Magnetic Monopoles:
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| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2010
|
| Edition: | 1. ed., [softcover version of orig. ed.] |
| Series: | Texts and monographs in physics
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XVIII, 532 S. graph. Darst. |
| ISBN: | 9783642064487 3642064485 |
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| 020 | |a 9783642064487 |c Pb. : EUR 112.30 (DE) |9 978-3-642-06448-7 | ||
| 020 | |a 3642064485 |c Pb. : EUR 112.30 (DE) (freier Pr.), sfr 150.50 (freier Pr.) |9 3-642-06448-5 | ||
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| 245 | 1 | 0 | |a Magnetic Monopoles |c Yakov M. Shnir |
| 250 | |a 1. ed., [softcover version of orig. ed.] | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2010 | |
| 300 | |a XVIII, 532 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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Record in the Search Index
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Contents
Part I Dirac
Monopole
1
Magnetic
Monopole
in Classical Theory
. 3
1.1
Non-Relativistic Scattering on a Magnetic Charge
. 3
1.2
Non-Relativistic Scattering on a Dyon
. 10
1.3
Vector Potential of
a
Monopole
Field
. 12
1.4
Transformations of the String
. 15
1.5
Dynamical Symmetries of the Charge-
Monopole
System
. 20
1.6
Dual
Invariance
of Classical Electrodynamics
. 22
2
The
Electron-Monopole
System:
Quantum-Mechanical Interaction
. 27
2.1
Charge Quantization Condition
. 27
2.2
Spin-Statistics Theorem in
a Monopole
Theory
. 31
2.3
Charge-Monopole
System: Quantum-Mechanical Description
. 33
2.3.1
The Generalized Spherical Harmonics
. 34
2.3.2
Solving the Radial
Schrödinger
Equation
. 37
2.4
Non-Relativistic Scattering on
a
Monopole:
Quantum Mechanical Description
. 40
2.5 Charge-Monopole
System: Spin in the
Pauli
Approximation
. 42
2.5.1
Dynamical Supersymmery
of the
Electron-Monopole
System
. 44
2.5.2
Generalized Spinor Harmonics:
j
>
μ +
1/2. 46
2.5.3
Generalized Spinor Harmonics:
j
=
μ
— 1/2. 48
2.5.4
Solving the Radial
Pauli
Equation
. 49
2.6 Charge-Monopole
System: Solving the Dirac Equation
. 53
2.6.1
Zero Modes and
Witten
Effect
. 55
2.6.2
Charge Quantization Condition
and the Group SL{2,
Ћ)
. 61
3
Topological Roots of the Abelian
Monopole. 67
3.1
Abelian
Wu-Yang Monopole. 67
3.2
Differential Geometry and Topology
. 70
3.2.1
Notions of Topology
. 70
3.2.2
Notions of Differential Geometry
. 81
XIV Contents
3.2.3
Maxwell
Ełectrodynaraics
and Differential Forms
. 89
3.3
Wu-Yang
Monopole
and the Fiber-Bundle Topology
. 93
3.3.1
Fiber Bundles
. 93
3.3.2
Principal Bundle and Connection
. 97
3.3.3
Wu-Yang
Monopole
Bundle
.102
3.3.4 Hopf
Bundle
.103
4
Abelian
Monopole:
Relativistic Quantum Theory
.109
4.1
Two Types of Charges
.110
4.2
Two-Potential Formulation of Electrodynamics
.112
4.2.1
Energy-Momentum Tensor and Angular Momentum
. 115
4.3
Canonical Quantization
.118
4.3.1
Relativistic
Invariance
of Two-Charge Electrodynamics
121
4.4
Renormalization of QED with a Magnetic Charge
.125
4.5
Vacuum Polarization by a Dyon Field
.128
4.6
Effective Lagrangian of QED with a Magnetic Charge
.132
Part II
Monopole
in
Non-
Abelian Gauge Theories
5
't Hooft—
Polyakov
Monopole
.141
5.1
SU
(2)
Georgi-Glashow Model and the Vacuum Structure.
. 141
5.1.1
Non-
Abelian Wu-Yang
Monopole
.141
5.1.2
Georgi-Glashow Model
.143
5.1.3
Topological Classification of the Solutions
.146
5.1.4
Definition of Magnetic Charge
.148
5.1.5
't Hooft-Polyakov
Ansatz .151
5.1.6
Singular Gauge Transformations
and the Connection between't Hooft-Polyakov
and Dirac
monopoles
.154
5.1.7
Dyons
.155
5.2
The Bogomol'nyi Limit
.157
5.2.1
Gauge Zero Mode and the Electric Dyon Charge
.161
5.3
Topological Classification of Non-Abelian
Monopoles
.163
5.3.1
SO(3) vs Si/
(2).163
5.3.2
Magnetic Charge and the Topology
of the Gauge Group
.165
5.3.3
Equivalence of Topological and Magnetic Charge
.166
5.3.4
Topology of the Dyon Sector
.168
5.4
The
θ
Term and the
Witten
Effect Again
.170
Contents
XV
6 Multimonopole
Configurations.
