Gauging what's real: the conceptual foundations of contemporary gauge theories
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2007
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XIX, 297 S. graph. Darst. |
| ISBN: | 9780199287963 0199287961 |
Staff View
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| 245 | 1 | 0 | |a Gauging what's real |b the conceptual foundations of contemporary gauge theories |c Richard Healey |
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Record in the Search Index
| _version_ | 1804136712422555648 |
|---|---|
| adam_text | Contents
Preface
ix
Acknowledgements
xiii
Introduction
xv
ι
.
What is a gauge theory?
ι
1.1 Classical
electromagnetism:
a paradigm gauge theory
3
1.2
A fiber bundle formulation
7
1.2.1
Electromagnetic interactions of quantum partides
14
1.2.2
Electromagnetic interactions of matter fields
18
2.
The Aharonov—
Bohm
efect
21
2.1
Fiber bundles
26
2.2
A gauge-invariant, local explanation?
31
2.3
Geometry and topology in the Aharonov—Bohm effect
40
2.4
Locality in the Aharonov—Bohm effect
44
2.5
Lessons for classical
electromagnetism
54
3.
Classical gauge theories
58
3.1
Non-Abelian Yang-Milk theories
58
3.1.1
The fiber bundle formulation
64
3.1.2
Loops, groups, and hoops
70
3.1.3
Topologica!
issues
74
3.2
A fiber bundle formulation of general relativity
77
3.2.1
A gravitational analog to the Aharonov—
Bohm efiect
78
4.
Interpreting classical gauge theories
82
4.1
The no gauge potential properties view
83
4.2
The localized gauge potential properties view
85
4.2.1
Problems defining theoretical terms
91
4.2.2
Leeds s view
99
4.2.3
Maudlin s interpretation
102
4.3
The non-localized gauge potential properties view
104
4.4
A holonomyinterpretation in
4.4.
r Epistemological
considerations
112
4.4.2
Objections considered
119
4.4.3
Semantic considerations
122
4.5
Metaphysical implications: non-separability and holism
123
VI
CONTENTS
5.
Quantized Yang—Mills gauge theories
129
5.1
How to quantize a classical field
131
5.2
Coulomb gauge quantization
133
5.3 Lorenz
gauge quantization
135
5.4
Classical electromagnetism as a constrained Hamiltonian system
136
5.5
The free Maxwell field as a Hamiltonian system
139
5.6
Path-integral quantization
141
5.7
Canonical quantization of non-Abelian fields
143
5.8
Path-integral quantization of non-Abelian fields
145
5.9
Interacting fields in the Lagrangian formulation
146
6.
The empirical import of gauge symmetry
149
6.1
Two kinds of symmetry
150
6.2
Observing gauge symmetry?
155
6.3
The gauge argument
159
6.4
Ghost fields
167
6.5
Spontaneous symmetry-breaking
169
6.6
The
ö-vacuum
175
6.7
Anomalies
182
7.
Loop representations
184
7.1
The significance of loop representations
185
7.2
Loop representations of the free Maxwell field
186
7.3
Loop representations of other free Yang—Mills fields
192
7.4
Interacting fields in loop representations
195
7.5
The
ö-vacuum in
a loop representation
197
7.6
Conclusion
198
8.
Interpreting quantized Yang—Mills gauge theories
200
8.1
Auyang s event ontology
200
8.2
Problems of interpreting a quantum field theory
203
8.2.1
Particle interpretations
205
8.2.2
Bohmian interpretations
209
8.2.3
Copenhagen interpretations
212
8.2.4
Everettian interpretations
215
8.2.5
Modal interpretations
218
9.
Conclusions
220
A. Electromagnetism and its generalizations
229
B. Fiber bundles
233
C. The constrained Hamiltonian formalism
248
CONTENTS
Vil
D.
Alternative
quantum
representations
257
E.
Algebraic quantum field theory
265
F. Interpretations of quantum mechanics
272
F.i The Copenhagen interpretation
272
F.2 Bohmian mechanics
274
F.3 Everettian interpretations
276
F.4 Modal interpretations
278
Bibliography
280
Index
287
Gauge theories have provided our most successful representations of the fundamental forces
of nature. How, though, do such representations work? Interpretations of gauge theory aim
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.
