The Experts below are selected from a list of 321 Experts worldwide ranked by ideXlab platform

Aristophanes Dimakis - One of the best experts on this subject based on the ideXlab platform.

  • Bi-Differential Calculus and the KdV equation
    2000
    Co-Authors: Aristophanes Dimakis, Folkert Müller-hoissen
    Abstract:

    A gauged bi-Differential Calculus over an associative (and not necessarily commutative) algebra A is an N0-graded left A-module with two covariant derivatives acting on it which, as a consequence of certain (e.g., nonlinear Differential) equations, are flat and anticommute. As a consequence, there is an iterative construction of generalized conserved currents. We associate a gauged bi-Differential Calculus with the Korteweg-de-Vries equation and use it to compute conserved densities of this equation.

  • Differential Calculus and gauge theory on finite sets
    Journal of Physics A: Mathematical and General, 1994
    Co-Authors: Aristophanes Dimakis, F. M"uller-hoissen
    Abstract:

    We develop Differential Calculus and gauge theory on a finite set G. An elegant formulation is obtained when G is supplied with a group structure and in particular for a cyclic group. Connes' two-point model (which is an essential ingredient of his reformulation of the standard model of elementary particle physics) is recovered in our approach. Reductions of the universal Differential Calculus to `lower-dimensional' Differential calculi are considered. The `complete reduction' leads to a Differential Calculus on a periodic lattice which is related to q-Calculus.

  • Differential Calculus and Discrete Structures
    arXiv: High Energy Physics - Theory, 1994
    Co-Authors: Aristophanes Dimakis, F. M"uller-hoissen
    Abstract:

    There is a deformation of the ordinary Differential Calculus which leads from the continuum to a lattice (and induces a corresponding deformation of physical theories). We recall some of its features and relate it to a general framework of Differential Calculus on discrete sets. This framework generalizes the usual (lattice) discretization.

  • Noncommutative Differential Calculus and lattice gauge theory
    Journal of Physics A: Mathematical and General, 1993
    Co-Authors: Aristophanes Dimakis, Folkert Müller-hoissen, T. Striker
    Abstract:

    The authors study consistent deformations of the classical Differential Calculus on algebras of functions (and, more generally, commutative algebras) such that Differentials and functions satisfy nontrivial commutation relations. For a class of such calculi it is shown that the deformation parameters correspond to the spacings of a lattice. These Differential calculi generate a lattice on a space continuum. The whole setting of a lattice theory can then be deduced from the continuum theory via deformation of the standard Differential Calculus. In this framework one just has to express the Lagrangian for the continuum theory in terms of Differential forms. This expression then also makes sense for the deformed Differential Calculus. There is a natural integral associated with the latter. Integration of the Lagrangian over a space continuum then produces the correct lattice action for a large class of theories. This is explicitly shown for the scalar field action and the action for SU(m) gauge theory.

  • From continuum to lattice theory via deformation of the Differential Calculus
    Physics Letters B, 1993
    Co-Authors: Aristophanes Dimakis, Folkert Müller-hoissen, T. Striker
    Abstract:

    Abstract It is shown that a lattice (gauge) theory can be obtained from a continuum theory via deformation of the standard Differential Calculus in such a way that functions and Differentials no longer commute. Any lagrangian for a continuum theory which can be expressed in terms of Differential forms is also defined for the deformed Differential Calculus. Using an integral which is naturally associated with the deformed Differential Calculus, one obtains an action for a lattice theory.

T. Striker - One of the best experts on this subject based on the ideXlab platform.

  • Noncommutative Differential Calculus and lattice gauge theory
    Journal of Physics A: Mathematical and General, 1993
    Co-Authors: Aristophanes Dimakis, Folkert Müller-hoissen, T. Striker
    Abstract:

    The authors study consistent deformations of the classical Differential Calculus on algebras of functions (and, more generally, commutative algebras) such that Differentials and functions satisfy nontrivial commutation relations. For a class of such calculi it is shown that the deformation parameters correspond to the spacings of a lattice. These Differential calculi generate a lattice on a space continuum. The whole setting of a lattice theory can then be deduced from the continuum theory via deformation of the standard Differential Calculus. In this framework one just has to express the Lagrangian for the continuum theory in terms of Differential forms. This expression then also makes sense for the deformed Differential Calculus. There is a natural integral associated with the latter. Integration of the Lagrangian over a space continuum then produces the correct lattice action for a large class of theories. This is explicitly shown for the scalar field action and the action for SU(m) gauge theory.

