n) group was introduced. In this paper, we study the more traditional group-theoretical method, and compare its strengths and weaknesses with those of the invariant method. As a result, we are able to introduce a “hybrid method” which combines the respective strengths of the other two methods. There are many examples in the paper illustrating how each of these methods works. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We perform the complete group classification in the class of nonlinear Schrödinger equations of the form iψt+ψxx+|ψ|γψ+V(t,x)ψ=0, where V is an arbitrary complex-valued potential depending on t and x, γ is a real nonzero constant. We construct all the possible inequivalent potentials for which these equations have nontrivial Lie symmetries using a combination of algebraic and compatibility methods. The proposed approach can be applied to solving group classification problems for a number of important classes of differential equations arising in mathematical physics. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

As an extension of the theory of Dyson’s Brownian motion models for the standard Gaussian random-matrix ensembles, we report a systematic study of Hermitian matrix-valued processes and their eigenvalue processes associated with the chiral and nonstandard random-matrix ensembles. In addition to the noncolliding Brownian motions, we introduce a one-parameter family of temporally homogeneous noncolliding systems of the Bessel processes and a two-parameter family of temporally inhomogeneous noncolliding systems of Yor’s generalized meanders and show that all of the ten classes of eigenvalue statistics in the Altland–Zirnbauer classification are realized as particle distributions in the special cases of these diffusion particle systems. As a corollary of each equivalence in distribution of a temporally inhomogeneous eigenvalue process and a noncolliding diffusion process, a stochastic-calculus proof of a version of the Harish–Chandra (Itzykson–Zuber) formula of integral over unitary group is established. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We study the lowest energy E of a relativistic system of N identical bosons bound by pair potentials of the form V(rij) = g(rij²) in thee spatial dimensions. In natural units &hstroke; = c = 1 the system has the semirelativistic ‘spinless-Salpeter’ Hamiltonian H = ∑I=1N √m² + pi² + ∑j>i=jNg(¦ri-rj¦²), where g is monotone increasing and has convexity gn≥0. We use ‘envelope theory’ to derive formulas for general lower energy bounds and we use a variational method to find complementary upper bounds valid for all N≥2. In particular, we determine the energy of the N-body oscillator g(r²) = cr² with error less than 0.15% for all m≥0, N≥2, and c>0. [ABSTRACT FROM AUTHOR]

To treat the front-form Hamiltonian approach to quantum field theory, called light cone quantum field theory, in a mathematically rigorous way, the existence of a well-defined restriction of the corresponding free fields to the hypersurface {x0+x3=0} in Minkowski space is of an essential necessity. However, even in the situation of a real scalar free field such a restriction does canonically not exist; this is called the restriction problem. Furthermore, since the beginning of light cone quantum field theory there is the problem of nonexistence of a well-defined Fock space expansion of a free quantum field in terms of light cone momenta which is called the zero-mode problem. In this paper we present solutions to these long outstanding problems where the study of the zero-mode problem (of the corresponding classical field) will lead us to a solution of the restriction problem. We introduce a new function space of “squeezed” smooth functions which can canonically be embedded into the Schwartz space S(R3). The restriction of the free field to {x0+x3=0} is canonically definable on this function space and we show that the covariant field is uniquely determined by this “tame” restriction. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The multi-instanton expansion for the eigenvalues of the symmetric double well is derived using a Langer–Cherry uniform asymptotic expansion of the solution of the corresponding Schrödinger equation. The Langer–Cherry expansion is anchored to either one of the minima of the potential, and by construction has the correct asymptotic behavior at large distance, while the quantization condition amounts to imposing the even or odd parity of the wave function. This method leads to an efficient algorithm for the calculation to virtually any desired order of all the exponentially small series of the multi-instanton expansion, and with trivial modifications can also be used for nonsymmetric double wells. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We construct a realization of the L-operator satisfying the RLL-relation of the face-type elliptic quantum group Bq,λ(A2(2)). The construction is based on the elliptic analog of the Drinfeld currents of Uq(A2(2)), which forms the elliptic algebra Uq,p(A2(2)). We give a realization of the elliptic currents E(z), F(z), and K(z) as a tensor product of the Drinfeld currents of Uq(A2(2)) and a Heisenberg algebra. In the level-one representation, we also give a free field realization of the elliptic currents. Applying these results, we derive a free field realization of the Uq,p(A2(2))-analog of the Bq,λ(A2(2))-intertwining operators. The resultant operators coincide with those of the vertex operators in the dilute AL model, which is known to be a RSOS restriction of the A2(2) face model. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We raise the possibility of developing a theory of constructing quantum dynamical observables independent from quantization and deriving classical dynamical observables from pure quantum mechanical consideration. We do so by giving a detailed quantum mechanical derivation of the classical time of arrival at arbitrary arrival points for a particle in one dimension. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We minimize the functional f->∫ afdμ under the entropy condition E(f)=-∫ f log fdμ>=E, ∫ fdμ=1 and f>=0, where E∈R is fixed. We prove that the minimum is attained for f=e-sa/∫ e-sadμ, where s∈R is chosen such that E(f)=E. We apply the result on minimizing problems in pseudodifferential calculus, where we minimize the harmonic oscillator. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

