The non-relativistic limits of the Maxwell and dirac equations: The role of galilean and gauge invariance

Abstract
The aim of this paper is to illustrate four properties of the non-relativistic limits of relativistic theories: (a) that a massless relativistic field may have a meaningful non-relativistic limit, (b) that a relativistic field may have more than one non-relativistic limit, (c) that coupled relativistic systems may be ''more relativistic'' than their uncoupled counterparts, and (d) that the properties of the non-relativistic 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 non-relativistic limit of the familiar equations of first-quantized QED, i.e., the Dirac and Maxwell equations. The conditions under which each set of equations admits non-relativistic limits are given, particular attention being given to a gauge-invariant 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.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 11,085
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Citations of this work BETA
Douglas Kutach (2010). A Connection Between Minkowski and Galilean Space-Times in Quantum Mechanics. International Studies in the Philosophy of Science 24 (1):15 – 29.
Similar books and articles
Francisco Flores (1998). Einstein's 1935 Derivation of E=Mc. Studies in History and Philosophy of Science Part B 29 (2):223-243.
Harvey Brown (1999). Aspects of Objectivity in Quantum Mechanics. In Jeremy Butterfield & Constantine Pagonis (eds.), From Physics to Philosophy. Cambridge University Press. 45--70.
Simon W. Saunders (1992). Locality, Complex Numbers, and Relativistic Quantum Theory. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:365 - 380.
Wayne C. Myrvold (2009). Chasing Chimeras. British Journal for the Philosophy of Science 60 (3):635-646.
Douglas Kutach (2010). A Connection Between Minkowski and Galilean Space-Times in Quantum Mechanics. International Studies in the Philosophy of Science 24 (1):15 – 29.
Wayne C. Myrvold (2003). Relativistic Quantum Becoming. British Journal for the Philosophy of Science 54 (3):475-500.
Analytics

Monthly downloads

Added to index

2009-01-28

Total downloads

14 ( #114,504 of 1,101,653 )

Recent downloads (6 months)

3 ( #116,934 of 1,101,653 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.