173
6.1 Multimonopoles
Configurations
and Singular
Gauge Transformations
.174
6.1.1
Singular SU(2)
Monopole
with Charge
g
=
ngo
.174
6.1.2
Magnetic
Dipole .176
6.2
Rebbi-Rossi
Multimonopoles, Chains
of
Monopoles
and Closed Vortices
.178
6.3
Interaction of Magnetic
Monopoles
.192
6.3.1
Monopole
in External Magnetic Field
.192
6.3.2
The Interaction Energy of
Monopoles
.194
6.3.3
Classical Interaction
of Two Widely Separated Dyons
.197
6.4
The rc-Monopole Configuration in the
BPS
Limit
.201
6.4.1
BPS
Multimonopoles: A Bird's Eye View
.201
6.4.2
Projective
Spaces and Twistor Methods
.203
6.4.3
The n-Monopole Twistor Construction
.206
6.4.4
Hitchin Approach and the Spectral Curve
.214
6.4.5 Nahm
Equations
.217
6.4.6
Solution of the
Nahm
Equations
.220
6.4.7
The
Nahm Data
and Spectral Curve
.223
6.5
Moduli Space and Low-Energy Multimonopoles Dynamics
. 227
6.5.1
Zero Modes Lagrangian and the Moduli Space Metric
. 227
6.5.2
Metric on the Space M2
.232
6.5.3
Low-Energy Scattering of Two
Monopoles
.236
7
SU(2)
Monopole
in Quantum Theory
.241
7.1
Field Fluctuations on
Monopole
Background
.241
7.1.1
Generalized Angular Momentum and the Spectrum
of Fluctuations
.245
7.1.2
Quantum Correction to the Mass of
a Monopole
.250
7.2
Non-Abelian
Monopole:
Quasiclassical Quantization
.254
7.2.1
Collective Coordinates and Constraints
.254
7.2.2
Quantum Mechanics on the Moduli Space
.258
7.2.3
Evaluation of the Generating Functional
.263
7.3
gg Pair Creation in an External Magnetic Field
.267
7.3.1
Dynamics of Non-Abelian
Monopole
in Weak External Field
.267
7.3.2
Met
ast
able Vacuum Decay and
Monopole Pair
Creation in an External Field
.269
8
Monopoles
Beyond SU(2) Group
.275
8.1
SU(N)
Monopoles
.276
8.1.1
Generalization of the Charge Quantization Condition
. 276
8.1.2
Towards Higher Rank Gauge Groups
.277
8.1.3
Montonen-Olive Conjecture
.279
XVI Contents
8.1.4
Cartari-Weyl
Basis and the Simple Roots
.282
8.1.5
SU{S) Cartan Algebra
.284
8.1.6 517(3)
Monopoles
.287
8.2
Massive and Massless
Monopoles
.301
8.2.1
Pathologies of Non-Abelian Gauge Transformations
. 303
8.3 5*7(3)
Monopole
Moduli Space
.306
8.3.1 5(7(3)
Monopoles:
Nahm
Equations
.314
9
Monopoles
and the Problem of Confinement
.319
9.1
Quark Confinement in QCD
.319
9.1.1
Dual Superconductor
.324
9.2
Monopoles
in the Lattice QCD
.328
9.2.1
Compact QED and Lattice
Monopoles
.331
9.2.2
Lattice Duality
.334
9.3
Abelian Projection
.339
9.3.1
"Monopoles"
from Abelian Projection
.339
9.3.2
Maximal Abelian Gauge
.346
9.4
Polyakov Solution of Confinement
in the
ti
= 3
Georgi-Glashow Model
.349
9.4.1
Dilute Gas of
Monopoles
in the
d
= 3
Georgi-Glashow Model
.349
9.4.2
Wilson Loop Operator in
d
= 3
Georgi-Glashow Model
.355
10
Rubakov-Callan Effect
.359
10.1
Dirac Hamiltonian
on the Non-Abelian
Monopole
Background
.359
10.1.1
Fermionic Zero Modes
.363
10.1.2
Zero Modes and the Index Theorem
.367
10.1.3
S-Wave Fermion Scattering on
a Monopole
.373
10.2
Anomalous Non-Conservation of the Fermion Number
.378
10.2.1
Axial Anomaly and the Vacuum Structure
.378
10.2.2
Effective Action of Massless
Fermions
.379
10.2.3
Properties of the Anomalous Fermion Condensate
. 385
10.2.4
Properties of Other Condensates
.388
10.3
Monopole-Fermion Scattering
in the Bosonisation Technique
.390
10.3.1
Vertex Operator and Bosonization
of the Free Model
.391
10.3.2
Monopole
Catalysis of the Proton Decay
.397
10.3.3
Monopole
Catalysis of the Proton Decay:
Semiclassical Model
.400
Contents XVII
Part III Supersymmetric
Monopoles
11
Supersymmetric Yang-Mills Theories
.407
11.1
What is Supersymmetry?
