Magnetic monopole, vector potential and gauge transformation

1977 ◽  
Vol 20 (7) ◽  
pp. 227-231 ◽  
Author(s):  
M. Ikeda ◽  
T. Kawai ◽  
H. Yoshida
Keyword(s):  
Gauge Transformation ◽  
Vector Potential ◽  
Magnetic Monopole

scholarly journals On the gauge transformation for the rotation of the singular string in the Dirac monopole theory

2021 ◽  
Vol 36 (03) ◽  
pp. 2150019
Author(s):  
Xiao-Yin Pan ◽  
Yin Chen ◽  
Yu-Qi Li ◽  
Aaron G. Kogan ◽  
Juhao Wu
Keyword(s):  
Gauge Transformation ◽  
Electric Charge ◽  
Smooth Function ◽  
Vector Potential ◽  
Magnetic Monopole ◽  
Quantization Condition ◽  
Quantum Mechanical ◽  
Mechanical Interaction ◽  
Dirac Theory ◽  
Dirac Monopole

In the Dirac theory of the quantum-mechanical interaction of a magnetic monopole and an electric charge, the vector potential is singular from the origin to infinity along a certain direction — the so-called Dirac string. Imposing the famous quantization condition, the singular string attached to the monopole can be rotated arbitrarily by a gauge transformation, and hence is not physically observable. By deriving its analytical expression and analyzing its properties, we show that the gauge function [Formula: see text] which rotates the string to another one is a smooth function everywhere in space, except their respective strings. On the strings, [Formula: see text] is a multi-valued function. Consequently, some misunderstandings in the literature are clarified.

A Comment on Zeeman Effects in Rotation Spectra

1970 ◽  
Vol 25 (12) ◽  
pp. 2004 ◽  
Author(s):  
B.J. Howard ◽  
R.E. Moss
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Coordinate System ◽  
Gauge Transformation ◽  
Vector Potential ◽  
Molecular Vibrations ◽  
Centre Of Gravity ◽  
Elec Tromagnetic Field ◽  
Constant External Magnetic Field

Abstract Recently SUTTER et al. 1 obtained a Hamiltonian for a molecule in the presence of a constant external elec-tromagnetic field. (A similar Hamiltonian has been de-veloped 2 , but including molecular vibrations, relativis-tic corrections and allowance for the fact that the mo-lecular centre of gravity differs from the nuclear centre of gravity.) We believe that the Hamiltonian of Sutter et al. is not correct, since they make two errors of principle in performing their gauge transformation. They start with a Lagrangian expressed in terms of the particle positions, rn\ in a space-fixed coordinate system. Each particle is associated with an external vector potential,-^«' = rn', where H is the constant external magnetic field. At this stage a gauge transfor-mation may be performed: An'-+An'-VnX, (1)

The electromagnetic potentials

2018 ◽  
Author(s):  
J. Pierrus
Keyword(s):  
Electromagnetic Radiation ◽  
Gauge Transformation ◽  
Vector Potential ◽  
Point Charge ◽  
Wave Equations ◽  
Multipole Expansion ◽  
Inhomogeneous Wave ◽  
Electromagnetic Potentials ◽  
Starting Point

This chapter expresses the fields E ( r, t) and B ( r, t) in terms of the electromagnetic potentials Ф( r, t) and A ( r, t), and shows that these potentials are defined only up to a gauge transformation. This leads the reader naturally to the Coulomb and Lorenz gauges which are usually encountered in textbooks. The inhomogeneous wave equations whose solutions are the retarded electromagnetic potentials are also considered, as well as the Lienard–Wiechert potentials for an arbitrarily moving point charge. A few questions are included in which the Lagrangian and Hamiltonian of a point charge are expressed in terms of Ф and A. The chapter concludes by deriving a multipole expansion for the dynamic vector potential which will provide the starting point in our treatment of electromagnetic radiation later on in Chapter 11

scholarly journals Dirac's Magnetic Monopoles (Again)

2004 ◽  
Vol 19 (supp01) ◽  
pp. 137-143 ◽  
Author(s):  
Roman W. Jackiw
Keyword(s):  
Vector Potential ◽  
Magnetic Monopole ◽  
Magnetic Monopoles

Dirac's quantization of magnetic monopole strength is derived without reference to a (singular, patched) vector potential.

scholarly journals N-Fold Darboux Transformation for the Classical Three-Component Nonlinear Schrödinger Equations and Its Exact Solutions

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 733
Author(s):  
Yu-Shan Bai ◽  
Peng-Xiang Su ◽  
Wen-Xiu Ma
Keyword(s):  
Exact Solutions ◽  
Gauge Transformation ◽  
Darboux Transformation ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Lax Pairs ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
The Given

In this paper, by using the gauge transformation and the Lax pairs, the N-fold Darboux transformation (DT) of the classical three-component nonlinear Schrödinger (NLS) equations is given. In addition, by taking seed solutions and using the DT, exact solutions for the given NLS equations are constructed.

scholarly journals Field-Induced Magnetic Monopole Plasma in Artificial Spin Ice

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
M. Goryca ◽  
X. Zhang ◽  
J. Li ◽  
A. L. Balk ◽  
J. D. Watts ◽  
...  
Keyword(s):  
Magnetic Monopole ◽  
Spin Ice ◽  
Artificial Spin Ice
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