Classical solutions in quantum field theory: solitons and instantons in high energy physics
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
2012
|
| Edition: | 1. publ. |
| Series: | Cambridge monographs on mathematical physics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XIV, 326 S. graph. Darst. |
| ISBN: | 9780521114639 0521114632 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface
page
xiii
1
Introduction
1
1.1
Overview
1
1.2
Conventions
3
2
One-dimensional solitons
6
2.1
Kinks
6
2.2
Quantizing about the kink
13
2.3
Zero modes and collective coordinates
22
2.4
Fermions
and fermion zero modes
24
2.5
Kinks in more spacetime dimensions
27
2.6
Multikink dynamics
29
2.7
The sine-Gordon-massive Thirring model equivalence
34
3
Solitons in more dimensions
—
Vortices and strings
38
3.1
First attempt
—
global vortices
38
3.2
Derrick s theorem
42
3.3
Gauged vortices
44
3.4
Multivortex solutions
47
3.5
Quantization and zero modes
49
3.6
Adding
fermions
52
4
Some topology
57
4.1
Vacuum manifolds
57
4.2
Homotopy and the fundamental group
π (Μ)
58
4.3
Fundamental groups of Lie groups
61
4.4
Vortices and homotopy
64
4.5
Some illustrative vortex examples
68
4.6
Higher homotopy groups
74
4.7
Some results for higher homotopy groups
77
5
Magnetic
monopoles
with U(l) charges
81
5.1
Magnetic
monopoles
in
electromagnetism
81
5.2
The t Hooft-Polyakov
monopole
89
x
Contents
5.3
Another gauge, another viewpoint
94
5.4
Solutions with higher magnetic charge
96
5.5
Zero modes and dyons
97
5.6
Spin from isospin,
fermions
from bosons
100
5.7
Fermions
and
monopoles
104
6
Magnetic
monopoles
in larger gauge groups
108
6.1
Larger gauge groups
—
the external view
108
6.2
Larger gauge groups
—
topology
115
6.2.1
SU(3) broken to SU(2)xU(l)
115
6.2.2
A Z2
monopole
119
6.2.3
A light doubly charged
monopole
120
6.2.4
Electroweak
monopoles?
121
6.3
Monopoles
in grand unified theories
121
6.3.1
SU(5)
monopoles
122
6.3.2
SO(10)
monopoles
124
6.4
Chromodyons
125
6.5
The Callan-Rubakov effect
128
7
Cosmological implications and experimental bounds
130
7.1
Brief overview of big bang cosmology
130
7.2
Symmetry restoration and cosmological phase transitions
133
7.3
The Kibble mechanism
136
7.4
Gravitational and cosmological consequences of domain walls
and strings
139
7.5
Evolution of the primordial
monopole
abundance
142
7.6
Observational bounds and the primordial
monopole
problem
145
8
BPS solitons,
supersymmetry, and duality
149
8.1
The
BPS
limit as a limit of couplings
149
8.2
Energy bounds
151
8.3
Supersymmetry
155
8.4
Multisoliton solutions
160
8.5
The moduli space approximation
163
8.6
BPS monopoles
in larger gauge groups
166
8.7
Montonen-Olive duality
172
9
Euclidean solutions
175
9.1
Tunneling in one dimension
175
9.2
WKB tunneling with many degrees of freedom
178
9.3
Path integral approach to tunneling:
instantons
181
9.4
Path integral approach to tunneling: bounces
186
9.5
Field theory
190
Contents
Xl
10 Yang—
Mills
instantons
192
10.1
Ao
= 0
gauge
192
10.2
Yang-Mills vacua: Ao
= 0
gauge
194
10.3
Yang-Mills vacuum: axial gauge
201
10.4
Some topology
203
10.5
t Hooft
symbols
207
10.6
The unit
instanton
209
10.7
Mult
і-
inst
anton
solutions
212
10.8
Counting parameters with an index theorem
213
10.9
Larger gauge groups
220
10.10
The Atiyah Drinfeld-Hitchin
Manin
construction
223
10.11
The ADHM construction for larger gauge groups
228
10.12
One-loop corrections
231
11
Instantons,
fermions,
and physical consequences
236
11.1
Anomalies
236
11.2
Spectral flow and fermion zero modes
239
11.3
QCD and the U(l) problem
245
11.4 Baryon
number violation by electroweak processes
246
11.5
CP violation and the OFF term
248
12
Vacuum decay
254
12.1
Bounces in a scalar field theory
254
12.2
The
t
hin-
wall approximation
263
12.3
Evolution of the bubble after nucleation
265
12.4
Tunneling at finite temperature
267
12.5
Including gravity: bounce solutions
272
12.6
Interpretation of the bounce solutions
284
12.7
Curved spacetinie evolution after bubble nucleation
291
Appendix A: Roots and weights
295
A.I Root systems
295
A.