.407
11.1.1
Poincaré
Group and Algebra of Generators
.408
11.1.2
Algebra of Generators of Supersymmetry
.412
11.2
Representations of SUSY Algebra
.415
11.2.1
TV
= 1
Massive
Multiplets
.415
11.2.2
TV
= 1
Massless
Multiplets
.417
11.2.3
JV
= 2
Extended SUSY
.418
11.3
Local Representations of SUSY
.420
11.3.1
TV
= 1
Superspace
.420
11.3.2 N = 1
Superfields
.424
11.3.3
Non-Abelian
Multiplets
.428
11.4
TV
= 1
SUSY Lagrangians
.429
12
Magnetic
Monopoles
in the TV
= 2
Supersymmetric Yang—Mills Theory
.437
12.1
TV
= 2
Supersymmetric Lagrangian
.437
12.1.1
Praise of Beauty of TV
= 2
SUSY Yang-Mills
.441
12.2
TV
= 2
Supersymmetric SU(2) Magnetic
Monopoles
.443
12.2.1
Construction of TV
= 2
Supersymmetric
SU(2)
Monopoles
.443
12.3
Central Charges in the TV
= 2
SUSY Yang-Mills
.446
12.4
Fermionic Zero Modes in Supersymmetric Theory
.449
12.5
Low Energy Dynamics of Supersymmetric
Monopoles
.451
12.6
TV
= 2
Supersymmetric
Monopoles
beyond
S U
(2).453
12.6.1
SU(3) TV
= 2
Supersymmetric
Monopoles
.458
13 Seiberg-
Witten
Solution
of TV
= 2
SUSY Yang-Mills Theory
.465
13.1
Moduli Space
.466
13.1.1
Moduli Space and its Parameterization
.466
13.1.2
Quantum Moduli Space
of
N = 2
SUSY Yang-Mills Theory
.472
13.2
Global Parametrization of the Quantum Moduli Space
.478
13.2.1
Transformation of Duality
for
N = 2
Low-Energy Effective Theory
.478
13.2.2
BPS
Bound Reexamined
.483
13.3
Seiberg-Witten Explicit Solution
.485
13.3.1
Monodromies on the Moduli Space
.485
13.3.2
Solution of the Monodromy Problem
.492
13.3.3
Confinement and the
Monopole
Condensation
.496
13.4
Concluding Remarks
.498
XVIII
Contents
A Representations of SU(2)
.501
В
Quaternions
.505
С
SU
(2)
Transformations of the
Monopole
Potential
.509
References
.513
Index
.529 |
| any_adam_object | 1 |
| author | Shnir, Yakov M. |
| author_GND | (DE-588)130341231 |
| author_facet | Shnir, Yakov M. |
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| author_sort | Shnir, Yakov M. |
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| building | Verbundindex |
| bvnumber | BV039630908 |
| classification_rvk | UO 6430 |
| ctrlnum | (OCoLC)760128877 (DE-599)DNB100849982X |
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| format | Book |
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| id | DE-604.BV039630908 |
| illustrated | Illustrated |
| indexdate | 2024-07-21T00:12:24Z |
| institution | BVB |
| isbn | 9783642064487 3642064485 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024481043 |
| oclc_num | 760128877 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XVIII, 532 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series2 | Texts and monographs in physics |
| spelling | Shnir, Yakov M. Verfasser (DE-588)130341231 aut Magnetic Monopoles Yakov M. Shnir 1. ed., [softcover version of orig. ed.] Berlin [u.a.] Springer 2010 XVIII, 532 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts and monographs in physics Monopôles magnétiques Magnetic monopoles Magnetischer Monopol (DE-588)4168573-8 gnd rswk-swf Magnetischer Monopol (DE-588)4168573-8 s DE-604 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3605273&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024481043&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shnir, Yakov M. Magnetic Monopoles Monopôles magnétiques Magnetic monopoles Magnetischer Monopol (DE-588)4168573-8 gnd |
| subject_GND | (DE-588)4168573-8 |
| title | Magnetic Monopoles |
| title_auth | Magnetic Monopoles |
| title_exact_search | Magnetic Monopoles |
| title_full | Magnetic Monopoles Yakov M. Shnir |
| title_fullStr | Magnetic Monopoles Yakov M. Shnir |
| title_full_unstemmed | Magnetic Monopoles Yakov M. Shnir |
| title_short | Magnetic Monopoles |
| title_sort | magnetic monopoles |
| topic | Monopôles magnétiques Magnetic monopoles Magnetischer Monopol (DE-588)4168573-8 gnd |
| topic_facet | Monopôles magnétiques Magnetic monopoles Magnetischer Monopol |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3605273&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024481043&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT shniryakovm magneticmonopoles |