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  • Articles  (134)
  • American Institute of Physics (AIP)  (134)
  • 2020-2023
  • 2020-2020
  • 2015-2019  (36)
  • 1995-1999  (98)
  • 1965-1969
  • Mathematics  (134)
  • 1
    Electronic Resource
    Electronic Resource
    On q-deformed supersymmetric classical mechanical models (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 6121-6129 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Based on the idea of quantum groups and para-Grassmannian variables, we present a generalization of supersymmetric classical mechanics with a deformation parameter q=exp(2πi/k) dealing with the k=3 case. The coordinates of the q-superspace are a commuting parameter t and a para-Grassmannian variable θ, where θ3=0. The generator and covariant derivative are obtained, as well as the action for some possible superfields. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531767
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  • 2
    Electronic Resource
    Electronic Resource
    Microcanonical ensemble and algebra of conserved generators for generalized quantum dynamics (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 5429-5443 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It has recently been shown, by application of statistical mechanical methods to determine the canonical ensemble governing the equilibrium distribution of operator initial values, that complex quantum field theory can emerge as a statistical approximation to an underlying generalized quantum dynamics. This result was obtained by an argument based on a Ward identity analogous to the equipartition theorem of classical statistical mechanics. We construct here a microcanonical ensemble which forms the basis of this canonical ensemble. This construction enables us to define the microcanonical entropy and free energy of the field configuration of the equilibrium distribution and to study the stability of the canonical ensemble. We also study the algebraic structure of the conserved generators from which the microcanonical and canonical ensembles are constructed, and the flows they induce on the phase space. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531714
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  • 3
    Electronic Resource
    Electronic Resource
    Representation of complex probabilities (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 1710-1722 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Let a "complex probability'' be a normalizable complex distribution P(x) defined on RD. A real and positive probability distribution p(z), defined on the complex plane CD, is said to be a positive representation of P(x) if 〈Q(x)〉P=〈Q(z)〉p, where Q(x) is any polynomial in RD and Q(z) its analytical extension on CD. In this paper it is shown that every complex probability admits a real representation and a constructive method is given. Among other results, explicit positive representations, in any number of dimensions, are given for any complex distribution of the form Gaussian times polynomial, for any complex distributions with support at one point and for any periodic Gaussian times polynomial. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531906
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  • 4
    Electronic Resource
    Electronic Resource
    Algebraic treatment of the Kaluza–Klein monopole system (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 1016-1028 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In analogy to the Kepler problem, the Green's function for a particle in the background of the Kaluza–Klein monopole is constructed through the algebraic approach, with the help of the Kustaanheimo–Stiefel variables and the generators of the SO(2,1) group in the exponential representation of Schwinger. The bound and continuum states are also obtained. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531172
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  • 5
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    Quantum systems with position-dependent mass and spin-orbit interaction via Rashba and Dresselhaus terms (2015)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2015-01-31
    Description: We consider a particle with spin 1/2 with position-dependent mass moving in a plane. Considering separately Rashba and Dresselhaus spin-orbit interactions, we write down the Hamiltonian for this problem and solve it for Dirichlet boundary conditions. Our radial wavefunctions have two contributions: homogeneous ones which are written as Bessel functions of non-integer orders—that depend on angular momentum m —and particular solutions which are obtained after decoupling the non-homogeneous system. In this process, we find non-homogeneous Bessel equation, Laguerre, as well as biconfluent Heun equation. We also present the probability densities for m = 0, 1, 2 in an annular quantum well. Our results indicate that the background as well as the spin-orbit interaction naturally splits the spinor components.
