The Experts below are selected from a list of 69 Experts worldwide ranked by ideXlab platform

Jordi C Girona - One of the best experts on this subject based on the ideXlab platform.

  • Román-Roy: “On the construction of K-operators in field theories as sections along Legendre maps
    2013
    Co-Authors: Arturo Echeverría-enríquez, Jesús Marín-solano, Jordi C Girona, Miguel C. Muñoz-lec, Narciso Román-roy
    Abstract:

    The “time-evolution K-operator ” (or “relative Hamiltonian vector field”) in mechanics is a powerful tool which can be geometrically defined as a vector field along the Legendre map. It has been extensively used by several authors for studying the structure and properties of the dynamical systems (mainly the non-regular ones), such as the relation between the Lagrangian and Hamiltonian formalisms, constraints, and higher-order mechanics. This paper is devoted to defining a generalization of this operator for field theories, in a covariant formulation. In order to do this, we use sections along maps, in particular multivector fields (skew-symmetric Contravariant Tensor fields of order greater than 1), jet fields and connection forms along the Legendre map. As a relevant result, we use these geometrical objects to obtain the solutions of the Lagrangian and Hamiltonian field equations, and the equivalence among them (specially for non-regular field theories)

  • SECTIONS ALONG MAPS IN FIELD THEORIES: THE COVARIANT FIELD OPERATORS
    2008
    Co-Authors: Arturo Echeverría-enríquez, Jesús Marín-solano, Jordi C Girona, Miguel C. Muñoz-lec, Narciso Román-roy
    Abstract:

    The “evolution operator ” (or “relative Hamiltonian vector field”) in mechanics is a powerful tool which can be geometrically defined as a vector field along the Legendre map. It has been extensively used by several authors for studying the structure and properties of the dynamical systems (mainly the non-regular ones), such as the relation between the Lagrangian and Hamiltonian formalisms, constraints, and higher-order mechanics. This paper is devoted to defining a generalization of this operator for field theories, in a covariant formulation. In order to do this, we also use sections along maps, in particular multivector fields (skew-symmetric Contravariant Tensor fields of order greater than 1), jet fields and connection forms along the Legendre map. As a first relevant property, we use these geometrical objects to obtain the solutions of the Lagrangian and Hamiltonian field equations, and the equivalence among them (specially for non-regular field theories)

  • SECTIONS ALONG MAPS IN FIELD THEORIES: THE COVARIANT FIELD OPERATORS
    2008
    Co-Authors: Arturo Echeverría-enríquez, Jesús Marín-solano, Jordi C Girona, Miguel C. Muñoz-lec, Narciso Román-roy
    Abstract:

    The “time-evolution operator ” in mechanics is a powerful tool which can be geometrically defined as a vector field along the Legendre map. It has been extensively used by several authors for studying the structure and properties of the dynamical systems (mainly the non-regular ones), such as the relation between the Lagrangian and Hamiltonian formalisms, constraints, and higher-order mechanics. This paper is devoted to defining a generalization of this operator for field theories, in a covariant formulation. In order to do this, we also use sections along maps, in particular multivector fields (skew-symmetric Contravariant Tensor fields of order greater than 1), jet fields and connection forms along the Legendre map. As a first relevant property, we use these geometrical objects to obtain the solutions of the Lagrangian and Hamiltonian field equations, and the equivalence among them (specially for non-regular field theories)

Kofi Edee - One of the best experts on this subject based on the ideXlab platform.

  • metasurface homogenization based on Contravariant Tensor averaging in smooth field approximation
    Journal of The Optical Society of America B-optical Physics, 2020
    Co-Authors: Kofi Edee
    Abstract:

    The homogenization of the transverse parameters of metasurfaces is introduced through the concept of covariant permittivity Tensor averaging. The proposed scheme is based on a covariant form of Maxwell’s equations written in the matched coordinates system. Therefore, the average characteristics of the periodic structure take into account not only all of the physical boundary conditions, but also the geometrical details of the periodic structure that affect the electromagnetic field propagation. The proposed method is successfully applied to analyze the extraordinary optical transmission through a thick layer subwavelength periodic annular slit array.

