scholarly journals SYMMETRIES AND CONSERVATION LAWS IN THE GÜNTHER k-SYMPLECTIC FORMALISM OF FIELD THEORY

2007 ◽  
Vol 19 (10) ◽  
pp. 1117-1147 ◽  
Author(s):  
NARCISO ROMÁN-ROY ◽  
MODESTO SALGADO ◽  
SILVIA VILARIÑO
Keyword(s):  
Field Theory ◽  
Conservation Laws ◽  
Classical Field ◽  
Field Theories ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
First Order ◽  
Gauge Symmetries ◽  
Classical Field Theories

This paper is devoted to studying symmetries of k-symplectic Hamiltonian and Lagrangian first-order classical field theories. In particular, we define symmetries and Cartan symmetries and study the problem of associating conservation laws to these symmetries, stating and proving Noether's theorem in different situations for the Hamiltonian and Lagrangian cases. We also characterize equivalent Lagrangians, which lead to an introduction of Lagrangian gauge symmetries, as well as analyzing their relation with Cartan symmetries.

scholarly journals A geometrical analysis of the field equations in field theory

2002 ◽  
Vol 29 (12) ◽  
pp. 687-699 ◽  
Author(s):  
A. Echeverría-Enríquez ◽  
M. C. Muñoz-Lecanda ◽  
N. Román-Roy
Keyword(s):  
Field Theory ◽  
Classical Field ◽  
Field Theories ◽  
Geometrical Analysis ◽  
Field Equations ◽  
First Order ◽  
Nonuniqueness Of Solutions ◽  
Lagrangian And Hamiltonian Formalisms ◽  
Classical Field Theories ◽  
Geometric Formulation

We give a geometric formulation of the field equations in the Lagrangian and Hamiltonian formalisms of classical field theories (of first order) in terms of multivector fields. This formulation enables us to discuss the existence and nonuniqueness of solutions of these equations, as well as their integrability.

scholarly journals HIGHER-ORDER NOETHER SYMMETRIES IN k-SYMPLECTIC HAMILTONIAN FIELD THEORY

2013 ◽  
Vol 10 (08) ◽  
pp. 1360013
Author(s):  
NARCISO ROMÁN-ROY ◽  
MODESTO SALGADO ◽  
SILVIA VILARIÑO
Keyword(s):  
Field Theory ◽  
Conservation Laws ◽  
Vector Fields ◽  
Higher Order ◽  
Field Theories ◽  
Noether Symmetries ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Infinitesimal Transformations

For k-symplectic Hamiltonian field theories, we study infinitesimal transformations generated by some kinds of vector fields which are not Noether symmetries, but which allow us to obtain conservation laws by means of suitable generalizations of Noether's theorem.

scholarly journals SYMMETRIES IN CLASSICAL FIELD THEORY

2004 ◽  
Vol 01 (05) ◽  
pp. 651-710 ◽  
Author(s):  
MANUEL DE LEÓN ◽  
DAVID MARTÍN DE DIEGO ◽  
AITOR SANTAMARÍA-MERINO
Keyword(s):  
Field Theory ◽  
Conservation Laws ◽  
Classical Field Theory ◽  
Cauchy Data ◽  
Classical Field ◽  
Field Theories ◽  
Classical Field Theories

The multisymplectic description of Classical Field Theories is revisited, including its relation with the presymplectic formalism on the space of Cauchy data. Both descriptions allow us to give a complete scheme of classification of infinitesimal symmetries, and to obtain the corresponding conservation laws.

scholarly journals Gauged double field theory as an L∞ algebra

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Eric Lescano ◽  
Martín Mayo
Keyword(s):  
Field Theory ◽  
Algebraic Structure ◽  
Classical Field ◽  
Field Theories ◽  
Lie Derivative ◽  
Linear Perturbation ◽  
Double Field Theory ◽  
Generalized Frame ◽  
Symmetry Transformations ◽  
Classical Field Theories

Abstract L∞ algebras describe the underlying algebraic structure of many consistent classical field theories. In this work we analyze the algebraic structure of Gauged Double Field Theory in the generalized flux formalism. The symmetry transformations consist of a generalized deformed Lie derivative and double Lorentz transformations. We obtain all the non-trivial products in a closed form considering a generalized Kerr-Schild ansatz for the generalized frame and we include a linear perturbation for the generalized dilaton. The off-shell structure can be cast in an L3 algebra and when one considers dynamics the former is exactly promoted to an L4 algebra. The present computations show the fully algebraic structure of the fundamental charged heterotic string and the $$ {L}_3^{\mathrm{gauge}} $$ L 3 gauge structure of (Bosonic) Enhanced Double Field Theory.

scholarly journals Lagrangian constraint analysis of first-order classical field theories with an application to gravity

2020 ◽  
Vol 102 (6) ◽  
Author(s):  
Verónica Errasti Díez ◽  
Markus Maier ◽  
Julio A. Méndez-Zavaleta ◽  
Mojtaba Taslimi Tehrani
Keyword(s):  
Classical Field ◽  
Field Theories ◽  
First Order ◽  
Constraint Analysis ◽  
Classical Field Theories

scholarly journals A new application of k-symplectic Lie systems

2015 ◽  
Vol 12 (07) ◽  
pp. 1550071 ◽  
Author(s):  
Javier de Lucas ◽  
Mariusz Tobolski ◽  
Silvia Vilariño
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Classical Field ◽  
Diffusion Equations ◽  
Field Theories ◽  
Symplectic Structures ◽  
First Order ◽  
Classical Field Theories ◽  
Lie Systems ◽  
Geometric Study

The k-symplectic structures appear in the geometric study of the partial differential equations of classical field theories. Meanwhile, we present a new application of the k-symplectic structures to investigate a certain type of systems of first-order ordinary differential equations, the k-symplectic Lie systems. In particular, we analyze the properties, e.g., the superposition rules, of a new example of k-symplectic Lie system which occurs in the analysis of diffusion equations.

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