An analysis is performed of instanton configurations in pure Euclidean Yang–Mills theory containing small Lorentz-violating perturbations that maintain gauge invariance. Conventional topological arguments are used to show that the general classification of instanton solutions involving the topological charge is the same as in the standard case. Explicit solutions are constructed for general gauge invariant corrections to the action that are quadratic in the curvature. The value of the action is found to be unperturbed to lowest order in the Lorentz-violating parameters. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The concept of partially invariant solutions is discussed in the framework of the group analysis of models derived from the Nambu–Goto action. In particular, we consider the nonrelativistic Chaplygin gas and the relativistic Born–Infeld theory for a scalar field. Using a general systematic approach based on subgroup classification methods, nontrivial partially invariant solutions with defect structure δ=1 are constructed. For this purpose, a classification of the subgroups of the Lie point symmetry group, which have generic orbits of dimension 2, has been performed. These subgroups allow us to introduce the corresponding symmetry variables and next to reduce the initial equations to different nonequivalent classes of partial differential equations and ordinary differential equations. The latter can be transformed to standard form and, in some cases, solved in terms of elementary and Jacobi elliptic functions. This results in a large number of new partially invariant solutions, which are determined to be either reducible or irreducible with respect to the symmetry group. Some physical interpretation of the results in the area of fluid dynamics and field theory are discussed. The solutions represent traveling and centered waves, algebraic solitons, kinks, bumps, cnoidal and snoidal waves. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products is constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations of the Hopf pairs introduced by Takeuchi. As a special case, the quantum double of a finite dimensional biperfect (noncocommutative) weak Hopf algebra is built. Examples of quantum doubles from a Clifford monoid as well as a noncommutative and noncocommutative weak Hopf algebra are given, generalizing quantum doubles from a group and a noncommutative and noncocommutative Hopf algebra, respectively. Moreover, some characterizations of quantum doubles of finite dimensional biperfect weak Hopf algebras are obtained. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We consider the “thermodynamic limit” of a d-dimensional lattice of hyperbolic dynamical systems on the 2-torus, interacting via weak and nearest neighbor coupling. We prove that the SRB measure is analytic in the strength of the coupling. The proof is based on symbolic dynamics techniques that allow us to map the SRB measure into a Gibbs measure for a spin system on a (d+1)-dimensional lattice. This Gibbs measure can be studied by an extension (decimation) of the usual “cluster expansion” techniques. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We study a (quenched) random-field quantum model of an anharmonic crystal for displacive structural phase transitions in spherical approximation: the random-field quantum spherical (ferroelectric) model. For stationary ergodic random fields its behavior depends on the quantum parameter of the model and on the expectation and covariance of the field. If quantum fluctuations are small enough not to destroy the phase transition, then it can be suppressed when the field fluctuations are large. For the field of independent identically distributed random variables and the short-range interaction we obtain that the lower critical dimensionality dl=4 (dl=2 for the zero-field) and that it decreases for long-range interactions. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We consider the Lie-algebra of the group of diffeomorphisms of a d-dimensional torus which is also known to be the algebra of derivations on a Laurent polynomial ring A in d commuting variables denoted by Der A. The universal central extension of Der A for d=1 is the so-called Virasoro algebra. The connection between Virasoro algebra and physics is well known. See, for example, the book on Conformal Field Theory by Di Francesco, Mathieu, and Senechal. In this paper we classify (A, Der A) modules which are irreducible and have finite dimensional weight spaces. Earlier Larsson constructed a large class of modules, the so-called tensor fields, based on gld modules which are also A modules. We prove that they exhaust all (A, Der A) irreducible modules. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

