Multivector Fields of Noether Symmetries in the Lagrangian Formalism and Belinfante Tensor

2021 ◽  
Vol 61 ◽  
pp. 53-78
Author(s):  
Halima Loumi-Fergane ◽  
Keyword(s):  
Angular Momentum ◽  
Energy Momentum Tensor ◽  
Internal Symmetry ◽  
Momentum Tensor ◽  
Gauge Fields ◽  
Lagrangian Formalism ◽  
Order Partial Differential Equation ◽  
Spin Angular Momentum ◽  
Relativistic Mechanic ◽  
Invariant Gauge

Elsewhere, we gave the explicit expressions of the multivectors fields associated to infinitesimal symmetries which gave rise to Noether currents for classical field theories and relativistic mechanic using the Second Order Partial Differential Equation SOPDE condition for the Poincar\'e-Cartan form.\\ The main objective of this paper is to reformulate the multivector fields associated to translational and rotational symmetries of the gauge fields in particular those of the electromagnetic field which gave rise to symmetrical and invariant gauge energy-momentum tensor and the orbital angular momentum. The spin angular momentum appears however because of the internal symmetry inside the fiber.

On Hypermomentum in General Relativity I. The Notion of Hypermomentum

1976 ◽  
Vol 31 (2) ◽  
pp. 111-114 ◽  
Author(s):  
Friedrich W. Hehl ◽  
G. David Kerlick ◽  
Paul von der Heyde
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Angular Momentum ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Spin Angular Momentum ◽  
Relativistic Field ◽  
Rank Tensor ◽  
General Relativistic ◽  
Matter Fields

Abstract In this series of notes, we introduce a new quantity into the theory of classical matter fields. Besides the usual energy-momentum tensor, we postulate the existence of a further dynamical attribute of matter, the 3rd rank tensor ⊿ijk of hypermomentum. Subsequently, a general relativistic field theory of energy-momentum and hypermomentum is outlined. In Part I we motivate the need for hypermomentum. We split it into spin angular momentum, the dilatation hypermomentum, and traceless proper hypermomentum and discuss their physical meanings and conservation laws.

scholarly journals Energy-momentum tensor and helicity for gauge fields coupled to a pseudoscalar inflaton

2019 ◽  
Vol 100 (12) ◽  
Author(s):  
M. Ballardini ◽  
M. Braglia ◽  
F. Finelli ◽  
G. Marozzi ◽  
A. A. Starobinsky
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Gauge Fields

scholarly journals Observables for Quarks and Gluons Orbital Angular Momentum Distributions

2015 ◽  
Vol 37 ◽  
pp. 1560039
Author(s):  
Simonetta Liuti ◽  
Aurore Courtoy ◽  
Gary R. Goldstein ◽  
J. Osvaldo Gonzalez Hernandez ◽  
Abha Rajan
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Spin Asymmetry ◽  
Energy Momentum Tensor ◽  
Deeply Virtual Compton Scattering ◽  
Virtual Compton Scattering ◽  
Momentum Tensor ◽  
Transverse Momentum Distribution ◽  
Kinetic Term ◽  
Momentum Distributions

We discuss the observables that have been recently put forth to describe quarks and gluons orbital angular momentum distributions. Starting from a standard parameterization of the energy momentum tensor in QCD one can single out two forms of angular momentum, a so-called kinetic term – Ji decomposition – or a canonical term – Jaffe-Manohar decomposition. Orbital angular momentum has been connected in each decomposition to a different observable, a Generalized Transverse Momentum Distribution (GTMD), for the canonical term, and a twist three Generalized Parton Distribution (GPD) for the kinetic term. While the latter appears as an azimuthal angular modulation in the longitudinal target spin asymmetry in deeply virtual Compton scattering, due to parity constraints, the GTMD associated with canonical angular momentum cannot be measured in a similar set of experiments.

The Maxwell equations

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Variational Principle ◽  
Maxwell Equations ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Field Energy ◽  
Total Charge ◽  
Faraday’S Law ◽  
System Energy

This chapter presents Maxwell equations determining the electromagnetic field created by an ensemble of charges. It also derives these equations from the variational principle. The chapter studies the equation’s invariances: gauge invariance and invariance under Poincaré transformations. These allow us to derive the conservation laws for the total charge of the system and also for the system energy, momentum, and angular momentum. To begin, the chapter introduces the first group of Maxwell equations: Gauss’s law of magnetism, and Faraday’s law of induction. It then discusses current and charge conservation, a second set of Maxwell equations, and finally the field–energy momentum tensor.

scholarly journals BRANEWORLDS AND DARK MATTER

2011 ◽  
Vol 20 (01) ◽  
pp. 77-91 ◽  
Author(s):  
SHAHAB SHAHIDI ◽  
HAMID REZA SEPANGI
Keyword(s):  
Dark Matter ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Gauge Fields ◽  
Anisotropic Energy ◽  
The Galaxy ◽  
Virial Mass ◽  
Braneworld Model ◽  
Geometrical Term ◽  
Galaxy Rotation Curves

