Group theory for the standard model of particle physics and beyond:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton
Taylor & Francis
2010
|
| Series: | Series in high energy physics, cosmology, and gravitation
|
| Subjects: | |
| Online Access: | Volltext Volltext Inhaltsverzeichnis |
| Physical Description: | XIII, 241 Seiten Illustrationen |
| ISBN: | 9781420078749 |
| DOI: | 10.1201/9781439895207 |
Staff View
MARC
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| 245 | 1 | 0 | |a Group theory for the standard model of particle physics and beyond |c Ken J. Barnes |
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| 300 | |a XIII, 241 Seiten |b Illustrationen | ||
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Record in the Search Index
| _version_ | 1804140702121066497 |
|---|---|
| adam_text | Contents
Preface
..................................................................ix
Acknowledgments
.......................................................xi
Introduction
............................................................xiii
1
Symmetries and Conservation Laws
................................1
Lagrangian and Hamiltonian Mechanics
.............................2
Quantum Mechanics
.................................................6
The Oscillator Spectrum: Creation and Annihilation Operators
.....8
Coupled Oscillators: Normal Modes
................................10
One-Dimensional Fields: Waves
....................................13
The Final Step: Lagrange—Hamilton Quantum Field Theory
.........16
References
..........................................................20
Problems
...........................................................20
2
Quantum Angular Momentum
.....................................23
Index Notation
.....................................................23
Quantum Angular Momentum
.....................................25
Result
..............................................................27
Matrix Representations
.............................................28
Spin
1..............................................................28
Addition of Angular Momenta
.....................................30
Clebsch-Gordan Coefficients
.......................................32
Notes
............................................................33
Matrix Representation of Direct (Outer,
Kronecker)
Products
........34
i(g)ì=:10Oin
Matrix Representation
............................35
Checks
..........................................................36
Change of Basis
....................................................37
Exercise
.........................................................38
References
..........................................................38
Problems
...........................................................38
3
Tensors and Tensor Operators
......................................41
Scalars
...........................................................41
Scalar Fields
.....................................................42
Invariant functions
..............................................42
Contravariant
Vectors
(ŕ
->
Index at Top)
.........................43
Covariant Vectors (Co
=
Goes Below)
............................44
Notes
............................................................44
vi
Contents
Tensors.............................................................45
Notes
and Properties
.............................................45
Rotations...........................................................
47
Vector Fields
.......................................................48
Tensor Operators
...................................................49
Scalar Operator
..................................................49
Vector Operator
..................................................49
Notes
............................................................50
Connection with Quantum Mechanics
..............................51
Observables
.....................................................51
Rotations
........................................................52
Scalar Fields
.....................................................52
Vector Fields
.....................................................53
Specification of Rotations
...........................................55
Transformation of Scalar Wave Functions
............................56
Finite Angle Rotations
..............................................57
Consistency with the Angular Momentum Commutation Rules
......58
Rotation of Spinor Wave Function
..................................58
Orbital Angular Momentum (x_
x p)
................................60
The Spinors Revisited
..............................................65
Dimensions of Projected Spaces
.....................................67
Connection between the Mixed Spinor
and the Adjoint (Regular) Representation
...........................67
Finite Angle Rotation of SO(3) Vector
...............................68
References
..........................................................69
Problems
...........................................................69
4
Special Relativity and the Physical Particle States
.................71
The Dirac Equation
.................................................71
The Clifford Algebra: Properties of
γ
Matrices
......................72
Structure of the Clifford Algebra and Representation
................74
Lorentz
Covariance of the Dirac Equation
...........................76
The Adjoint
........................................................78
The Nonrelativistic Limit
...........................................79
Poincaré
Group: Inhomogeneous
Lorentz
Group
....................80
Homogeneous (Later Restricted)
Lorentz
Group
....................82
Notes
............................................................84
The
Poincaré
Algebra
...............................................88
The
Casimir
Operators and the States
...............................89
References
..........................................................93
Problems
...........................................................93
5
The Internal Symmetries
...........................................95
References
........................................................105
Problems
..........................................................105
Contents
vii
6
Lie Group Techniques
for the
Standard
Model Lie Groups
.......107
Roots
and Weights
................................................108
Simple Roots
......................................................111
The
Cartari
Matrix
.................................................113
Finding All the
Roots
..............................................113
Fundamental Weights
.............................................115
The Weyl Group
...................................................116
Young Tableaux
...................................................117
Raising the Indices
................................................117
The Classification Theorem (Dynkin)
..............................119
Result
.............................................................119
Coincidences
......................................................119
References
........................................................120
Problems
..........................................................120
7
Noether s Theorem and Gauge Theories of the First
and Second Kinds
................................................125
References
........................................................129
Problems
..........................................................129
8
Basic Couplings of the Electromagnetic, Weak,
and Strong Interactions
...........................................131
References
........................................................136
Problems
..........................................................136
9
Spontaneous Symmetry Breaking and the Unification
of the Electromagnetic and Weak Forces
..........................139
References
........................................................144
Problems
..........................................................145
10
The
Goldstone
Theorem and the Consequent Emergence
of Nonlinearly Transforming Massless
Goldstone
Bosons
........147
References
........................................................151
Problems
..........................................................151
U
The Higgs Mechanism and the Emergence of Mass
from Spontaneously Broken Symmetries
.........................153
References
........................................................155
Problems
..........................................................155
12
Lie Group Techniques for beyond the Standard
Model Lie Groups
................................................157
References
........................................................159
Problems
......................................................160
vüi Contents
13
The Simple Sphere
...............................................161
References
........................................................181
Problems
..........................................................182
14
Beyond the Standard Model
......................................185
Massive Case
......................................................188
Massless Case
.....................................................188
Projection Operators
...............................................189
Weyl Spinors and Representation
..................................190
Charge Conjugation and
Majorana
Spinor.........................
