Theory of collective magnetic excitations in strong crystal fields. I. Dynamics of the angular momentum tensor operators

1975 ◽  
Vol 12 (3) ◽  
pp. 1021-1028 ◽  
Author(s):  
T. Egami ◽  
M. S. S. Brooks
Keyword(s):  
Angular Momentum ◽  
Momentum Tensor ◽  
Magnetic Excitations ◽  
Crystal Fields ◽  
Tensor Operators

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.

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.

Raman Scattering by Magnetic Excitations in Diluted Magnetic Semiconductors

1986 ◽  
Vol 89 ◽  
Author(s):  
A. K. Ramdas ◽  
S. Rodriguez
Keyword(s):  
Angular Momentum ◽  
Raman Scattering ◽  
Diluted Magnetic Semiconductors ◽  
Magnetic Semiconductors ◽  
Total Spin ◽  
Electromagnetic Spectrum ◽  
Significant Information ◽  
Magnetic Excitations ◽  
Microscopic Models ◽  
Diluted Magnetic

AbstractRaman scattering provides significant information on the nature of the magnetic excitations of diluted magnetic semiconductors (DMS). Transitions involving an exchange of a quantum of angular momentum between the system and the radiation field result in Raman lines with shifts equal to the energy of the magnetic excitations in which the total spin of the crystal changes by ħ. Such transitions have a one-to-one correspondence with those seen in magnetic resonance but observed in the optical rather than in the microwave region of the electromagnetic spectrum. In the Mn-based II-VI DMS a variety of magnetic excitations have been observed in their Raman spectra. Microscopic models underlying these phenomena provide powerful insights into the nature of the magnetism of DMS.

MOMENTUM MAPS, INDEPENDENT FIRST INTEGRALS AND INTEGRABILITY FOR CENTRAL POTENTIALS

2009 ◽  
Vol 06 (08) ◽  
pp. 1323-1341 ◽  
Author(s):  
EMANUELE FIORANI
Keyword(s):  
Angular Momentum ◽  
First Integral ◽  
Functional Independence ◽  
Negative Energy ◽  
Momentum Tensor ◽  
First Integrals ◽  
Central Potential ◽  
Momentum Maps ◽  
Kepler System ◽  
Natural Symmetry

It is shown that all the motions of a natural Hamiltonian H(q, p) = ½‖p‖2+V(q) lie on planes through 0 ∈ Rn if and only if V is a central potential, i.e. H admits SO(n) symmetry. Then, using the momentum maps associated to their natural symmetry groups, we study in detail the functional independence of first integrals of a general central potential, of the isotropic harmonic potential and of the Kepler potential. We show that all the smooth first integral of the isotropic harmonic oscillator are dependent of the angular momentum tensor L and of the Fradkin tensor H, and that all the smooth first integrals of the Kepler system on the region of negative energy are dependent of the angular momentum tensor L and of the Laplace–Runge–Lenz vector B.

scholarly journals On the angular momentum and spin of generalized electromagnetic field for r-vectors in (k, n) space-time dimensions

2021 ◽  
Vol 136 (10) ◽  
Author(s):  
Alfonso Martinez ◽  
Ivano Colombaro ◽  
Josep Font-Segura
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Normal Modes ◽  
Natural Generalization ◽  
Momentum Tensor ◽  
Space Time ◽  
Time Coordinate ◽  
Complex Valued

AbstractThis paper studies the relativistic angular momentum for the generalized electromagnetic field, described by r-vectors in (k, n) space-time dimensions, with exterior-algebraic methods. First, the angular-momentum tensor is derived from the invariance of the Lagrangian to space-time rotations (Lorentz transformations), avoiding the explicit need of the canonical tensor in Noether’s theorem. The derivation proves the conservation law of angular momentum for generic values of r, k, and n. Second, an integral expression for the flux of the tensor across a $$(k+n-1)$$ ( k + n - 1 ) -dimensional surface of constant $$\ell $$ ℓ -th space-time coordinate is provided in terms of the normal modes of the field; this analysis is a natural generalization of the standard analysis of electromagnetism, i. e. a three-dimensional space integral at constant time. Third, a brief discussion on the orbital angular momentum and the spin of the generalized electromagnetic field, including their expression in complex-valued circular polarizations, is provided for generic values of r, k, and n.

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