scholarly journals VARIATIONAL PROBLEM FOR THE FRENKEL AND THE BARGMANN–MICHEL–TELEGDI (BMT) EQUATIONS

2013 ◽  
Vol 28 (01) ◽  
pp. 1250234 ◽  
Author(s):  
A. A. DERIGLAZOV
Keyword(s):  
Abelian Group ◽  
Variational Problem ◽  
Classical Theory ◽  
Equations Of Motion ◽  
Lagrangian Formulation ◽  
Gauge Invariant ◽  
Local Symmetries

We propose Lagrangian formulation for the particle with value of spin fixed within the classical theory. The Lagrangian is invariant under non-Abelian group of local symmetries. On this reason, all the initial spin variables turn out to be unobservable quantities. As the gauge-invariant variables for description of spin we can take either the Frenkel tensor or the Bargmann–Michel–Telegdi (BMT) vector. Fixation of spin within the classical theory implies O(ℏ)-corrections to the corresponding equations of motion.

scholarly journals LAGRANGIAN APPROACH OF THE FIRST-CLASS CONSTRAINED SYSTEMS

1998 ◽  
Vol 13 (33) ◽  
pp. 2653-2663 ◽  
Author(s):  
YONG-WAN KIM ◽  
YOUNG-JAI PARK ◽  
SEUNG-KOOK KIM
Keyword(s):  
Hamiltonian Formulation ◽  
Constrained Systems ◽  
Lagrangian Approach ◽  
Lagrangian Formalism ◽  
Exact Form ◽  
Gauge Invariant ◽  
Symmetry Transformations ◽  
Local Symmetries

We show how to systematically derive the exact form of local symmetries for the Abelian Proca and CS models, which are converted into first-class constrained systems by the BFT formalism, in the Lagrangian formalism. As a result, without resorting to a Hamiltonian formulation we obtain the well-known U(1) symmetry for the gauge-invariant Proca model, while showing that for the CS model there exist novel symmetries as well as the usual symmetry transformations.

scholarly journals LOOP VARIABLES AND THE INTERACTING OPEN STRING IN A CURVED BACKGROUND

2005 ◽  
Vol 20 (14) ◽  
pp. 1037-1045
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Gauge Invariance ◽  
Equations Of Motion ◽  
Interaction Strength ◽  
Flat Space ◽  
Open String ◽  
Target Space ◽  
Gauge Invariant ◽  
Free Case ◽  
New Feature ◽  
Generally Covariant

Applying the loop variable proposal to a sigma model (with boundary) in a curved target space, we give a systematic method for writing the gauge and generally covariant interacting equations of motion for the modes of the open string in a curved background. As in the free case described in an earlier paper, the equations are obtained by covariantizing the flat space (gauge invariant) interacting equations and then demanding gauge invariance in the curved background. The resulting equation has the form of a sum of terms that would individually be gauge invariant in flat space or at zero interaction strength, but mix amongst themselves in curved space when interactions are turned on. The new feature is that the loop variables are deformed so that there is a mixing of modes. Unlike the free case, the equations are coupled, and all the modes of the open string are required for gauge invariance.

scholarly journals Lévy differential operators and Gauge invariant equations for Dirac and Higgs fields

2019 ◽  
Vol 22 (01) ◽  
pp. 1950001 ◽  
Author(s):  
Boris O. Volkov
Keyword(s):  
Differential Operators ◽  
Equations Of Motion ◽  
Parallel Transport ◽  
System Of Differential Equations ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Dirac Equations ◽  
Lévy Laplacian ◽  
Higgs Fields

We study the Lévy infinite-dimensional differential operators (differential operators defined by the analogy with the Lévy Laplacian) and their relationship to the Yang–Mills equations. We consider the parallel transport on the space of curves as an infinite-dimensional analogue of chiral fields and show that it is a solution to the system of differential equations if and only if the associated connection is a solution to the Yang–Mills equations. This system is an analogue of the equations of motion of chiral fields and contains the Lévy divergence. The systems of infinite-dimensional equations containing Lévy differential operators, that are equivalent to the Yang–Mills–Higgs equations and the Yang–Mills–Dirac equations (the equations of quantum chromodynamics), are obtained. The equivalence of two ways to define Lévy differential operators is shown.

scholarly journals LOOP VARIABLES IN STRING THEORY

2003 ◽  
Vol 18 (05) ◽  
pp. 767-809 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Equations Of Motion ◽  
Renormalization Group Equation ◽  
Group Method ◽  
Group Equation ◽  
World Sheet ◽  
Gauge Invariant ◽  
Variable Approach ◽  
Exact Renormalization Group

The loop variable approach is a proposal for a gauge-invariant generalization of the sigma-model renormalization group method of obtaining equations of motion in string theory. The basic guiding principle is space–time gauge invariance rather than world sheet properties. In essence it is a version of Wilson's exact renormalization group equation for the world sheet theory. It involves all the massive modes and is defined with a finite world sheet cutoff, which allows one to go off the mass-shell. On shell the tree amplitudes of string theory are reproduced. The equations are gauge-invariant off shell also. This paper is a self-contained discussion of the loop variable approach as well as its connection with the Wilsonian RG.

scholarly journals Lattice vibrations with Rayleigh dissipation

2000 ◽  
Vol 42 (2) ◽  
pp. 244-253 ◽  
Author(s):  
J. N. Boyd ◽  
P. N. Raychowdhury
Keyword(s):  
Natural Frequencies ◽  
Linear Array ◽  
Equations Of Motion ◽  
Dissipation Function ◽  
Lagrangian Formulation ◽  
Harmonic Oscillators ◽  
Lattice Vibrations ◽  
Circular Array ◽  
Coupled Harmonic Oscillators ◽  
Symmetry Coordinates

AbstractWe approximate a linear array of coupled harmonic oscillators as a symmetric circular array of identical masses and springs. The springs are taken to possess mass distributed along their lengths. We give a Lagrangian formulation of the problem of finding the natural frequencies of oscillation for the array. Damping terms are included by means of the Rayleigh dissipation function. A transformation to symmetry coordinates as determined by the group of rotations of the circle uncouples the equations of motion.

Classical electrodynamics of spinning particles

1984 ◽  
Vol 62 (10) ◽  
pp. 943-947
Author(s):  
Bruce Hoeneisen
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Wave Equations ◽  
Dipole Moments ◽  
Equations Of Motion ◽  
Radiation Reaction ◽  
Classical Electrodynamics ◽  
Electric Dipole Moments ◽  
Gauge Invariant ◽  
Intrinsic Angular Momentum

We consider particles with mass, charge, intrinsic magnetic and electric dipole moments, and intrinsic angular momentum in interaction with a classical electromagnetic field. From this action we derive the equations of motion of the position and intrinsic angular momentum of the particle including the radiation reaction, the wave equations of the fields, the current density, and the energy-momentum and angular momentum of the system. The theory is covariant with respect to the general Lorentz group, is gauge invariant, and contains no divergent integrals.

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