Search results for "Noether's theorem"
showing 10 items of 26 documents
Cubic interactions of Maxwell-like higher spins
2017
We study the cubic vertices for Maxwell-like higher-spins in flat and (A)dS background spaces of any dimension. Reducibility of their free spectra implies that a single cubic vertex involving any three fields subsumes a number of couplings among different particles of various spins. The resulting vertices do not involve traces of the fields and in this sense are simpler than their Fronsdal counterparts. We propose an extension of both the free theory and of its cubic deformation to a more general class of partially reducible systems, that one can obtain from the original theory upon imposing trace constraints of various orders. The key to our results is a version of the Noether procedure al…
Cohomological analysis of gauged-fixed gauge theories
1999
The relation between the gauge-invariant local BRST cohomology involving the antifields and the gauge-fixed BRST cohomology is clarified. It is shown in particular that the cocycle conditions become equivalent once it is imposed, on the gauge-fixed side, that the BRST cocycles should yield deformations that preserve the nilpotency of the (gauge-fixed) BRST differential. This shows that the restrictions imposed on local counterterms by the Quantum Noether condition in the Epstein--Glaser construction of gauge theories are equivalent to the restrictions imposed by BRST invariance on local counterterms in the standard Lagrangian approach.
Lorentz harmonics and superfield action. D=10, N=1 superstring
2000
We propose a new version of the superfield action for a closed D=10, N=1 superstring where the Lorentz harmonics are used as auxiliary superfields. The incorporation of Lorentz harmonics into the superfield action makes possible to obtain superfield constraints of the induced worldsheet supergravity as equations of motion. Moreover, it becomes evident that a so-called 'Wess-Zumino part' of the superfield action is basically a Lagrangian form of the generalized action principle. We propose to use the second Noether theorem to handle the essential terms in the transformation lows of hidden gauge symmetries, which remove dynamical degrees of freedom from the Lagrange multiplier superfield.
Quasi-Lie Brackets and the Breaking of Time-Translation Symmetry for Quantum Systems Embedded in Classical Baths
2018
Many open quantum systems encountered in both natural and synthetic situations are embedded in classical-like baths. Often, the bath degrees of freedom may be represented in terms of canonically conjugate coordinates, but in some cases they may require a non-canonical or non-Hamiltonian representation. Herein, we review an approach to the dynamics and statistical mechanics of quantum subsystems embedded in either non-canonical or non-Hamiltonian classical-like baths which is based on operator-valued quasi-probability functions. These functions typically evolve through the action of quasi-Lie brackets and their associated Quantum-Classical Liouville Equations, or through quasi-Lie brackets a…
Lagrangian dynamics and possible isochronous behavior in several classes of non-linear second order oscillators via the use of Jacobi last multiplier
2015
Abstract In this paper, we employ the technique of Jacobi Last Multiplier (JLM) to derive Lagrangians for several important and topical classes of non-linear second-order oscillators, including systems with variable and parametric dissipation, a generalized anharmonic oscillator, and a generalized Lane–Emden equation. For several of these systems, it is very difficult to obtain the Lagrangians directly, i.e., by solving the inverse problem of matching the Euler–Lagrange equations to the actual oscillator equation. In order to facilitate the derivation of exact solutions, and also investigate possible isochronous behavior in the analyzed systems, we next invoke some recent theoretical result…
Minimal coupling in presence of non-metricity and torsion
2020
We deal with the question of what it means to define a minimal coupling prescription in presence of torsion and/or non-metricity, carefully explaining while the naive substitution $\partial\to\na$ introduces extra couplings between the matter fields and the connection that can be regarded as non-minimal in presence of torsion and/or non-metricity. We will also investigate whether minimal coupling prescriptions at the level of the action (MCPL) or at the level of field equations (MCPF) lead to different dynamics. To that end, we will first write the Euler-Lagrange equations for matter fields in terms of the covariant derivatives of a general non-Riemannian space, and derivate the form of the…
SUPERFIELDS AND CANONICAL METHODS IN SUPERSPACE
1986
We consider the “supersymmetric roots” of the Heisenberg evolution equation as describing the dynamics of superfields in superspace. We investigate the superfield commutators and their equal time limits and exhibit their noncanonical character even for free superfields. For simplicity, we concentrate on the D=1 case, i.e., the superfield formulation of supersymmetric quantum mechanics in the Heisenberg picture and, as a soluble example, the supersymmetric oscillator. Finally, we express Noether’s theorem in superspace and give the definition of the global conserved supercharges.
Maxwell Theory as a Classical FieldTheory
2012
Hamilton’s variational principle and the Lagrangian mechanics that rests on it are exceedingly successful in their application to mechanical systems with a finite number of degrees of freedom. Hamilton’s principle characterizes the physically realizable orbits, among the set of all possible orbits, as being the critical elements of the action integral. The Lagrangian function, although not an observable on its own, is not only useful in deriving the equations of motion but is also an important tool for identifying symmetries of the theory and constructing the corresponding conserved quantities, via Noether’s theorem.
A new invariant-based method for building biomechanical behavior laws - Application to an anisotropic hyperelastic material with two fiber families
2013
Abstract In this article, we present a general constructive and original approach that allows us to calculate the invariants associated with an anisotropic hyperelastic material made of two families of collagen fibers. This approach is based on mathematical techniques from the theory of invariants: • Definition of the material symmetry group. • Analytical calculation of a set of generators using the Noether’s theorem. • Analytical calculation of an integrity basis. • Comparison between the proposed invariants and the classical ones.
Models as Research Tools: Plücker, Klein, and Kummer Surfaces
2018
In the late summer of 1869, 20-year-old Felix Klein made his way to Berlin, where he planned to attend the renowned seminar founded by Ernst Eduard Kummer and Karl Weierstrass. Klein had already taken his doctorate in Bonn and he would soon be recognized as a leading expert on line geometry, a new approach to 3-space launched by his mentor in Bonn, Julius Plucker. Just before Plucker died in 1868, he entrusted Klein to complete the classic monograph, Neue Geometrie des Raumes gegrundet auf die Betrachtung der geraden Linie als Raumelement. Overall responsibility for this project fell to Alfred Clebsch in Gottingen, which was how Klein first came to the prestigious Georgia Augusta. There he …