scholarly journals Variational derivatives in locally Lagrangian field theories and Noether–Bessel-Hagen currents

2016 ◽  
Vol 13 (08) ◽  
pp. 1650067 ◽  
Author(s):  
Francesco Cattafi ◽  
Marcella Palese ◽  
Ekkehart Winterroth
Keyword(s):  
Conserved Quantity ◽  
Field Theories ◽  
Lie Derivative ◽  
Generalized Symmetry ◽  
Variational Sequence ◽  
Variational Derivatives ◽  
Noether Current

The variational Lie derivative of classes of forms in the Krupka’s variational sequence is defined as a variational Cartan formula at any degree, in particular for degrees lesser than the dimension of the basis manifold. As an example of application, we determine the condition for a Noether–Bessel-Hagen current, associated with a generalized symmetry, to be variationally equivalent to a Noether current for an invariant Lagrangian. We show that, if it exists, this Noether current is exact on-shell and generates a canonical conserved quantity.

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.

NON-EINSTEINIAN GRAVITY IN d=2: SYMMETRY AND CURRENT ALGEBRA

1994 ◽  
Vol 09 (15) ◽  
pp. 1407-1413 ◽  
Author(s):  
W. KUMMER ◽  
P. WIDERIN
Keyword(s):  
Phase Space ◽  
Current Algebra ◽  
Geometric Theory ◽  
Conserved Quantity ◽  
Global Symmetry ◽  
Field Dependent ◽  
A Current ◽  
Noether Current

For a geometric theory with dynamical torsion an absolutely conserved quantity can be related to a Noether current for a peculiar field dependent off-shell (global) symmetry. Moreover the nonlinear deformed iso(2,1) symmetry in phase space discovered previously, for which that conserved quantity is one element of the center, can be reinterpreted as a current algebra.

scholarly journals CONSERVED QUANTITIES ON MULTISYMPLECTIC MANIFOLDS

2018 ◽  
Vol 108 (1) ◽  
pp. 120-144 ◽  
Author(s):  
LEONID RYVKIN ◽  
TILMANN WURZBACHER ◽  
MARCO ZAMBON
Keyword(s):  
Symplectic Geometry ◽  
Vector Fields ◽  
General Setting ◽  
Conserved Quantity ◽  
Lie Derivative ◽  
Conserved Quantities ◽  
Hamiltonian Vector Fields ◽  
Special Case ◽  
Group Of Symmetries ◽  
Circulation Theorem

Given a vector field on a manifold $M$, we define a globally conserved quantity to be a differential form whose Lie derivative is exact. Integrals of conserved quantities over suitable submanifolds are constant under time evolution, the Kelvin circulation theorem being a well-known special case. More generally, conserved quantities are well behaved under transgression to spaces of maps into $M$. We focus on the case of multisymplectic manifolds and Hamiltonian vector fields. Our main result is that in the presence of a Lie group of symmetries admitting a homotopy co-momentum map, one obtains a whole family of globally conserved quantities. This extends a classical result in symplectic geometry. We carry this out in a general setting, considering several variants of the notion of globally conserved quantity.

scholarly journals Variations by generalized symmetries of local Noether strong currents equivalent to global canonical Noether currents

2016 ◽  
Vol 24 (2) ◽  
pp. 125-135
Author(s):  
Marcella Palese
Keyword(s):  
Inverse Problem ◽  
Variational Problem ◽  
Cohomology Class ◽  
Lie Derivative ◽  
Local Problem ◽  
Variational Derivative ◽  
Field Equations ◽  
Invariance Properties ◽  
Generalized Symmetries ◽  
Variational Sequence

Abstract We will pose the inverse problem question within the Krupka variational sequence framework. In particular, the interplay of inverse problems with symmetry and invariance properties will be exploited considering that the cohomology class of the variational Lie derivative of an equivalence class of forms, closed in the variational sequence, is trivial. We will focalize on the case of symmetries of globally defined field equations which are only locally variational and prove that variations of local Noether strong currents are variationally equivalent to global canonical Noether currents. Variations, taken to be generalized symmetries and also belonging to the kernel of the second variational derivative of the local problem, generate canonical Noether currents - associated with variations of local Lagrangians - which in particular turn out to be conserved along any section. We also characterize the variation of the canonical Noether currents associated with a local variational problem.

scholarly journals Conservation laws and variational sequences in gauge-natural theories

2001 ◽  
Vol 130 (3) ◽  
pp. 555-569 ◽  
Author(s):  
L. FATIBENE ◽  
M. FRANCAVIGLIA ◽  
M. PALESE
Keyword(s):  
Conservation Laws ◽  
General Setting ◽  
Symmetric Tensor ◽  
Field Theories ◽  
Lie Derivative ◽  
Derivative Operator ◽  
Tensor Density ◽  
Conserved Currents ◽  
Natural Bundle ◽  
Suitable Vector

In the classical Lagrangian approach to conservation laws of gauge-natural field theories a suitable vector density is known to generate the so-called conserved Noether currents. It turns out that along any section of the relevant gauge-natural bundle this density is the divergence of a skew-symmetric tensor density, which is called a superpotential for the conserved currents.We describe gauge-natural superpotentials in the framework of finite order variational sequences according to Krupka. We refer to previous results of ours on variational Lie derivatives concerning abstract versions of Noether's theorems, which are here interpreted in terms of ‘horizontal’ and ‘vertical’ conserved currents. The gauge-natural lift of principal automorphisms implies suitable linearity properties of the Lie derivative operator. Thus abstract results due to Kolář, concerning the integration by parts procedure, can be applied to prove the existence and globality of superpotentials in a very general setting.

Beyond the Standard Model

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Supergravity Models ◽  
Standard Model ◽  
Field Theories ◽  
Beyond The Standard Model ◽  
Super Symmetry ◽  
The Standard Model ◽  
Topological Field ◽  
Supersymmetric Theories

The motivation for supersymmetry. The algebra, the superspace, and the representations. Field theory models and the non-renormalisation theorems. Spontaneous and explicit breaking of super-symmetry. The generalisation of the Montonen–Olive duality conjecture in supersymmetric theories. The remarkable properties of extended supersymmetric theories. A brief discussion of twisted supersymmetry in connection with topological field theories. Attempts to build a supersymmetric extention of the standard model and its experimental consequences. The property of gauge supersymmetry to include general relativity and the supergravity models.

Introduction

2018 ◽  
Author(s):  
Marjorie Levinson
Keyword(s):  
Modern Philosophy ◽  
Early Modern ◽  
Martin Heidegger ◽  
Conceptual Structure ◽  
Field Theories ◽  
Self Organization ◽  
Physical Sciences ◽  
Early Modern Philosophy

The Introduction explains the combination of a narrative arc and conceptual structure in the organization of the book. The former, primarily diachronic, discussion is concerned with the development of the field of Romanticism since the 1980s, presented through both a review of scholarship and exemplary readings of well-known lyric poems. The latter, predominantly synchronic, presentation entails an argument for the analytical value of field theories of form—that is, frameworks drawn from early modern philosophy (Spinoza) and postclassical life- and physical sciences, especially models of self-organization. As an alternative to the external, retrospective perspective provided by, for example, Rita Felski in The Limits of Critique, it draws on the work of Martin Heidegger, Pierre Macherey, and the poet-critic J. H. Prynne to offer a conjunctural approach.

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