Holland, Peter and Brown, Harvey R. (2002) The nonrelativistic limits of the Maxwell and Dirac equations: the role of Galilean and gauge invariance. UNSPECIFIED. (In Press)
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Abstract
The aim of this paper is to illustrate four properties of the nonrelativistic limits of relativistic theories: (a) that a massless relativistic field may have a meaningful nonrelativistic limit, (b) that a relativistic field may have more than one nonrelativistic limit, (c) that coupled relativistic systems may be ?more relativistic? than their uncoupled counterparts, and (d) that the properties of the nonrelativistic limit of a dynamical equation may differ from those obtained when the limiting equation is based directly on exact Galilean kinematics. These properties are demonstrated through an examination of the nonrelativistic limit of the familiar equations of firstquantized QED, i.e., the Dirac and Maxwell equations. The conditions under which each set of equations admit nonrelativistic limits are given, particular attention being given to a gaugeinvariant formulation of the limiting process especially as it applies to the electromagnetic potentials. The difference between the properties of a limiting theory and an exactly Galilean covariant theory based on the same dynamical equation is demonstrated by examination of the Pauli equation.
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Item Type:  Other  

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Keywords:  Nonrelativistic limit, Maxwell equations, Dirac equations, Pauli equation  
Subjects:  Specific Sciences > Physics > Fields and Particles Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Relativity Theory 

Depositing User:  Prof Harvey R Brown  
Date Deposited:  16 Feb 2003  
Last Modified:  07 Oct 2010 15:11  
Item ID:  999  
Public Domain:  No  
URI:  http://philsciarchive.pitt.edu/id/eprint/999 
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