Poncin Norbert - One of the best experts on this subject based on the ideXlab platform.

  • Decomposition of symmetric Tensor fields in the presence of a flat contact projective structure
    2008
    Co-Authors: Fregier Yael, Mathonet Pierre, Poncin Norbert
    Abstract:

    Let M be an odd-dimensional Euclidean space endowed with a contact 1-form \alpha. We investigate the space of symmetric Contravariant Tensor fields over M as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up of those vector fields that preserve the contact structure defined by \alpha. If we consider symmetric Tensor fields with coefficients in Tensor densities (also called symbols), the vertical cotangent lift of the contact form \alpha defines a contact invariant operator. We also extend the classical contact Hamiltonian to the space of symbols. This generalized Hamiltonian operator on the space of symbols is invariant with respect to the action of the projective contact algebra sp(2n+2) the algebra of vector fields which preserve both the contact structure and the projective structure of the Euclidean space. These two operators lead to a decomposition of the space of symbols, except for some critical density weights, which generalizes a splitting proposed by V. Ovsienko.Peer reviewe

  • Decomposition of symmetric Tensor fields in the presence of a flat contact projective structure
    'Atlantis Press', 2008
    Co-Authors: Fregier Yael, Mathonet Pierre, Poncin Norbert
    Abstract:

    peer reviewedaudience: researcherLet M be an odd-dimensional Euclidean space endowed with a contact 1-form \alpha. We investigate the space of symmetric Contravariant Tensor fields over M as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up of those vector fields that preserve the contact structure defined by \alpha. If we consider symmetric Tensor fields with coefficients in Tensor densities (also called symbols), the vertical cotangent lift of the contact form \alpha defines a contact invariant operator. We also extend the classical contact Hamiltonian to the space of symbols. This generalized Hamiltonian operator on the space of symbols is invariant with respect to the action of the projective contact algebra sp(2n+2) the algebra of vector fields which preserve both the contact structure and the projective structure of the Euclidean space. These two operators lead to a decomposition of the space of symbols, except for some critical density weights, which generalizes a splitting proposed by V. Ovsienko

  • Decomposition of symmetric Tensor fields in the presence of a flat contact projective structure
    'Atlantis Press', 2007
    Co-Authors: Fregier Yael, Mathonet Pierre, Poncin Norbert
    Abstract:

    Let $M$ be an odd-dimensional Euclidean space endowed with a contact 1-form $\alpha$. We investigate the space of symmetric Contravariant Tensor fields on $M$ as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up by those vector fields that preserve the contact structure. If we consider symmetric Tensor fields with coefficients in Tensor densities, the vertical cotangent lift of contact form $\alpha$ is a contact invariant operator. We also extend the classical contact Hamiltonian to the space of symmetric density valued Tensor fields. This generalized Hamiltonian operator on the symbol space is invariant with respect to the action of the projective contact algebra $sp(2n+2)$. The preceding invariant operators lead to a decomposition of the symbol space (expect for some critical density weights), which generalizes a splitting proposed by V. Ovsienko

Fregier Yael - One of the best experts on this subject based on the ideXlab platform.

  • Decomposition of symmetric Tensor fields in the presence of a flat contact projective structure
    2008
    Co-Authors: Fregier Yael, Mathonet Pierre, Poncin Norbert
    Abstract:

    Let M be an odd-dimensional Euclidean space endowed with a contact 1-form \alpha. We investigate the space of symmetric Contravariant Tensor fields over M as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up of those vector fields that preserve the contact structure defined by \alpha. If we consider symmetric Tensor fields with coefficients in Tensor densities (also called symbols), the vertical cotangent lift of the contact form \alpha defines a contact invariant operator. We also extend the classical contact Hamiltonian to the space of symbols. This generalized Hamiltonian operator on the space of symbols is invariant with respect to the action of the projective contact algebra sp(2n+2) the algebra of vector fields which preserve both the contact structure and the projective structure of the Euclidean space. These two operators lead to a decomposition of the space of symbols, except for some critical density weights, which generalizes a splitting proposed by V. Ovsienko.Peer reviewe

  • Decomposition of symmetric Tensor fields in the presence of a flat contact projective structure
    'Atlantis Press', 2008
    Co-Authors: Fregier Yael, Mathonet Pierre, Poncin Norbert
    Abstract:

    peer reviewedaudience: researcherLet M be an odd-dimensional Euclidean space endowed with a contact 1-form \alpha. We investigate the space of symmetric Contravariant Tensor fields over M as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up of those vector fields that preserve the contact structure defined by \alpha. If we consider symmetric Tensor fields with coefficients in Tensor densities (also called symbols), the vertical cotangent lift of the contact form \alpha defines a contact invariant operator. We also extend the classical contact Hamiltonian to the space of symbols. This generalized Hamiltonian operator on the space of symbols is invariant with respect to the action of the projective contact algebra sp(2n+2) the algebra of vector fields which preserve both the contact structure and the projective structure of the Euclidean space. These two operators lead to a decomposition of the space of symbols, except for some critical density weights, which generalizes a splitting proposed by V. Ovsienko

  • Decomposition of symmetric Tensor fields in the presence of a flat contact projective structure
    'Atlantis Press', 2007
    Co-Authors: Fregier Yael, Mathonet Pierre, Poncin Norbert
    Abstract:

    Let $M$ be an odd-dimensional Euclidean space endowed with a contact 1-form $\alpha$. We investigate the space of symmetric Contravariant Tensor fields on $M$ as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up by those vector fields that preserve the contact structure. If we consider symmetric Tensor fields with coefficients in Tensor densities, the vertical cotangent lift of contact form $\alpha$ is a contact invariant operator. We also extend the classical contact Hamiltonian to the space of symmetric density valued Tensor fields. This generalized Hamiltonian operator on the symbol space is invariant with respect to the action of the projective contact algebra $sp(2n+2)$. The preceding invariant operators lead to a decomposition of the symbol space (expect for some critical density weights), which generalizes a splitting proposed by V. Ovsienko

N. Poncin - One of the best experts on this subject based on the ideXlab platform.

  • Poncin N., Decomposition of symmetric Tensor fields in the presence of a flat contact projective structure
    2012
    Co-Authors: Y. Frégier, P. Mathonet, N. Poncin
    Abstract:

    Abstract. Let M be an odd-dimensional Euclidean space endowed with a contact 1-form α. We investigate the space of symmetric Contravariant Tensor fields over M as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up of those vector fields that preserve the contact structure. If we consider symmetric Tensor fields with coefficients in Tensor densities (also called symbols), the vertical cotangent lift of the contact form α is a contact invariant operator. We also extend the classical contact Hamiltonian to the space of symmetric density valued Tensor fields. This generalized Hamiltonian operator on the space of symbols is invariant with respect to the action of the projective contact algebra sp(2n+2). These two operators lead to a decomposition of the space of symbols (except for some critical density weights), which generalizes a splitting proposed by V. Ovsienko in [18]. 1

  • Poncin N., Decomposition of symmetric Tensor fields in the presence of a flat contact projective structure
    2012
    Co-Authors: Y. Frégier, P. Mathonet, N. Poncin
    Abstract:

    Abstract. Let M be an odd-dimensional Euclidean space endowed with a contact 1-form α. We investigate the space of symmetric Contravariant Tensor fields on M as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up by those vector fields that preserve the contact structure. If we consider symmetric Tensor fields with coefficients in Tensor densities, the vertical cotangent lift of contact form α is a contact invariant operator. We also extend the classical contact Hamiltonian to the space of symmetric density valued Tensor fields. This generalized Hamiltonian operator on the symbol space is invariant with respect to the action of the projective contact algebra sp(2n + 2). The preceding invariant operators lead to a decomposition of the symbol space (expect for some critical density weights), which generalizes a splitting proposed by V. Ovsienko. 1