Understanding Abstract Physics: Gauge Functions & Properties of EM Fields

[francisco]

physics, abstract...

i am very confused about what the following abstract says:

The main purposes of this paper are (i) to illustrate explicitly by a number of examples the gauge functions chi(x, t) whose spatial and temporal derivatives transform one set of electromagnetic potentials into another equivalent set; and (ii) to show that, whatever propagation or non-propagation characteristics are exhibited by the potentials in a particular gauge, the electric and magnetic fields are always the same and display the experimentally verified properties of causality and propagation at the speed of light. The example of the transformation from the Lorenz gauge (retarded solutions for both scalar and vector potential) to the Coulomb gauge (instantaneous, action-at-a-distance, scalar potential) is treated in detail. A transparent expression is obtained for the vector potential in the Coulomb gauge, with a finite nonlocality in time replacing the expected spatial nonlocality of the transverse current. A class of gauges (v-gauge) is described in which the scalar potential propagates at an arbitrary speed v relative to the speed of light. The Lorenz and Coulomb gauges are special cases of the v-gauge. The last examples of gauges and explicit gauge transformation functions are the Hamiltonian or temporal gauge, the nonrelativistic Poincare or multipolar gauge, and the relativistic Fock-Schwinger gauge.

http://arxiv.org/abs/physics/0204034

can someone please help me understand? thanks

 

[samalkhaiat]

read the whole paper.

 

[Entropia]

Abstract physics is a branch of physics that deals with theoretical concepts and mathematical models rather than concrete physical objects. In this paper, the focus is on gauge functions and their properties in relation to electromagnetic (EM) fields.

The first purpose of the paper is to provide examples of gauge functions, denoted as chi(x, t), which can transform one set of EM potentials into another equivalent set. These transformations involve spatial and temporal derivatives and can be used to describe different characteristics of the EM potentials.

The second purpose is to show that regardless of the characteristics of the potentials in a particular gauge, the resulting electric and magnetic fields are always the same and exhibit properties that have been experimentally verified, such as causality and propagation at the speed of light.

One specific example discussed in detail is the transformation from the Lorenz gauge, which describes both scalar and vector potentials as retarded solutions, to the Coulomb gauge, which describes instantaneous, action-at-a-distance scalar potential. The paper also presents a transparent expression for the vector potential in the Coulomb gauge, which has a finite nonlocality in time instead of the expected spatial nonlocality of the transverse current.

The paper also introduces the concept of a "v-gauge," which is a class of gauges where the scalar potential propagates at an arbitrary speed relative to the speed of light. The Lorenz and Coulomb gauges are special cases of the v-gauge.

Finally, the paper discusses other examples of gauges and their explicit gauge transformation functions, including the Hamiltonian or temporal gauge, the nonrelativistic Poincare or multipolar gauge, and the relativistic Fock-Schwinger gauge.

In summary, this paper aims to provide a better understanding of gauge functions and their role in describing the properties of EM fields in different gauges. It also highlights the importance of gauge invariance in physics and the underlying connections between seemingly different gauges.