scholarly journals Spin Current in BF Theory

Physics ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 427-448
Author(s):  
Malik Almatwi
Keyword(s):  
Lie Algebra ◽  
Equations Of Motion ◽  
Spin Current ◽  
Spin Connection ◽  
Bf Theory ◽  
Cylindrically Symmetric ◽  
Covariant Derivation ◽  
A Current ◽  
Symmetric Systems

In this paper, a current that is called spin current and corresponds to the variation of the matter action in BF theory with respect to the spin connection A which takes values in Lie algebra so(3,C), in self-dual formalism is introduced. For keeping the 2-form Bi constraint (covariant derivation) DBi=0 satisfied, it is suggested adding a new term to the BF Lagrangian using a new field ψi, which can be used for calculating the spin current. The equations of motion are derived and the solutions are dicussed. It is shown that the solutions of the equations do not require a specific metric on the 4-manifold M, and one just needs to know the symmetry of the system and the information about the spin current. Finally, the solutions for spherically and cylindrically symmetric systems are found.

scholarly journals Holographic spin liquids and Lovelock Chern-Simons gravity

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
A.D. Gallegos ◽  
U. Gürsoy
Keyword(s):  
Constitutive Relations ◽  
Equations Of Motion ◽  
Spin Current ◽  
Analytic Solutions ◽  
Momentum Tensor ◽  
Spin Connection ◽  
Spin Liquids ◽  
Thermodynamic Potentials ◽  
Algebraic Constraints ◽  
Chern Simons

Abstract We explore the role of torsion as source of spin current in strongly interacting conformal fluids using holography. We establish the constitutive relations of the basic hydrodynamic variables, the energy-momentum tensor and the spin current based on the classification of the spin sources in irreducible Lorentz representations. The fluids we consider are assumed to be described by the five dimensional Lovelock-Chern-Simons gravity with independent vielbein and spin connection. We construct a hydrodynamic expansion that involves the stress tensor and the spin current and compute the corresponding one-point functions holographically. As a byproduct we find a class of interesting analytic solutions to the Lovelock-Chern-Simons gravity, including blackholes, by mapping the equations of motion into non-linear algebraic constraints for the sources. We also derive a Lee-Wald entropy formula for these blackholes in Chern-Simons theories with torsion. The blackhole solutions determine the thermodynamic potentials and the hydrodynamic constitutive relations in the corresponding fluid on the boundary. We observe novel spin induced transport in these holographic models: a dynamical version of the Barnett effect where vorticity generates a spin current and anomalous vortical transport transverse to a vector-like spin source.

Resistive Ballooning Modes in Three-Dimensional Configurations

1982 ◽  
Vol 37 (8) ◽  
pp. 848-858 ◽  
Author(s):  
D. Correa-Restrepo
Keyword(s):  
Growth Rates ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Coupled System ◽  
Small Constant ◽  
Ballooning Mode ◽  
The Stability ◽  
The Magnetic Field ◽  
Symmetric Systems ◽  
The Ideal

Resistive ballooning modes in general three-dimensional configurations are studied on the basis of the equations of motion of resistive MHD. Assuming small, constant resistivity and perturbations localized transversally to the magnetic field, a stability criterion is derived in the form of a coupled system of two second-order differential equations. This criterion contains several limiting cases, in particular the ideal ballooning mode criterion and criteria for the stability of symmetric systems. Assuming small growth rates, analytical results are derived by multiple-length-scale expansion techniques. Instabilities are found, their growth rates scaling as fractional powers of the resistivity

Small disturbances in a conducting fluid in the presence of a current-carrying conductor

1964 ◽  
Vol 60 (2) ◽  
pp. 325-339
Author(s):  
A. M. J. Davis
Keyword(s):  
Uniform Magnetic Field ◽  
Equations Of Motion ◽  
Conducting Fluid ◽  
Alfven Wave ◽  
Displacement Current ◽  
Wave Fronts ◽  
Acoustic Disturbance ◽  
Linear Partial Differential Equations ◽  
A Current ◽  
Small Disturbances

