Symmetries in Physics
Philosophical Reflections
Edited by Katherine Brading
Edited by Elena Castellani
Publisher: Cambridge University Press
Print Publication Year: 2003
Online Publication Date:October 2009
Online ISBN:9780511535369
Hardback ISBN:9780521821377
Paperback ISBN:9780521528894
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511535369.010
Subjects: General and Classical Physics
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Introduction
Mathematically, gauge theories are extraordinarily rich – so rich, in fact, that it can be all too easy to lose track of the connections between results, and become lost in a mass of beautiful theorems and properties: indeterminism, constraints, Noether identities, local and global symmetries, and so on.
One purpose of this short article is to provide some sort of a guide through the mathematics, to the conceptual core of what is actually going on. Its focus is on the Lagrangian, variational-problem description of classical mechanics, from which the link between gauge symmetry and the apparent violation of determinism is easy to understand; only towards the end will the Hamiltonian description be considered.
The other purpose is to warn against adopting too unified a perspective on gauge theories. It will be argued that the meaning of gauge freedom in a theory such as general relativity is (at least from the Lagrangian viewpoint) significantly different from its meaning in theories such as electromagnetism. The Hamiltonian framework blurs this distinction, and orthodox methods of quantization obliterate it; this may, in fact, be genuine progress, but it is dangerous to be guided by mathematics into conflating two conceptually distinct notions without appreciating the physical consequences.
The price paid by this article for abandoning the mathematics of gauge theory as far as possible is an inevitable loss of rigour. Virtually nothing will be ‘proved’ below; at most, the shape of proofs will be gestured at and strong plausibility-arguments advanced.
pp. i-iv
pp. v-vi
List of contributors : Read PDF
pp. vii-viii
pp. ix-x
Copyright acknowledgements : Read PDF
pp. xi-xii
pp. 1-18
Part I - Continuous symmetries : Read PDF
pp. 19-20
2 - Classic texts: extracts from Weyl and Wigner : Read PDF
pp. 21-28
3 - On continuous symmetries and the foundations of modern physics : Read PDF
pp. 29-60
4 - The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism : Read PDF
pp. 61-88
5 - Symmetries and Noether's theorems : Read PDF
pp. 89-109
6 - General covariance, gauge theories, and the Kretschmann objection : Read PDF
pp. 110-123
7 - The interpretation of gauge symmetry : Read PDF
pp. 124-139
8 - Tracking down gauge: an ode to the constrained Hamiltonian formalism : Read PDF
pp. 140-162
9 - Time-dependent symmetries: the link between gauge symmetries and indeterminism : Read PDF
pp. 163-173
10 - A fourth way to the Aharonov–Bohm effect : Read PDF
pp. 174-200
Part II - Discrete symmetries : Read PDF
pp. 201-202
11 - Classic texts: extracts from Leibniz, Kant, and Black : Read PDF
pp. 203-211
12 - Understanding permutation symmetry : Read PDF
pp. 212-238
13 - Quarticles and the identity of indiscernibles : Read PDF
pp. 239-249
14 - Handedness, parity violation, and the reality of space : Read PDF
pp. 250-280
15 - Mirror symmetry: what is it for a relational space to be orientable? : Read PDF
pp. 281-288
16 - Physics and Leibniz's principles : Read PDF
pp. 289-308
Part III - Symmetry breaking : Read PDF
pp. 309-310
17 - Classic texts: extracts from Curie and Weyl : Read PDF
pp. 311-314
18 - Cross fertilization in theoretical physics: the case of condensed matter and particle physics : Read PDF
pp. 315-320
19 - On the meaning of symmetry breaking : Read PDF
pp. 321-334
20 - Rough guide to spontaneous symmetry breaking : Read PDF
pp. 335-346
21 - Spontaneous symmetry breaking: theoretical arguments and philosophical problems : Read PDF
pp. 347-364
Part IV - General interpretative issues : Read PDF
pp. 365-366
22 - Classic texts: extracts from Wigner : Read PDF
pp. 367-370
23 - Symmetry as a guide to superfluous theoretical structure : Read PDF
pp. 371-392
24 - Notes on symmetries : Read PDF
pp. 393-412
25 - Symmetry, objectivity, and design : Read PDF
pp. 413-424
26 - Symmetry and equivalence : Read PDF
pp. 425-436
pp. 437-445