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El. knyga: Group Theory for High Energy Physicists

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  • Formatas: 230 pages
  • Išleidimo metai: 19-Apr-2016
  • Leidėjas: CRC Press Inc
  • Kalba: eng
  • ISBN-13: 9781466510647
Kitos knygos pagal šią temą:
Group Theory for High Energy PhysicistsDidesnis paveikslėlis
  • Formatas: 230 pages
  • Išleidimo metai: 19-Apr-2016
  • Leidėjas: CRC Press Inc
  • Kalba: eng
  • ISBN-13: 9781466510647
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For graduate and undergraduate students in physics and mathematics and researchers in high energy physics, Saleem (emeritus, physics) and Rafique (applied mathematics, both U. of the Punjab, India), introduce group theory from the beginning and describe its applications in high energy physics. They cover elements of group theory; group representations; continuous groups; and symmetry, Lie groups, and physics. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)

Although group theory has played a significant role in the development of various disciplines of physics, there are few recent books that start from the beginning and then build on to consider applications of group theory from the point of view of high energy physicists. Group Theory for High Energy Physicists fills that role. It presents groups, especially Lie groups, and their characteristics in a way that is easily comprehensible to physicists.

The book first introduces the concept of a group and the characteristics that are imperative for developing group theory as applied to high energy physics. It then describes group representations since matrix representations of a group are often more convenient to deal with than the abstract group itself. With a focus on continuous groups, the text analyzes the root structure of important groups and obtains the weights of various representations of these groups. It also explains how symmetry principles associated with group theoretical techniques can be used to interpret experimental results and make predictions.

This concise, gentle introduction is accessible to undergraduate and graduate students in physics and mathematics as well as researchers in high energy physics. It shows how to apply group theory to solve high energy physics problems.

Preface ix
About the Author xi
1 Elements of Group Theory
1(30)
1.1 Definition of a Group
1(3)
1.2 Some Characteristics of Group Elements
4(2)
1.3 Permutation Groups
6(4)
1.4 Multiplication Table
10(1)
1.5 Subgroups
10(3)
1.6 Power of an Element of a Group
13(1)
1.7 Cyclic Groups
14(2)
1.8 Cosets
16(1)
1.9 Conjugate Elements and Conjugate Classes
17(1)
1.10 Conjugate Subgroups
17(1)
1.11 Normal Subgroups
18(1)
1.12 Center of a Group
18(1)
1.13 Factor Group
19(1)
1.14 Mapping
20(2)
1.15 Homomorphism
22(2)
1.16 Kernel
24(1)
1.17 Isomorphism
25(2)
1.18 Direct Product of Groups
27(2)
1.19 Direct Product of Subgroups
29(2)
2 Group Representations
31(30)
2.1 Linear Vector Spaces
31(2)
2.2 Linearly Independent Vectors
33(1)
2.3 Basis Vectors
33(1)
2.4 Operators
34(1)
2.5 Unitary and Hilbert Vector Spaces
35(1)
2.6 Matrix Representative of a Linear Operator
36(4)
2.7 Change of Basis and Matrix Representative of a Linear Operator
40(4)
2.8 Group Representations
44(3)
2.9 Equivalent and Unitary Representations
47(1)
2.10 Reducible and Irreducible Representations
48(1)
2.11 Complex Conjugate and Adjoint Representations
49(1)
2.12 Construction of Representations by Additions
49(2)
2.13 Analysis of Representations
51(1)
2.14 Irreducible Invariant Subspace
52(1)
2.15 Matrix Representations and Invariant Subspaces
52(5)
2.16 Product Representations
57(4)
3 Continuous Groups
61(86)
3.1 Definition of a Continuous Group
61(1)
3.2 Groups of Linear Transformations
62(7)
3.3 Order of a Group of Transformations
69(3)
3.4 Lie Groups
72(3)
3.5 Generators of Lie Groups
75(9)
3.6 Real Orthogonal Group in Two Dimensions: O(2)
84(7)
3.7 Generators of SU(2)
91(4)
3.8 Generators of SU(3)
95(3)
3.9 Generators and Parameterization of a Group
98(1)
3.10 Matrix Representatives of Generators
99(2)
3.11 Structure Constants
101(2)
3.12 Rank of a Lie Group
103(1)
3.13 Lie Algebras
104(1)
3.14 Commutation Relations between the Generators of a Semisimple Lie Group
105(3)
3.15 Properties of the Roots
108(3)
3.16 Structure Constants Nαβ
111(1)
3.17 Classification of Simple Groups
112(2)
3.18 Roots of SU(2)
114(1)
3.19 Roots of SU(3)
115(7)
3.20 Numerical Values of the Structure Constants of SU(3)
122(1)
3.21 Weights of a Representation
122(5)
3.22 Computation of the Highest Weight of Any Irreducible Representation of SU(3)
127(4)
3.23 Dimension of any Irreducible Representation of SU(N)
131(2)
3.24 Computation of the Weights of Any Irreducible Representation of SU(3)
133(2)
3.25 Weights of Irreducible Representation D8(1,1) of SU(3)
135(3)
3.26 Weight Diagrams
138(1)
3.27 Decomposition of a Product of Two Irreducible Representations
139(8)
3.27.1 First Method
139(2)
3.27.2 Second Method
141(6)
4 Symmetry, Lie Groups, and Physics
147(43)
4.1 Symmetry
147(18)
4.1.1 Rotational Symmetry
147(4)
4.1.2 Higher and Lower Symmetries
151(1)
4.1.3 Reflection/Inversion Symmetry
151(2)
4.1.4 Concept of Parity
153(2)
4.1.5 Multiple Symmetries
155(1)
4.1.6 Combination of Symmetry Operations
155(1)
4.1.7 Translational Symmetry in Space
156(1)
4.1.8 Time-Reversal Symmetry
157(2)
4.1.9 Charge Conjugation
159(3)
4.1.10 Symmetry Groups and Physics
162(3)
4.2 Casimir Operators
165(1)
4.3 Symmetry Group and Unitary Symmetry
166(1)
4.4 Symmetry and Physics
166(4)
4.5 Group Theory and Elementary Particles
170(20)
Reference 190(1)
Appendix A 191(4)
Appendix B 195(4)
Appendix C 199(4)
Appendix D 203(4)
Index 207
Dr. Mohammad Saleem is a professor emeritus at the University of the Punjab and a professor at the Institute for Basic Research in Florida. He has written more than 150 research papers on high energy physics and is an editor of the Hadronic Journal.





Dr. Muhammad Rafique was a professor of applied mathematics at University of the Punjab.
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