Two problems related to dark matter are considered in the context of a braneworld model in which the confinement of gauge fields on the brane is achieved by invoking a confining potential. First, we show that the virial mass discrepancy can be addressed if the conserved geometrical term appearing in this model is considered as an energy–momentum tensor of an unknown type of matter, the so-called X-matter whose equation of state (EoS) is also obtained. Second, the galaxy rotation curves are explained by assuming an anisotropic energy–momentum tensor for the X-matter.

scholarly journals ON THE NATURAL GAUGE FIELDS OF MANIFOLDS

2000 ◽  
Vol 15 (32) ◽  
pp. 1991-2005 ◽  
Author(s):  
A. B. PESTOV ◽  
BIJAN SAHA
Keyword(s):  
Displacement Field ◽  
Energy Momentum Tensor ◽  
Linear Connection ◽  
Momentum Tensor ◽  
Gauge Fields ◽  
Spherically Symmetric ◽  
Time Inversion ◽  
Field Equations ◽  
Gauge Invariant ◽  
Minkowski Space Time

The gauge symmetry inherent in the concept of manifold has been discussed. Within the scope of this symmetry the linear connection or displacement field can be considered as a natural gauge field on the manifold. The gauge-invariant equations for the displacement field have been derived. It has been shown that the energy–momentum tensor of this field conserves and hence the displacement field can be treated as one that transports energy and gravitates. To show the existence of the solutions of the field equations, we have derived the general form of the displacement field in Minkowski space–time which is invariant under rotation and space and time inversion. With this ansatz we found spherically-symmetric solutions of the equations in question.

scholarly journals On the theory of point-particles

1944 ◽  
Vol 183 (993) ◽  
pp. 134-141 ◽  
Keyword(s):  
Angular Momentum ◽  
Energy Momentum Tensor ◽  
Proper Time ◽  
World Line ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Singular Terms ◽  
Point Particles ◽  
The World ◽  
Energy And Momentum

It is deduced from the conservation of the energy -momentum tensor that if the flow of energy and momentum into a tube surrounding a time-like world-line, on which the field is singular, become singular as the size of the tube is contracted to zero, then the singular terms are necessarily perfect differentials of quantities on the world-line with respect to the proper time along the world-line. The same can be proved of any other tensor, as, for example, the angular-momentum tensor, which is conserved. It is proved from this that for any point -particle whatever having charge, spin or other properties, which need not be specified, it is always possible to deduce exact equations of motion which are finite. It is proved further that if the energy-momentum tensor is altered by the addition of ∂ K μvσ /∂x σ , where K μvσ is any tensor antisymmetric in v and σ , then the equations of motion are unaltered, but it is possible to choose K μvσ in such a way as to make the flow of energy and momentum into a given tube non-singular.

On the theory of spinning particles

1947 ◽  
Vol 43 (1) ◽  
pp. 106-117 ◽  
Author(s):  
S. Shanmugadhasan
Keyword(s):  
Electromagnetic Field ◽  
Dipole Moment ◽  
Angular Momentum ◽  
Quantum Theory ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Hamiltonian Equation ◽  
Hamiltonian Form ◽  
Spin Angular Momentum ◽  
Spinning Particle

A classical theory of a spinning particle with charge and dipole moment in an electromagnetic field is obtained by working symmetrically with respect to retarded and advanced fields, and with respect to the ingoing and outgoing fields. The equations are in a simpler form than those of Bhabha and Corben or those of Bhabha, and involve fewer constants. On the assumption that the spin angular momentum tensor θμν satisfies the equation θ2 ≡ θμν θμν = constant, the value of the dipole moment Zμν is chosen to be Cθμν, where C is a constant. The theory is generalized to the case of several particles with charge and dipole moment. By using a suitable Hamiltonian equation, the classical equations of motion, obtained on the assumption that θ is a constant, are put into Hamiltonian form by means of the ‘Wentzel field’ and the λ-limiting process. The passage to the quantum theory is effected by the usual rules of quantization. The theory is extended to the case of particles with charge and dipole moment in the generalized wave field by defining the Wentzel potential in terms of the generalized relativistic δ-function.

Hard thermal loops and their Noether currents

1993 ◽  
Vol 71 (5-6) ◽  
pp. 300-305 ◽  
Author(s):  
H. Arthur Weldon
Keyword(s):  
Angular Momentum ◽  
Effective Action ◽  
Energy Momentum Tensor ◽  
Axial Vector ◽  
Momentum Density ◽  
Momentum Tensor ◽  
Field Equations ◽  
Nonlocal Field ◽  
N Vector ◽  
Hard Thermal Loops

The effective action found by Braaten and Pisarski, and by Frenkel, Taylor, and Wong that summarizes all hard thermal loops is investigated. Nonlocal field equations for ψ and Aμ are derived. Nonlocal forms are constructed for the U(1)-vector and axial-vector currents, the SU(N)-vector and axial-vector currents, the energy-momentum tensor, and the angular momentum density.

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