A gauge theory s representations are mathematical structures. These may be transformed
among themselves while certain features remain the same. Do the representations related
by such a gauge transformation merely offer alternative ways of representing the very same
situation? If so, then gauge symmetry is a purely formal property since it reflects no
corresponding symmetry in nature.
Gauging What s Real describes the representations provided by gauge theories in both
classical and quantum physics. Richard Healey defends the thesis that gauge transformations
are purely formal symmetries of almost all the classes of representations provided by each of
our theories of fundamental forces. He argues that evidence for classical gauge theories offerees
(other than gravity) gives us reason to believe that loops rather than points are the locations of
fundamental properties. In addition to exploring the prospects of extending this conclusion
to the quantum gauge theories of the Standard Model of elementary particle physics, Healey
assesses the difficulties faced by attempts to base such ontological conclusions on the success
of these theories.
|
| adam_txt |
Contents
Preface
ix
Acknowledgements
xiii
Introduction
xv
ι
.
What is a gauge theory?
ι
1.1 Classical
electromagnetism:
a paradigm gauge theory
3
1.2
A fiber bundle formulation
7
1.2.1
Electromagnetic interactions of quantum partides
14
1.2.2
Electromagnetic interactions of matter fields
18
2.
The Aharonov—
Bohm
efect
21
2.1
Fiber bundles
26
2.2
A gauge-invariant, local explanation?
31
2.3
Geometry and topology in the Aharonov—Bohm effect
40
2.4
Locality in the Aharonov—Bohm effect
44
2.5
Lessons for classical
electromagnetism
54
3.
Classical gauge theories
58
3.1
Non-Abelian Yang-Milk theories
58
3.1.1
The fiber bundle formulation
64
3.1.2
Loops, groups, and hoops
70
3.1.3
Topologica!
issues
74
3.2
A fiber bundle formulation of general relativity
77
3.2.1
A gravitational analog to the Aharonov—
Bohm efiect
78
4.
Interpreting classical gauge theories
82
4.1
The no gauge potential properties view
83
4.2
The localized gauge potential properties view
85
4.2.1
Problems defining theoretical terms
91
4.2.2
Leeds's view
99
4.2.3
Maudlin's interpretation
102
4.3
The non-localized gauge potential properties view
104
4.4
A holonomyinterpretation in
4.4.
r Epistemological
considerations
112
4.4.2
Objections considered
119
4.4.3
Semantic considerations
122
4.5
Metaphysical implications: non-separability and holism
123
VI
CONTENTS
5.
Quantized Yang—Mills gauge theories
129
5.1
How to quantize a classical field
131
5.2
Coulomb gauge quantization
133
5.3 Lorenz
gauge quantization
135
5.4
Classical electromagnetism as a constrained Hamiltonian system
136
5.5
The free Maxwell field as a Hamiltonian system
139
5.6
Path-integral quantization
141
5.7
Canonical quantization of non-Abelian fields
143
5.8
Path-integral quantization of non-Abelian fields
145
5.9
Interacting fields in the Lagrangian formulation
146
6.
The empirical import of gauge symmetry
149
6.1
Two kinds of symmetry
150
6.2
Observing gauge symmetry?
155
6.3
The gauge argument
159
6.4
Ghost fields
167
6.5
Spontaneous symmetry-breaking
169
6.6
The
ö-vacuum
175
6.7
Anomalies
182
7.
Loop representations
184
7.1
The significance of loop representations
185
7.2
Loop representations of the free Maxwell field
186
7.3
Loop representations of other free Yang—Mills fields
192
7.4
Interacting fields in loop representations
195
7.5
The
ö-vacuum in
a loop representation
197
7.6
Conclusion
198
8.
Interpreting quantized Yang—Mills gauge theories
200
8.1
Auyang's event ontology
200
8.2
Problems of interpreting a quantum field theory
203
8.2.1
Particle interpretations
205
8.2.2
Bohmian interpretations
209
8.2.3
Copenhagen interpretations
212
8.2.4
Everettian interpretations
215
8.2.5
Modal interpretations
218
9.
Conclusions
220
A. Electromagnetism and its generalizations
229
B. Fiber bundles
233
C. The constrained Hamiltonian formalism
248
CONTENTS
Vil
D.
Alternative
quantum
representations
257
E.
