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E-grāmata: Group Theory for the Standard Model of Particle Physics and Beyond

(University of Southampton, UK)
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Group Theory for the Standard Model of Particle Physics and BeyondPalielināt
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Based on the authors well-established courses, Group Theory for the Standard Model of Particle Physics and Beyond explores the use of symmetries through descriptions of the techniques of Lie groups and Lie algebras. The text develops the models, theoretical framework, and mathematical tools to understand these symmetries.

After linking symmetries with conservation laws, the book works through the mathematics of angular momentum and extends operators and functions of classical mechanics to quantum mechanics. It then covers the mathematical framework for special relativity and the internal symmetries of the standard model of elementary particle physics. In the chapter on Noethers theorem, the author explains how Lagrangian formalism provides a natural framework for the quantum mechanical interpretation of symmetry principles. He then examines electromagnetic, weak, and strong interactions; spontaneous symmetry breaking; the elusive Higgs boson; and supersymmetry. He also introduces new techniques based on extending spacetime into dimensions described by anticommuting coordinates.

Designed for graduate and advanced undergraduate students in physics, this text provides succinct yet complete coverage of the group theory of the symmetries of the standard model of elementary particle physics. It will help students understand current knowledge about the standard model as well as the physics that potentially lies beyond the standard model.

Recenzijas

The book is clearly written In addition to references, there are copious problems at the end of each chapter which add to the value of the book This readable text will be of value to theoreticians entering the area of quantum field theory and also to more seasoned researchers in other areas of physics who wish to remind themselves of the basic group theoretical underpinning of that most fundamental of all physical theories. Allan I. Solomon, Contemporary Physics, 52, 2011

This book provides a lucid and readable account of group theory relevant to gauge theories and is a welcome addition to the available texts in the area. The presentation of difficult topics is clear and suitable for a reader new to the subject, while enough material is included to make this book useful as a reference for more experienced researchers. The material is a pleasure to read and enlightening. Overall, this book is well written and presents this important topic in an excellent and clear way. readers with a more theoretical background will find this book an essential read. In conclusion, every student and researcher in high energy physics should read this excellent book. Robert Appleby, Reviews, Volume 11, Issue 2, 2010