    Print ISSN: 0022-2488
    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
    Published by American Institute of Physics (AIP)
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  • 6
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    Group classification and conservation laws of anisotropic wave equations with a source (2016)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2016-08-13
    Description: Linear and nonlinear waves in anisotropic media are useful in investigating complex materials in physics, biomechanics, biomedical acoustics, etc. The present paper is devoted to investigation of symmetries and conservation laws for nonlinear anisotropic wave equations with specific external sources when the equations in question are nonlinearly self-adjoint. These equations involve two arbitrary functions. Construction of conservation laws associated with symmetries is based on the generalized conservation theorem for nonlinearly self-adjoint partial differential equations. First we calculate the conservation laws for the basic equation without any restrictions on the arbitrary functions. Then we make the group classification of the basic equation in order to specify all possible values of the arbitrary functions when the equation has additional symmetries and construct the additional conservation laws.
    Print ISSN: 0022-2488
    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
    Published by American Institute of Physics (AIP)
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  • 7
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    A world-line framework for 1D topological conformal σ-models (2015)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2015-11-17
    Description: We use world-line methods for pseudo-supersymmetry to construct sl (2|1)-invariant actions for the (2, 2, 0) chiral and (1, 2, 1) real supermultiplets of the twisted D -module representations of the sl (2|1) superalgebra. The derived one-dimensional topological conformal σ -models are invariant under nilpotent operators. The actions are constructed for both parabolic and hyperbolic/trigonometric realizations (with extra potential terms in the latter case). The scaling dimension λ of the supermultiplets defines a coupling constant, 2 λ + 1, the free theories being recovered at λ = − 1 2 . We also present, generalizing previous works, the D -module representations of one-dimensional superconformal algebras induced by N = ( p , q ) pseudo-supersymmetry acting on ( k , n , n − k ) supermultiplets. Besides sl (2|1), we obtain the superalgebras A (1, 1), D (2, 1; α ), D (3, 1), D (4, 1), A (2, 1) from ( p , q ) = (1, 1), (2, 2), (3, 3), (4, 4), (5, 1), at given k , n and critical values of λ .
    Print ISSN: 0022-2488
    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
    Published by American Institute of Physics (AIP)
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  • 8
    Electronic Resource
    Electronic Resource
    The Levi-Civita space–time as a limiting case of the γ space–time (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4064-4071 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the Levi-Civita metric can be obtained from a family of the Weyl metric, the γ metric, by taking the limit when the length of its Newtonian image source tends to infinity. In this process a relationship appears between two fundamental parameters of both metrics. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532943
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  • 9
    Electronic Resource
    Electronic Resource
    Gödel-type space–times in induced matter gravity theory (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4011-4027 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Five-dimensional (5D) generalized Gödel-type manifolds are examined in the light of the equivalence problem techniques, as formulated by Cartan. The necessary and sufficient conditions for local homogeneity of these 5D manifolds are derived. The local equivalence of these homogeneous Riemannian manifolds is studied. It is found that they are characterized by three essential parameters k, m2, and ω: identical triads (k,m2,ω) correspond to locally equivalent 5D manifolds. An irreducible set of isometrically nonequivalent 5D locally homogeneous Riemannian generalized Gödel-type metrics are exhibited. A classification of these manifolds based on the essential parameters is presented, and the Killing vector fields as well as the corresponding Lie algebra of each class are determined. It is shown that the generalized Gödel-type 5D manifolds admit maximal group of isometry Gr with r=7, r=9, or r=15 depending on the essential parameters k, m2, and ω. The breakdown of causality in all these classes of homogeneous Gödel-type manifolds are also examined. It is found that in three out of the six irreducible classes the causality can be violated. The unique generalized Gödel-type solution of the induced matter (IM) field equations is found. The question as to whether the induced matter version of general relativity is an effective therapy for these types of causal anomalies of general relativity is also discussed in connection with a recent work by Romero, Tavakol, and Zalaletdinov. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532939
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  • 10
    Electronic Resource
    Electronic Resource
    Product integral formalism and non-Abelian Stokes theorem (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 6033-6043 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We make use of the properties of product integrals to obtain a surface product integral representation for the Wilson loop operator. The result can be interpreted as the non-Abelian version of Stokes' theorem. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533068
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