By means of complex representation and companion vector, this paper studies the problems of eigenvalues and eigenvectors of quaternion matrices, and gives a technique of computing the eigenvalues and eigenvectors of the quaternion matrices in quaternionic quantum mechanics. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The Schrödinger equation is considered with the first order time derivative changed to a Caputo fractional derivative, the time fractional Schrödinger equation. The resulting Hamiltonian is found to be non-Hermitian and nonlocal in time. The resulting wave functions are thus not invariant under time reversal. The time fractional Schrödinger equation is solved for a free particle and for a potential well. Probability and the resulting energy levels are found to increase over time to a limiting value depending on the order of the time derivative. New identities for the Mittag–Leffler function are also found and presented in an Appendix. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The unified description of the main thermodynamical functions of the Bose and Fermi ideal gases, obtained by Lee [J. Math. Phys. 36, 1217 (1995)] in terms of the polylogarithmic functions, can also be obtained by analytic continuation in the chemical potential owing to the analytic properties of the Lerch function that is simply related to the polylogarithmic ones. By this procedure we also show that the Fourier coefficients of the thermal Green function of the ideal Bose gas convert into those of the Fermi one. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this work, the Balian–Low theorem is extended to Gabor (also called Weyl–Heisenberg) frames for subspaces and, more particularly, its relationship with the unique Gabor dual property for subspace Gabor frames is pointed out. To achieve this goal, the subspace Gabor frames which have a unique Gabor dual of type I (resp. type II) are defined and characterized in terms of the Zak transform for the rational parameter case. This characterization is then used to prove the Balian–Low theorem for subspace Gabor frames. Along the same line, the same characterization is used to prove a duality theorem for the unique Gabor dual property which is an analogue of the Ron and Shen duality theorem. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

For relativistic stars rotating slowly and differentially with a positive angular velocity, some properties in relation to the positiveness of the rate of rotational dragging and of the angular momentum density are derived. Moreover, the proof for the bounds on the rotational mass-energy, which we have generalized (outside the slow rotation limit) in a previous paper, is briefly exposed. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The modified Dirac equation in the Lorentz-violating Standard-Model Extension (SME) is considered. Within this framework, the construction of a Hermitian Hamiltonian to all orders in the Lorentz-breaking parameters is investigated, discrete symmetries and the first-order roots of the dispersion relation are determined, and various properties of the eigenspinors are discussed. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We study the lowest energy E of a relativistic system of N identical bosons bound by pair potentials of the form V(rij) = g(rij²) in thee spatial dimensions. In natural units &hstroke; = c = 1 the system has the semirelativistic ‘spinless-Salpeter’ Hamiltonian H = ∑I=1N √m² + pi² + ∑j>i=jNg(¦ri-rj¦²), where g is monotone increasing and has convexity gn≥0. We use ‘envelope theory’ to derive formulas for general lower energy bounds and we use a variational method to find complementary upper bounds valid for all N≥2. In particular, we determine the energy of the N-body oscillator g(r²) = cr² with error less than 0.15% for all m≥0, N≥2, and c>0. [ABSTRACT FROM AUTHOR]

We construct a realization of the L-operator satisfying the RLL-relation of the face-type elliptic quantum group Bq,λ(A2(2)). The construction is based on the elliptic analog of the Drinfeld currents of Uq(A2(2)), which forms the elliptic algebra Uq,p(A2(2)). We give a realization of the elliptic currents E(z), F(z), and K(z) as a tensor product of the Drinfeld currents of Uq(A2(2)) and a Heisenberg algebra. In the level-one representation, we also give a free field realization of the elliptic currents. Applying these results, we derive a free field realization of the Uq,p(A2(2))-analog of the Bq,λ(A2(2))-intertwining operators. The resultant operators coincide with those of the vertex operators in the dilute AL model, which is known to be a RSOS restriction of the A2(2) face model. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A grading of a Lie algebra is called fine if it cannot be further refined. Fine gradings provide basic information about the structure of the algebra. There are six fine gradings of the semisimple Lie algebra of type A1×A1 over the complex number field. An explicit description of all the fine gradings of A1×A1 is given in terms of the four-dimensional representation o(4,C) of the algebra. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

After a detailed ab initio description of the exterior structure of graphs as handled by Connes and Kreimer in their work on renormalization (illustrated by the example of the [lowercase_phi_synonym]3 model in six dimensions) we spell out in detail their study of the Lie algebra of infinitesimal characters and of the group of characters of the Hopf algebra of Feynman graphs. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We introduce the free N=1 supersymmetric derivation ring and prove the existence of an exact sequence of supersymmetric rings and linear transformations. We apply necessary and sufficient conditions arising from this exact supersymmetric sequence to obtain the essential relations between conserved quantities, gradients and the N=1 super Korteweg–de Vries (KdV) hierarchy. We combine this algebraic approach with an analytic analysis of the super heat operator. We obtain the explicit expression for the Green’s function of the super heat operator in terms of a series expansion and discuss its properties. The expansion is convergent under the assumption of bounded bosonic and fermionic potentials. We show that the asymptotic expansion when t→0+ of the Green’s function for the superheat operator evaluated over its diagonal generates all the members of the N=1 super KdV hierarchy.© 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

By applying higher powers of Bogoliubov’s transformation operator b†=ν*a+μ*a† to the even and odd coherent states we construct mathematically two new types of quantum states. Various special functions and mathematical formulations are used to obtain the matrix elements for the states in the coherent state representation. The nonclassical nature of these states is found to be related to their quantum coherence in phase space. The interference effects can also be regarded as a consequence of the oscillatory behavior of the special functions in the structure of the states. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]