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 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.

EXTENDED AFFINE CLASSES OF LAGRANGIANS AND HAMILTONIANS RELATED TO CLASSICAL FIELD THEORIES

2009 ◽  
Vol 06 (07) ◽  
pp. 1161-1180
Author(s):  
CONSTANTIN UDRIŞTE ◽  
MARCELA POPESCU ◽  
PAUL POPESCU
Keyword(s):  
Field Theory ◽  
Classical Field Theory ◽  
Variational Problems ◽  
Classical Field ◽  
Field Theories ◽  
Classical Field Theories

The aim of the paper is to establish a natural affine frame for affine Lagrangians and Hamiltonians, generalizing the well-known classical field theory. Scalar and volume-valued Lagrangians and Hamiltonians can be lifted to the new classes. Using the Hamilton–Jacobi principle, we analyze variational problems corresponding to actions defined by the affine Lagrangians and Hamiltonians. The extremals verify generalizations of the Euler–Lagrange and De Donder–Weyl PDEs. They improve the information about the dynamical solutions of the classical variational problems and refresh the Lagrange–Hamilton theories.

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 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 Jacobi-Lie T-plurality

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Jose J. Fernandez-Melgarejo ◽  
Yuho Sakatani
Keyword(s):  
Field Theory ◽  
Leibniz Algebra ◽  
Lie Derivative ◽  
Lie Bialgebra ◽  
Drinfel’D Double ◽  
Double Field Theory ◽  
Generalized Frame ◽  
Structure Constants ◽  
One To One ◽  
The Spectator

We propose a Leibniz algebra, to be called DD^++, which is a generalization of the Drinfel’d double. We find that there is a one-to-one correspondence between a DD^++ and a Jacobi–Lie bialgebra, extending the known correspondence between a Lie bialgebra and a Drinfel’d double. We then construct generalized frame fields E_A{}^M\in\text{O}(D,D)\times\mathbb{R}^+EAM∈O(D,D)×ℝ+ satisfying the algebra \hat{\pounds}_{E_A}E_B = - X_{AB}{}^C\,E_C£̂EAEB=−XABCEC, where X_{AB}{}^CXABC are the structure constants of the DD^++ and \hat{\pounds}£̂ is the generalized Lie derivative in double field theory. Using the generalized frame fields, we propose the Jacobi–Lie TT-plurality and show that it is a symmetry of double field theory. We present several examples of the Jacobi–Lie TT-plurality with or without Ramond–Ramond fields and the spectator fields.

scholarly journals Energy–momentum tensors in classical field theories — A modern perspective

2016 ◽  
Vol 13 (08) ◽  
pp. 1640001 ◽  
Author(s):  
Nicoleta Voicu
Keyword(s):  
Geometric Approach ◽  
Classical Field ◽  
Field Theories ◽  
Diffeomorphism Invariance ◽  
Type Definition ◽  
Classical Field Theories ◽  
Opening Up ◽  
Hilbert Type ◽  
Modern Perspective

The paper presents a general geometric approach to energy–momentum tensors in Lagrangian field theories, based on a global Hilbert-type definition. The approach is consistent with the ones defining energy–momentum tensors in terms of hypermomentum maps given by the diffeomorphism invariance of the Lagrangian — and, in a sense, complementary to these, with the advantage of an increased simplicity of proofs and also, opening up new insights on the topic. A special attention is paid to the particular cases of metric and metric-affine theories.

scholarly journals Crystal plasticity: The Hamilton-Eshelby stress in terms of the metric in the intermediate configuration

2012 ◽  
Vol 39 (1) ◽  
pp. 55-69 ◽  
Author(s):  
Paolo Mariano
Keyword(s):  
Free Energy ◽  
Energy Momentum Tensor ◽  
Large Strain ◽  
Momentum Tensor ◽  
Classical Field ◽  
Field Theories ◽  
Relative Power ◽  
Eshelby Stress ◽  
Classical Field Theories ◽  
Intermediate Configuration

The Hamilton-Eshelby stress is a basic ingredient in the description of the evolution of point, lines and bulk defects in solids. The link between the Hamilton-Eshelby stress and the derivative of the free energy with respect to the material metric in the plasticized intermediate configuration, in large strain regime, is shown here. The result is a modified version of Rosenfeld-Belinfante theorem in classical field theories. The origin of the appearance of the Hamilton-Eshelby stress (the non-inertial part of the energy-momentum tensor) in dissipative setting is also discussed by means of the concept of relative power.

scholarly journals HAMILTON–JACOBI THEORY IN k-COSYMPLECTIC FIELD THEORIES

2013 ◽  
Vol 11 (01) ◽  
pp. 1450007 ◽  
Author(s):  
MANUEL DE LEÓN ◽  
SILVIA VILARIÑO
Keyword(s):  
Classical Field ◽  
Time Dependent ◽  
Field Theories ◽  
Classical Field Theories

In this paper, we extend the geometric formalism of the Hamilton–Jacobi theory for time-dependent Mechanics to the case of classical field theories in the k-cosymplectic framework.

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