Generalized Quantum Mechanics and Nonlinear Gauge Transformations

1997 ◽  
pp. 269-280
Author(s):  
Peter Nattermann
Keyword(s):  
Quantum Mechanics ◽  
Gauge Transformations ◽  
Nonlinear Gauge

scholarly journals On the Hamiltonian approach: Applications to geophysical flows

1998 ◽  
Vol 5 (4) ◽  
pp. 219-240 ◽  
Author(s):  
V. Goncharov ◽  
V. Pavlov
Keyword(s):  
Degrees Of Freedom ◽  
Fluid Motion ◽  
Gauge Transformations ◽  
Motion Models ◽  
Canonical Variables ◽  
Long Time ◽  
Minimum Number ◽  
Nonlinear Gauge ◽  
Hydrodynamical System ◽  
General Method

Abstract. This paper presents developments of the Harniltonian Approach to problems of fluid dynamics, and also considers some specific applications of the general method to hydrodynamical models. Nonlinear gauge transformations are found to result in a reduction to a minimum number of degrees of freedom, i.e. the number of pairs of canonically conjugated variables used in a given hydrodynamical system. It is shown that any conservative hydrodynamic model with additional fields which are in involution may be always reduced to the canonical Hamiltonian system with three degrees of freedom only. These gauge transformations are associated with the law of helicity conservation. Constraints imposed on the corresponding Clebsch representation are determined for some particular cases, such as, for example. when fluid motions develop in the absence of helicity. For a long time the process of the introduction of canonical variables into hydrodynamics has remained more of an intuitive foresight than a logical finding. The special attention is allocated to the problem of the elaboration of the corresponding regular procedure. The Harniltonian Approach is applied to geophysical models including incompressible (3D and 2D) fluid motion models in curvilinear and lagrangian coordinates. The problems of the canonical description of the Rossby waves on a rotating sphere and of the evolution of a system consisting of N singular vortices are investigated.

scholarly journals Structure of nonlinear gauge transformations

1998 ◽  
Vol 57 (4) ◽  
pp. R2263-R2266 ◽  
Author(s):  
Marek Czachor
Keyword(s):  
Gauge Transformations ◽  
Nonlinear Gauge

scholarly journals Derivation of the Local Lorentz Gauge Transformation of a Dirac Spinor Field in Quantum Einstein-Cartan Theory

2019 ◽  
Author(s):  
Rainer Kühne
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Quantum Electrodynamics ◽  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Relativistic Quantum Mechanics ◽  
Dirac Spinor ◽  
Dirac Algebra ◽  
Gauge Transformations ◽  
Cartan Theory

I examine the groups which underly classical mechanics, non-relativistic quantum mechanics, special relativity, relativistic quantum mechanics, quantum electrodynamics, quantum flavourdynamics, quantum chromodynamics, and general relativity. This examination includes the rotations SO(2) and SO(3), the Pauli algebra, the Lorentz transformations, the Dirac algebra, and the U(1), SU(2), and SU(3) gauge transformations. I argue that general relativity must be generalized to Einstein-Cartan theory, so that Dirac spinors can be described within the framework of gravitation theory.

Conditions for a Solitonic Solution of the Doener–Goldin Equation of Quantum Mechanics

1998 ◽  
Vol 12 (13) ◽  
pp. 519-527
Author(s):  
E. C. Caparelli ◽  
S. S. Mizrahi ◽  
V. V. Dodonov
Keyword(s):  
Quantum Mechanics ◽  
Nonlinear Equation ◽  
Plane Wave ◽  
Gauge Transformation ◽  
Particle Motion ◽  
Continuity Equation ◽  
Free Particle ◽  
Solitonic Solution ◽  
The Mean ◽  
Nonlinear Gauge

A solitonic solution to the free-particle motion of Doebner–Goldin nonlinear equation is shown to exist under special conditions. For small values of the nonlinearity parameters, the solution is a plane wave modulated by a cos function, and the solitonic one arises when the parameters surpass some critical values. The mean energy of the particle is a conserved quantity and the continuity equation holds. We also verify that there is no nonlinear gauge transformation (in the sense of Ref. 12) that linearizes that equation.

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