Annales de la Fondation Louis de Broglie Volume no

Louis Debroglie

Description

Niveau: Supérieur, Doctorat, Bac+8
Annales de la Fondation Louis de Broglie, Volume 30 no 3-4, 2005 1 The gauge non-invariance of Classical Electromagnetism Germain Rousseaux Institut Non-Lineaire de Nice, Sophia-Antipolis. UMR 6618 CNRS. 1361, route des Lucioles. 06560 Valbonne, France. E-mail: Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is de- scribed by more variables than there are physically independent degree of freedom. The physically meaningful degrees of freedom then reemerge as being those invariant under a transformation connecting the vari- ables (gauge transformation). Thus, one introduces extra variables to make the description more transparent and brings in at the same time a gauge symmetry to extract the physically relevant content. It is a remarkable occurrence that the road to progress has invariably been to- wards enlarging the number of variables and introducing a more power- ful symmetry rather than conversely aiming at reducing the number of variables and eliminating the symmetry [1]. We claim that the poten- tials of Classical Electromagnetism are not indetermined with respect to the so-called gauge transformations. Indeed, these transformations raise paradoxes that imply their rejection. Nevertheless, the potentials are still indetermined up to a constant. 1 Introduction In Classical electromagnetism, the electric field E and the magnetic field B are related to the scalar V and vector A potentials by the following definitions [2] : E = ? ∂A ∂t ??V and B

• dependent vector


• called magnetic


• effect contradicts


• vector potentials differing


• known aharonov-bohm


• gauge function


• effect


• physical constraints


• potential


• electromagnetic field

Sujets

• Rousseau
• Louis-Victor de Broglie
• Gauge function
• Effect
• Potential
• Electromagnetic field

Informations

• Publié par: profil-zyak-2012
• Nombre de lectures: 64
• Langue: English

Extrait

Annales de la Fondation Louis de Broglie, Volume 30 no 3-4, 2005

The gauge non-invariance of Classical Electromagnetism

Germain Rousseaux

InstitutNon-Line´airedeNice,Sophia-Antipolis. UMR 6618 CNRS. 1361, route des Lucioles. 06560 Valbonne, France. E-mail:[e-mail]

Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is de- scribed by more variables than there are physically independent degree of freedom. The physically meaningful degrees of freedom then reemerge as being those invariant under a transformation connecting the vari- ables (gauge transformation). Thus, one introduces extra variables to make the description more transparent and brings in at the same time a gauge symmetry to extract the physically relevant content. It is a remarkable occurrence that the road to progress has invariably been to- wards enlarging the number of variables and introducing a more power- ful symmetry rather than conversely aiming at reducing the number of variables and eliminating the symmetryclaim that the poten-[1]. We tials of Classical Electromagnetism are not indetermined with respect to the so-called gauge transformations. Indeed, these transformations raise paradoxes that imply their rejection. Nevertheless, the potentials are still indetermined up to a constant.

1

1 Introduction In Classical electromagnetism, the electric fieldEand the magnetic field Bare related to the scalarVand vectorApotentials by the following definitions [2] :

∂A E=− − rV ∂t

and

B=r ×A

(1)

One century ago, H.A. Lorentz noticed that the electromagnetic field 0 0 remains invariant (E=EandB=B) under the so-called gauge trans- formations [3]: