Gauging What's Real The Conceptual Foundations of Contemporary Gauge Theories

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ISBN: 9780199576937 | 0199576939
Cover: Paperback
Copyright: 11/16/2009

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Gauge theories have provided our most successful representations of the fundamental forces of nature. How, though, do such representations work? Interpretations of gauge theory answer to answer this question. Through understanding how a gauge theory's representations work, we are able to say what kind, of world our gauge theories reveal to us.

Preface	p. ix
Acknowledgements	p. xiii
Introduction	p. xv
What is a gauge theory?	p. 1
Classical electromagnetism: a paradigm gauge theory	p. 3
A fiber bundle formulation	p. 7
Electromagnetic interactions of quantum particles	p. 14
Electromagnetic interactions of matter fields	p. 18
The Aharonov-Bohm effect	p. 21
Fiber bundles	p. 26
A gauge-invariant, local explanation?	p. 31
Geometry and topology in the Aharonov-Bohm effect	p. 40
Locality in the Aharonov-Bohm effect	p. 44
Lessons for classical electromagnetism	p. 54
Classical gauge theories	p. 58
Non-Abelian Yang-Mills theories	p. 58
The fiber bundle formulation	p. 64
Loops, groups, and hoops	p. 70
Topological issues	p. 74
A fiber bundle formulation of general relativity	p. 77
A gravitational analog to the Aharonov-Bohm effect	p. 78
Interpreting classical gauge theories	p. 82
The no gauge potential properties view	p. 83
The localized gauge potential properties view	p. 85
Problems defining theoretical terms	p. 91
Leeds's view	p. 99
Maudlin's interpretation	p. 102
The non-localized gauge potential properties view	p. 104
A holonomy interpretation	p. 111
Epistemological considerations	p. 112
Objections considered	p. 119
Semantic considerations	p. 122
Metaphysical implications: non-separability and holism	p. 123
Quantized Yang-Mills gauge theories	p. 129
How to quantize a classical field	p. 131
Coulomb gauge quantization	p. 133
Lorenz gauge quantization	p. 135
Classical electromagnetism as a constrained Hamiltonian system	p. 136
The free Maxwell field as a Hamiltonian system	p. 139
Path-integral quantization	p. 141
Canonical quantization of non-Abelian fields	p. 143
Path-integral quantization of non-Abelian fields	p. 145
Interacting fields in the Lagrangian formulation	p. 146
The empirical import of gauge symmetry	p. 149
Two kinds of symmetry	p. 150
Observing gauge symmetry?	p. 155
The gauge argument	p. 159
Ghost fields	p. 167
Spontaneous symmetry-breaking	p. 169
The ¿-vacuum	p. 175
Anomalies	p. 182
Loop representations	p. 184
The significance of loop representations	p. 185
Loop representations of the free Maxwell field	p. 186
Loop representations of other free Yang-Mills fields	p. 192
Interacting fields in loop representations	p. 195
The ¿-vacuum in a loop representation	p. 197
Conclusion	p. 198
Interpreting quantized Yang-Mills gauge theories	p. 200
Auyang's event ontology	p. 200
Problems of interpreting a quantum field theory	p. 203
Particle interpretations	p. 205
Bohmian interpretations	p. 209
Copenhagen interpretations	p. 212
Everettian interpretations	p. 215
Modal interpretations	p. 218
Conclusions	p. 220
Electromagnetism and its generalizations	p. 229
Fiber bundles	p. 233
The constrained Hamiltonian formalism	p. 248
Alternative quantum representations	p. 257
Algebraic quantum field theory	p. 265
Interpretations of quantum mechanics	p. 272
The Copenhagen interpretation	p. 272
Bohmian mechanics	p. 274
Everettian interpretations	p. 276
Modal interpretations	p. 278
Bibliography	p. 280
Index	p. 287
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Gauging What's Real The Conceptual Foundations of Contemporary Gauge Theories

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Gauging What's Real The Conceptual Foundations of Contemporary Gauge Theories

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