1. Introduction. The problem considered here derives its motivation from a paper by Friedlander (8) on the propagation of small disturbances in a compressible, conducting fluid in the presence of a uniform magnetic field (see also Courant and Hilbert (3), VI, §3a). In this the displacement current and energy dissipation by viscosity, heat conduction and Joule heat are neglected and a system of linear partial differential equations is obtained, which generalizes the equations of motion of the theory of sound. Their solution is in general the superposition of an arbitrary incompressible Alfven wave and a magneto-acoustic disturbance. This latter was considered by constructing a Green's function by means of suitable combinations of plane wave solutions and it was found that there are fast and slow wave fronts diverging from a point disturbance. The latter are conoidal in shape and have a singularity at their vertices which propagate along the field line in either direction from the source.

Propagation of a nonlinear seismic pulse in an anelastic homogeneous medium

Geophysics ◽  
1993 ◽  
Vol 58 (7) ◽  
pp. 949-963 ◽  
Author(s):  
Dan W. Kosik
Keyword(s):  
Wave Propagation ◽  
Equations Of Motion ◽  
Surrounding Medium ◽  
Homogeneous Medium ◽  
Seismic Surveys ◽  
Linear Elastic ◽  
Cylindrically Symmetric ◽  
Unconsolidated Material ◽  
Linear Pulse ◽  
Implicit Finite Difference

Seismic surveys are often conducted using dynamite charges buried near the surface in unconsolidated material. In such material a large zone near the source should exist wherein nonlinear anelastic wave propagation, can be expected to take place, and have a significant impact on the way in which a seismic pulse forms and how its energy gets distributed into the surrounding medium. To obtain a solution for a propagating pulse in this zone, the equations of motion for nonlinear anelastic wave propagation, good to second order in the displacements, are solved numerically for the problem of a Gaussian pressure pulse acting on the interior cavity of a cylindrically symmetric hole in the medium. An implicit finite‐difference algorithm is used for the solution to the equations of motion for this problem. The anelastic medium is characterized by multivalued stress‐strain relations that exhibit hysteresis, and therefore a loss of energy per cycle, corresponding to a medium with a constant Q factor. Several numerical examples are calculated contrasting the nonlinear anelastic, linear anelastic, and linear elastic propagating pulses to one another. The nonlinear anelastic propagating pulse is found to have an amplitude that is several times larger than would be expected for a pulse in a linear medium and has a peak propagation velocity that is slightly less than that for a linear pulse. Dispersive effects are also evident for the nonlinear pulse.

scholarly journals A COHOMOLOGICAL INTERPRETATION OF THE MIGDAL–MAKEENKO EQUATIONS

2002 ◽  
Vol 17 (08) ◽  
pp. 481-489 ◽  
Author(s):  
A. AGARWAL ◽  
S. G. RAJEEV
Keyword(s):  
Lie Algebra ◽  
Equations Of Motion ◽  
Generating Functional ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Change Of Variables ◽  
Anomalous Term ◽  
Large N ◽  
Infinite Dimensional Lie Algebra ◽  
Cohomological Interpretation

The equations of motion of quantum Yang–Mills theory (in the planar "large-N" limit), when formulated in loop-space are shown to have an anomalous term, which makes them analogous to the equations of motion of WZW models. The anomaly is the Jacobian of the change of variables from the usual ones, i.e. the connection one-form A, to the holonomy U. An infinite-dimensional Lie algebra related to this change of variables (the Lie algebra of loop substitutions) is developed, and the anomaly is interpreted as an element of the first cohomology of this Lie algebra. The Migdal–Makeenko equations are shown to be the condition for the invariance of the Yang–Mills generating functional Z under the action of the generators of this Lie algebra. Connections of this formalism to the collective field approach of Jevicki and Sakita are also discussed.

