Cauchy data space and multisymplectic formulation of conformal 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.

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Gauged double field theory as an L∞ algebra

Journal of High Energy Physics ◽

10.1007/jhep06(2021)058 ◽

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.

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

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887816400016 ◽

2016 ◽

Vol 13 (08) ◽

pp. 1640001 ◽

Cited By ~ 2

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.

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

Theoretical and Applied Mechanics ◽

10.2298/tam1201055m ◽

2012 ◽

Vol 39 (1) ◽

pp. 55-69 ◽

Cited By ~ 2

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.

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HAMILTON–JACOBI THEORY IN k-COSYMPLECTIC FIELD THEORIES

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887814500078 ◽

2013 ◽

Vol 11 (01) ◽

pp. 1450007 ◽

Cited By ~ 9

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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