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The mathematical style of modern physics

Mukunda, N (1987) The mathematical style of modern physics. In: Collection: Recent developments in theoretical physics, 1987, Kottayam, pp. 1-20.

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In the author's opinion, two main features are characteristic for modern applications of mathematics to physics: the use of symmetries and the use of unobservable quantities (antioperationalistic approach). He gives a brief history of symmetry in physics: first, symmetry as a tool for describing useful features of given theories, then symmetry as a tool for restricting possible equations (e.g. the Dirac equation was thus obtained) and, finally, symmetry as a creative tool allowing one to obtain equations almost uniquely (Yang-Mills, etc.). Whenever equations are invariant with respect to some group, in the case that our observation data are invariant with respect to some subgroup $G$, one cannot tell the state $x$ from the state $gx$, where $g\in G$, so the parameters telling $x$ from $gx$ become unobservable---of this kind are potentials in electrodynamics, coordinate effects in general relativity, etc. This unobservability can be ultimate (e.g. phase of wave function in quantum theory) or only approximate---in all other theories where symmetry is only approximate.

Item Type: Conference Paper
Publisher: World Sci. Publishing
Additional Information: Copyright of this article belongs to World Sci. Publishing.
Department/Centre: Division of Physical & Mathematical Sciences > Centre for Theoretical Studies (Ceased to exist at the end of 2003)
Date Deposited: 31 Aug 2004
Last Modified: 10 Jan 2012 05:31
URI: http://eprints.iisc.ac.in/id/eprint/967

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