scholarly journals NOISE AND DISSIPATION IN QUANTUM THEORY

1990 ◽  
Vol 02 (02) ◽  
pp. 127-176 ◽  
Author(s):  
LUIGI ACCARDI
Keyword(s):  
Quantum Theory ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Langevin Equation ◽  
Equations Of Motion ◽  
Natural Generalization ◽  
Usual Sense ◽  
Heisenberg Equation ◽  
Generalized Langevin Equation ◽  
Solid State Physics

A model independent generalization of quantum mechanics, including the usual as well as the dissipative quantum systems, is proposed. The theory is developed deductively from the basic principles of the standard quantum theory, the only new qualitative assumption being that we allow the wave operator at time t of a quantum system to be non-differentiable (in t) in the usual sense, but only in an appropriately defined (Sec. 5) stochastic sense. The resulting theory is shown to lead to a natural generalization of the usual quantum equations of motion, both in the form of the Schrödinger equation in interaction representation (Sec. 6) and of the Heisenberg equation (Sec. 8). The former equation leads in particular to a quantum fluctuation-dissipation relation of Einstein’s type. The latter equation is a generalized Langevin equation, from which the known form of the generalized master equation can be deduced via the quantum Feynmann-Kac technique (Secs. 9 and 10). For quantum noises with increments commuting with the past the quantum Langevin equation defines a closed system of (usually nonlinear) stochastic differential equations for the observables defining the coefficients of the noises. Such systems are parametrized by certain Lie algebras of observables of the system (Sec. 10). With appropriate choices of these Lie algebras one can deduce generalizations and corrections of several phenomenological equations previously introduced at different times to explain different phenomena. Two examples are considered: the Lie algebra [q, p]=i (Sec. 12), which is shown to lead to the equations of the damped harmonic oscillator; and the Lie algebra of SO(3) (Sec. 13) which is shown to lead to the Bloch equations. In both cases the equations obtained are independent of the model of noise. Moreover, in the former case, it is proved that the only possible noises which preserve the commutation relations of p, q are the quantum Brownian motions, commonly used in laser theory and solid state physics.

Variational principles of guiding centre motion

1983 ◽  
Vol 29 (1) ◽  
pp. 111-125 ◽  
Author(s):  
Robert G. Littlejohn
Keyword(s):  
Angular Momentum ◽  
Variational Principle ◽  
Conservation Laws ◽  
Variational Principles ◽  
Equations Of Motion ◽  
Phase Volume ◽  
Rigorous Derivation ◽  
Volume Energy ◽  
Symmetric Systems

An elementary but rigorous derivation is given for a variational principle for guiding centre motion. The equations of motion resulting from the variational principle (the drift equations) possess exact conservation laws for phase volume, energy (for time-independent systems), and angular momentum (for azimuthally symmetric systems). The results of carrying the variational principle to higher order in the adiabatic parameter are displayed. The behaviour of guiding centre motion in azimuthally symmetric fields is discussed, and the role of angular momentum is clarified. The application of variational principles in the derivation and solution of gyrokinetic equations is discussed.

AN INTEGRABLE MODEL WITH SOLITON SOLUTIONS WHICH HAVE APPLICATIONS TO TWO-DIMENSIONAL GRAVITY

2005 ◽  
Vol 20 (07) ◽  
pp. 1503-1514 ◽  
Author(s):  
PAUL BRACKEN
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Integrable Model ◽  
Soliton Solutions ◽  
Integrable Equation ◽  
Two Dimensions ◽  
Spin Connection ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
Chern Simons

The equations of motion for a theory described by a Chern–Simons type of action in two dimensions are obtained and investigated. The equation for the classical, continuous Heisenberg model is used as a form of gauge constraint to obtain a result which provides a completely integrable dynamics and which partially fixes the gauge degrees of freedom. Under a particular form of the spin connection, an integrable equation which can be analytically extended to a form of the nonlinear Schrödinger equation is obtained. Some explicit solutions are presented, and in particular a soliton solution is shown to lead to an integrable two-dimensional model of gravity.

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