Algebraic quantum field theory
265
F. Interpretations of quantum mechanics
272
F.i The Copenhagen interpretation
272
F.2 Bohmian mechanics
274
F.3 Everettian interpretations
276
F.4 Modal interpretations
278
Bibliography
280
Index
287
Gauge theories have provided our most successful representations of the fundamental forces
of nature. How, though, do such representations work? Interpretations of gauge theory aim
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.
A gauge theory's representations are mathematical structures. These may be transformed
among themselves while certain features remain the same. Do the representations related
by such a gauge transformation merely offer alternative ways of representing the very same
situation? If so, then gauge symmetry is a purely formal property since it reflects no
corresponding symmetry in nature.
Gauging What's Real describes the representations provided by gauge theories in both
classical and quantum physics. Richard Healey defends the thesis that gauge transformations
are purely formal symmetries of almost all the classes of representations provided by each of
our theories of fundamental forces. He argues that evidence for classical gauge theories offerees
(other than gravity) gives us reason to believe that loops rather than points are the locations of
fundamental properties. In addition to exploring the prospects of extending this conclusion
to the quantum gauge theories of the Standard Model of elementary particle physics, Healey
assesses the difficulties faced by attempts to base such ontological conclusions on the success
of these theories. |
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| id | DE-604.BV022576326 |
| illustrated | Illustrated |
| index_date | 2024-07-02T18:15:09Z |
| indexdate | 2024-07-09T21:00:45Z |
| institution | BVB |
| isbn | 9780199287963 0199287961 |
| language | English |
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| physical | XIX, 297 S. graph. Darst. |
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| spelling | Healey, Richard Verfasser (DE-588)142209716 aut Gauging what's real the conceptual foundations of contemporary gauge theories Richard Healey 1. publ. Oxford [u.a.] Oxford Univ. Press 2007 XIX, 297 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Champs de jauge (physique) ram Physique - Philosophie ram Philosophie Gauge fields (Physics) Gauge fields (Physics) / Philosophy Eichtheorie (DE-588)4122125-4 gnd rswk-swf Erkenntnistheorie (DE-588)4070914-0 gnd rswk-swf Messtheorie (DE-588)4169537-9 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Messtheorie (DE-588)4169537-9 s Physik (DE-588)4045956-1 s DE-604 Erkenntnistheorie (DE-588)4070914-0 s Eichtheorie (DE-588)4122125-4 s Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015782585&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015782585&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Healey, Richard Gauging what's real the conceptual foundations of contemporary gauge theories Champs de jauge (physique) ram Physique - Philosophie ram Philosophie Gauge fields (Physics) Gauge fields (Physics) / Philosophy Eichtheorie (DE-588)4122125-4 gnd Erkenntnistheorie (DE-588)4070914-0 gnd Messtheorie (DE-588)4169537-9 gnd Physik (DE-588)4045956-1 gnd |
| subject_GND | (DE-588)4122125-4 (DE-588)4070914-0 (DE-588)4169537-9 (DE-588)4045956-1 |
| title | Gauging what's real the conceptual foundations of contemporary gauge theories |
| title_auth | Gauging what's real the conceptual foundations of contemporary gauge theories |
| title_exact_search | Gauging what's real the conceptual foundations of contemporary gauge theories |
| title_exact_search_txtP | Gauging what's real the conceptual foundations of contemporary gauge theories |
| title_full | Gauging what's real the conceptual foundations of contemporary gauge theories Richard Healey |
| title_fullStr | Gauging what's real the conceptual foundations of contemporary gauge theories Richard Healey |
| title_full_unstemmed | Gauging what's real the conceptual foundations of contemporary gauge theories Richard Healey |
| title_short | Gauging what's real |
| title_sort | gauging what s real the conceptual foundations of contemporary gauge theories |
| title_sub | the conceptual foundations of contemporary gauge theories |
| topic | Champs de jauge (physique) ram Physique - Philosophie ram Philosophie Gauge fields (Physics) Gauge fields (Physics) / Philosophy Eichtheorie (DE-588)4122125-4 gnd Erkenntnistheorie (DE-588)4070914-0 gnd Messtheorie (DE-588)4169537-9 gnd Physik (DE-588)4045956-1 gnd |
| topic_facet | Champs de jauge (physique) Physique - Philosophie Philosophie Gauge fields (Physics) Gauge fields (Physics) / Philosophy Eichtheorie Erkenntnistheorie Messtheorie Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015782585&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015782585&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT healeyrichard gaugingwhatsrealtheconceptualfoundationsofcontemporarygaugetheories |