2
Weights
302
Appendix B: Index theorems for
BPS
solitone
305
B.I Vortices
306
B.2
Monopoles
308
References
312
Index
324
CAMBRIDGE MONOGRAPHS ON MATHEMATICAL PHYSICS
»SHOFF ft of Mathematical Physics, University of
Cantàridi
d.r.nelson Professor of
Ρ
Harvard University
Regenial
Professor of Science, University of Texas at Austin
This high!
med
series of monographs provides introductory accounts o specialized topics
in mathematical pi
r
graduate students and research workers. The monographs in this
ι
re of outstanding scholarship and written
b
at the very frontiers of research. Subject
areas covered include cosmology, astro} relativity theory, particle physics, quantum theory,
nuclear ph1 ttistical mechanics, condensed matter ph
ta
physics and the theory
липі
ι ι
his hook
Classical solutions play an important role in quantum field theory, high energy
p¡
and cosmology Real time soliton solutions give rise to particles, such as magnetic
monopoles,
and extended structures, such as domain walls and cosmic strings, that
e
implications for the cosmology of the early universe. Imaginary time Euclidean
instantom
are responsible for important nonperturbative effects, while Euclidean
bounce solutions govern transitions between metastable states.
Written for advanced graduate students and researchers in elementary particle
ph and related fields, this book brings the reader up to the level of
current re in the field. The first half of the book discusses the most important
classes of
sothöns:
kinks, vortices, and magnetic
monopoles.
The cosmological and
observational constraints on these are covered, as are more formal aspects, including
BPS
solitons and their connection with supersymmetry. The second half is devoted to
Euclid tattoos, with particular emphasis on Yang-Mills
instantons
and on bounce
solutions.
-
|
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| ctrlnum | (OCoLC)811550102 (DE-599)OBVAC09357575 |
| dewey-full | 530.143 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.143 |
| dewey-search | 530.143 |
| dewey-sort | 3530.143 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 1. publ. |
| format | Book |
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| spelling | Weinberg, Erick J. Verfasser aut Classical solutions in quantum field theory solitons and instantons in high energy physics Erick J. Weinberg 1. publ. Cambridge Cambridge Univ. Press 2012 XIV, 326 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge monographs on mathematical physics Instanton (DE-588)4161874-9 gnd rswk-swf Quasiklassisches Modell (DE-588)4318601-4 gnd rswk-swf Soliton (DE-588)4135213-0 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Quantum field theory. Quantenfeldtheorie (DE-588)4047984-5 s Quasiklassisches Modell (DE-588)4318601-4 s DE-604 Instanton (DE-588)4161874-9 s 1\p DE-604 Soliton (DE-588)4135213-0 s 2\p DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025671390&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025671390&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Weinberg, Erick J. Classical solutions in quantum field theory solitons and instantons in high energy physics Instanton (DE-588)4161874-9 gnd Quasiklassisches Modell (DE-588)4318601-4 gnd Soliton (DE-588)4135213-0 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| subject_GND | (DE-588)4161874-9 (DE-588)4318601-4 (DE-588)4135213-0 (DE-588)4047984-5 |
| title | Classical solutions in quantum field theory solitons and instantons in high energy physics |
| title_auth | Classical solutions in quantum field theory solitons and instantons in high energy physics |
| title_exact_search | Classical solutions in quantum field theory solitons and instantons in high energy physics |
| title_full | Classical solutions in quantum field theory solitons and instantons in high energy physics Erick J. Weinberg |
| title_fullStr | Classical solutions in quantum field theory solitons and instantons in high energy physics Erick J. Weinberg |
| title_full_unstemmed | Classical solutions in quantum field theory solitons and instantons in high energy physics Erick J. Weinberg |
| title_short | Classical solutions in quantum field theory |
| title_sort | classical solutions in quantum field theory solitons and instantons in high energy physics |
| title_sub | solitons and instantons in high energy physics |
| topic | Instanton (DE-588)4161874-9 gnd Quasiklassisches Modell (DE-588)4318601-4 gnd Soliton (DE-588)4135213-0 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| topic_facet | Instanton Quasiklassisches Modell Soliton Quantenfeldtheorie |
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