  • From continuum to lattice theory via deformation of the Differential Calculus
    Physics Letters B, 1993
    Co-Authors: Aristophanes Dimakis, Folkert Müller-hoissen, T. Striker
    Abstract:

    Abstract It is shown that a lattice (gauge) theory can be obtained from a continuum theory via deformation of the standard Differential Calculus in such a way that functions and Differentials no longer commute. Any lagrangian for a continuum theory which can be expressed in terms of Differential forms is also defined for the deformed Differential Calculus. Using an integral which is naturally associated with the deformed Differential Calculus, one obtains an action for a lattice theory.

André Lieutier - One of the best experts on this subject based on the ideXlab platform.

  • Domain theory and Differential Calculus (functions of one variable)
    Proceedings - Symposium on Logic in Computer Science, 2002
    Co-Authors: Abbas Edalat, André Lieutier
    Abstract:

    A data-type for Differential Calculus is introduced, which is based on domain theory. We define the integral and also the derivative of a Scott continuous function on the domain of intervals, and present a domain-theoretic generalization of the fundamental theorem of Calculus. We then construct a domain for differentiable real valued functions of a real variable. The set of classical C1 functions, equipped with its C1 norm, is embedded into the set of maximal elements of this domain, which is a countably based bounded complete continuous domain. This gives a data type for Differential Calculus. The construction can be generalized to Ck and C∞ functions. As an immediate application, we present a domain-theoretic generalization of Picard's theorem, which provides a data type for solving Differential equations.

Abbas Edalat - One of the best experts on this subject based on the ideXlab platform.

  • Domain theory and Differential Calculus (functions of one variable)
    Proceedings - Symposium on Logic in Computer Science, 2002
    Co-Authors: Abbas Edalat, André Lieutier
    Abstract:

    A data-type for Differential Calculus is introduced, which is based on domain theory. We define the integral and also the derivative of a Scott continuous function on the domain of intervals, and present a domain-theoretic generalization of the fundamental theorem of Calculus. We then construct a domain for differentiable real valued functions of a real variable. The set of classical C1 functions, equipped with its C1 norm, is embedded into the set of maximal elements of this domain, which is a countably based bounded complete continuous domain. This gives a data type for Differential Calculus. The construction can be generalized to Ck and C∞ functions. As an immediate application, we present a domain-theoretic generalization of Picard's theorem, which provides a data type for solving Differential equations.

Folkert Müller-hoissen - One of the best experts on this subject based on the ideXlab platform.

  • Bi-Differential Calculus and the KdV equation
    2000
    Co-Authors: Aristophanes Dimakis, Folkert Müller-hoissen
    Abstract:

    A gauged bi-Differential Calculus over an associative (and not necessarily commutative) algebra A is an N0-graded left A-module with two covariant derivatives acting on it which, as a consequence of certain (e.g., nonlinear Differential) equations, are flat and anticommute. As a consequence, there is an iterative construction of generalized conserved currents. We associate a gauged bi-Differential Calculus with the Korteweg-de-Vries equation and use it to compute conserved densities of this equation.

  • Noncommutative Differential Calculus and lattice gauge theory
    Journal of Physics A: Mathematical and General, 1993
    Co-Authors: Aristophanes Dimakis, Folkert Müller-hoissen, T. Striker
    Abstract:

    The authors study consistent deformations of the classical Differential Calculus on algebras of functions (and, more generally, commutative algebras) such that Differentials and functions satisfy nontrivial commutation relations. For a class of such calculi it is shown that the deformation parameters correspond to the spacings of a lattice. These Differential calculi generate a lattice on a space continuum. The whole setting of a lattice theory can then be deduced from the continuum theory via deformation of the standard Differential Calculus. In this framework one just has to express the Lagrangian for the continuum theory in terms of Differential forms. This expression then also makes sense for the deformed Differential Calculus. There is a natural integral associated with the latter. Integration of the Lagrangian over a space continuum then produces the correct lattice action for a large class of theories. This is explicitly shown for the scalar field action and the action for SU(m) gauge theory.

  • From continuum to lattice theory via deformation of the Differential Calculus
    Physics Letters B, 1993
    Co-Authors: Aristophanes Dimakis, Folkert Müller-hoissen, T. Striker
    Abstract:

    Abstract It is shown that a lattice (gauge) theory can be obtained from a continuum theory via deformation of the standard Differential Calculus in such a way that functions and Differentials no longer commute. Any lagrangian for a continuum theory which can be expressed in terms of Differential forms is also defined for the deformed Differential Calculus. Using an integral which is naturally associated with the deformed Differential Calculus, one obtains an action for a lattice theory.