192
A Notational Trick
.................................................194
SL(2, C) View
.....................................................194
Unitary Representations
...........................................195
Supersymmetry: A First Look at the Simplest (N
— 1)
Case
........196
Massive Representations
..........................................197
Massless Representations
..........................................199
Superspace
........................................................200
Three-Dimensional Euclidean Space (Revisited)
....................200
Covariant Derivative Operators from Right Action
.................207
Superfields
........................................................209
Supertransformations
.............................................211
Notes
...........................................................211
The Chiral Scalar
Multiplet
........................................212
Superspace Methods
..............................................213
Covariant Definition of Component Fields
.........................214
Supercharges Revisited
............................................214
Invariants and Lagrangians
........................................217
Notes
...........................................................220
Superpotential
....................................................221
References
........................................................225
Problems
..........................................................225
Index
..................................................................229
|
| any_adam_object | 1 |
| author | Barnes, Ken J. 1938- |
| author_GND | (DE-588)13945537X |
| author_facet | Barnes, Ken J. 1938- |
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| callnumber-subject | QC - Physics |
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| collection | ebook ZDB-94-OAL ZDB-7-TOA |
| ctrlnum | (OCoLC)367421710 (DE-599)BVBBV035771952 |
| dewey-full | 539.7/25 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 539 - Modern physics |
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| dewey-tens | 530 - Physics |
| discipline | Physik |
| doi_str_mv | 10.1201/9781439895207 |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T22:04:10Z |
| institution | BVB |
| isbn | 9781420078749 |
| language | English |
| lccn | 2009021685 |
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| physical | XIII, 241 Seiten Illustrationen |
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| spelling | Barnes, Ken J. 1938- Verfasser (DE-588)13945537X aut Group theory for the standard model of particle physics and beyond Ken J. Barnes Boca Raton Taylor & Francis 2010 XIII, 241 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Series in high energy physics, cosmology, and gravitation Quantentheorie Group theory Quantum theory Particle range (Nuclear physics) Elementarteilchenphysik (DE-588)4014414-8 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Standardmodell Elementarteilchenphysik (DE-588)4297710-1 gnd rswk-swf Elementarteilchenphysik (DE-588)4014414-8 s Gruppentheorie (DE-588)4072157-7 s DE-604 Standardmodell Elementarteilchenphysik (DE-588)4297710-1 s Erscheint auch als Online-Ausgabe 978-1-439-89520-7 Erscheint auch als Online-Ausgabe 10.1201/9781439895207 978-0-429-18455-0 https://doi.org/10.1201/9781439895207 Verlag kostenfrei Volltext https://library.oapen.org/handle/20.500.12657/50881 Aggregator kostenfrei Volltext Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018631635&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Barnes, Ken J. 1938- Group theory for the standard model of particle physics and beyond Quantentheorie Group theory Quantum theory Particle range (Nuclear physics) Elementarteilchenphysik (DE-588)4014414-8 gnd Gruppentheorie (DE-588)4072157-7 gnd Standardmodell Elementarteilchenphysik (DE-588)4297710-1 gnd |
| subject_GND | (DE-588)4014414-8 (DE-588)4072157-7 (DE-588)4297710-1 |
| title | Group theory for the standard model of particle physics and beyond |
| title_auth | Group theory for the standard model of particle physics and beyond |
| title_exact_search | Group theory for the standard model of particle physics and beyond |
| title_full | Group theory for the standard model of particle physics and beyond Ken J. Barnes |
| title_fullStr | Group theory for the standard model of particle physics and beyond Ken J. Barnes |
| title_full_unstemmed | Group theory for the standard model of particle physics and beyond Ken J. Barnes |
| title_short | Group theory for the standard model of particle physics and beyond |
| title_sort | group theory for the standard model of particle physics and beyond |
| topic | Quantentheorie Group theory Quantum theory Particle range (Nuclear physics) Elementarteilchenphysik (DE-588)4014414-8 gnd Gruppentheorie (DE-588)4072157-7 gnd Standardmodell Elementarteilchenphysik (DE-588)4297710-1 gnd |
| topic_facet | Quantentheorie Group theory Quantum theory Particle range (Nuclear physics) Elementarteilchenphysik Gruppentheorie Standardmodell Elementarteilchenphysik |
| url | https://doi.org/10.1201/9781439895207 https://library.oapen.org/handle/20.500.12657/50881 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018631635&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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