Preface ix
Acknowledgments xi
Introduction xiii
Symmetries and Conservation Laws
1(22)
Lagrangian and Hamiltonian Mechanics
2(4)
Quantum Mechanics
6(2)
The Oscillator Spectrum: Creation and Annihilation Operators
8(2)
Coupled Oscillators: Normal Modes
10(3)
One-Dimensional Fields: Waves
13(3)
The Final Step: Lagrange-Hamilton Quantum Field Theory
16(4)
References
20(1)
Problems
20(3)
Quantum Angular Momentum
23(18)
Index Notation
23(2)
Quantum Angular Momentum
25(2)
Result
27(1)
Matrix Representations
28(1)
Spin 1/2
28(2)
Addition of Angular Momenta
30(2)
Clebsch-Gordan Coefficients
32(2)
Notes
33(1)
Matrix Representation of Direct (Outer, Kronecker) Products
34(1)
1/2 ⊗ 1/2 = 1 0 in Matrix Representation
35(2)
Checks
36(1)
Change of Basis
37(1)
Exercise
38(1)
References
38(1)
Problems
38(3)
Tensors and Tensor Operators
41(30)
Scalars
41(1)
Scalar Fields
42(1)
Invariant functions
42(1)
Contravariant Vectors (t → Index at Top)
43(1)
Covariant Vectors (Co = Goes Below)
44(1)
Notes
44(1)
Tensors
45(2)
Notes and Properties
45(2)
Rotations
47(1)
Vector Fields
48(1)
Tensor Operators
49(2)
Scalar Operator
49(1)
Vector Operator
49(1)
Notes
50(1)
Connection with Quantum Mechanics
51(4)
Observables
51(1)
Rotations
52(1)
Scalar Fields
52(1)
Vector Fields
53(2)
Specification of Rotations
55(1)
Transformation of Scalar Wave Functions
56(1)
Finite Angle Rotations
57(1)
Consistency with the Angular Momentum Commutation Rules
58(1)
Rotation of Spinor Wave Function
58(2)
Orbital Angular Momentum (x × p)
60(5)
The Spinors Revisited
65(2)
Dimensions of Projected Spaces
67(1)
Connection between the ``Mixed Spinor'' and the Adjoint (Regular) Representation
67(1)
Finite Angle Rotation of SO(3) Vector
68(1)
References
69(1)
Problems
69(2)
Special Relativity and the Physical Particle States
71(24)
The Dirac Equation
71(1)
The Clifford Algebra: Properties of γ Matrices
72(2)
Structure of the Clifford Algebra and Representation
74(2)
Lorentz Covariance of the Dirac Equation
76(2)
The Adjoint
78(1)
The Nonrelativistic Limit
79(1)
Poincare Group: Inhomogeneous Lorentz Group
80(2)
Homogeneous (Later Restricted) Lorentz Group
82(2)
Notes
84(4)
The Poincare Algebra
88(1)
The Casimir Operators and the States
89(4)
References
93(1)
Problems
93(2)
The Internal Symmetries
95(12)
References
105(1)
Problems
105(2)
Lie Group Techniques for the Standard Model Lie Groups
107(18)
Roots and Weights
108(3)
Simple Roots
111(2)
The Cartan Matrix
113(1)
Finding All the Roots
113(2)
Fundamental Weights
115(1)
The Weyl Group
116(1)
Young Tableaux
117(1)
Raising the Indices
117(2)
The Classification Theorem (Dynkin)
119(1)
Result
119(1)
Coincidences
119(1)
References
120(1)
Problems
120(5)
Noether's Theorem and Gauge Theories of the First and Second Kinds
125(6)
References
129(1)
Problems
129(2)
Basic Couplings of the Electromagnetic, Weak, and Strong Interactions
131(8)
References
136(1)
Problems
136(3)
Spontaneous Symmetry Breaking and the Unification of the Electromagnetic and Weak Forces
139(8)
References
144(1)
Problems
145(2)
The Goldstone Theorem and the Consequent Emergence of Nonlinearly Transforming Massless Goldstone Bosons
147(6)
References
151(1)
Problems
151(2)
The Higgs Mechanism and the Emergence of Mass from Spontaneously Broken Symmetries
153(4)
References
155(1)
Problems
155(2)
Lie Group Techniques for beyond the Standard Model Lie Groups
157(4)
References
159(1)
Problems
160(1)
The Simple Sphere
161(24)
References
181(1)
Problems
182(3)
Beyond the Standard Model
185(44)
Massive Case
188(1)
Massless Case
188(1)
Projection Operators
189(1)
Weyl Spinors and Representation
190(2)
Charge Conjugation and Majorana Spinor
192(2)
A Notational Trick
194(1)
SL(2, C) View
194(1)
Unitary Representations
195(1)
Supersymmetry: A First Look at the Simplest (N = 1) Case
196(1)
Massive Representations
197(2)
Massless Representations
199(1)
Superspace
200(1)
Three-Dimensional Euclidean Space (Revisited)
200(7)
Covariant Derivative Operators from Right Action
207(2)
Superfields
209(2)
Supertransformations
211(1)
Notes
211(1)
The Chiral Scalar Multiplet
212(1)
Superspace Methods
213(1)
Covariant Definition of Component Fields
214(1)
Supercharges Revisited
214(3)
Invariants and Lagrangians
217(3)
Notes
220(1)
Superpotential
221(4)
References
225(1)
Problems
225(4)
Index 229
Ken J. Barnes is a Professor Emeritus in the School of Physics and Astronomy at the University of Southampton.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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