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دانلود کتاب Group theory in physics

دانلود کتاب تئوری گروه در فیزیک

Group theory in physics

مشخصات کتاب

Group theory in physics

دسته بندی: فیزیک
ویرایش:  
نویسندگان:   
سری:  
ISBN (شابک) : 9971966565, 9971966573 
ناشر: World Scientific 
سال نشر: 1985 
تعداد صفحات: 364 
زبان: English 
فرمت فایل : DJVU (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود) 
حجم فایل: 3 مگابایت

قیمت کتاب (تومان) : 39,000



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کتاب درسی مقدماتی برای فارغ التحصیلان و دانش آموختگان پیشرفته در زمینه تئوری بازنمایی گروهی. بر نقش نظریه گروه به عنوان چارچوب ریاضی برای توصیف ویژگی‌های تقارن سیستم‌های مکانیکی کلاسیک و کوانتومی تأکید می‌کند.

آشنایی با مفاهیم و تکنیک های اولیه گروه در آموزش یک فیزیکدان امروزی بسیار ارزشمند است. این کتاب بر ویژگی‌های کلی و روش‌هایی تأکید می‌کند که قدرت رویکرد نظری گروهی را در افشای سیستماتیک سیستم‌های فیزیکی با تقارن مرتبط نشان می‌دهد.


توضیحاتی درمورد کتاب به خارجی

An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems.

Familiarity with basic group concepts and techniques is invaluable in the education of a modern-day physicist. This book emphasizes general features and methods which demonstrate the power of the group-theoretical approach in exposing the systematics of physical systems with associated symmetry.



فهرست مطالب

PREFACE/7,Black,notBold,notItalic,open,FitWidth,-1
CHAPTER 1: INTRODUCTION/21,Black,notBold,notItalic,open,FitWidth,-1
	1.1 Particle on a One-Dimensional Lattice/22,Black,notBold,notItalic,open,FitWidth,-1
	1.2 Representations of the Discrete Translation Operators/24,Black,notBold,notItalic,open,FitWidth,-1
	1.3 Physical Consequences of Translational Symmetry/26,Black,notBold,notItalic,open,FitWidth,-1
	1.4 The Representation Functions and Fourier Analysis/28,Black,notBold,notItalic,open,FitWidth,-1
	1.5 Symmetry Groups of Physics/29,Black,notBold,notItalic,open,FitWidth,-1
CHAPTER 2: BASIC GROUP THEORY/32,Black,notBold,notItalic,open,FitWidth,-1
	2.1 Basic Definitions and Simple Examples/32,Black,notBold,notItalic,open,FitWidth,-1
	2.2 Further Examples, Subgroups/34,Black,notBold,notItalic,open,FitWidth,-1
	2.3 The Rearrangement Lemma and the Symmetric Permutation) Group/36,Black,notBold,notItalic,open,FitWidth,-1
	2.4 Classes and Invariant Subgroups/39,Black,notBold,notItalic,open,FitWidth,-1
	2.5 Cosets and Factor (Quotient) Groups/41,Black,notBold,notItalic,open,FitWidth,-1
	2.6 Homomorphisms/43,Black,notBold,notItalic,open,FitWidth,-1
	2.7 Direct Products/44,Black,notBold,notItalic,open,FitWidth,-1
	Problems/45,Black,notBold,notItalic,open,FitWidth,-1
CHAPTER 3: GROUP REPRESENTATIONS/47,Black,notBold,notItalic,open,FitWidth,-1
	3.1 Representations/47,Black,notBold,notItalic,open,FitWidth,-1
	3.2 Irreducible, Inequivalent Representations/52,Black,notBold,notItalic,open,FitWidth,-1
	3.3 Unitary Representations/55,Black,notBold,notItalic,open,FitWidth,-1
	3.4 Schur\'s Lemmas/57,Black,notBold,notItalic,open,FitWidth,-1
	3.5 Orthonormality and Completeness Relations of Irreducible Representation Matrices/59,Black,notBold,notItalic,open,FitWidth,-1
	3.6 Orthonormality and Completeness Relations of Irreducible Characters/62,Black,notBold,notItalic,open,FitWidth,-1
	3.7 The Regular Representation/65,Black,notBold,notItalic,open,FitWidth,-1
	3.8 Direct Product Representations, Clebsch-Gordan Coefficients/68,Black,notBold,notItalic,open,FitWidth,-1
	Problems/72,Black,notBold,notItalic,open,FitWidth,-1
CHAPTER 4: GENERAL PROPERTIES OF IRREDUCIBLE VECORS AND OPERATORS/74,Black,notBold,notItalic,open,FitWidth,-1
	4.1 Irreducible Basis Vectors/74,Black,notBold,notItalic,open,FitWidth,-1
	4.2 The Reduction of Vectors — Projection Operators for Irreducible Components/76,Black,notBold,notItalic,open,FitWidth,-1
	4.3 Irreducible Operators and the Wigner-Eckart Theorem/79,Black,notBold,notItalic,open,FitWidth,576
	Problems/82,Black,notBold,notItalic,open,FitWidth,-1
CHAPTER 5: REPRESENTATIONS OF THE SYMMETRIC GROUPS/84,Black,notBold,notItalic,open,FitWidth,-1
	5.1 One-Dimensional Representations/85,Black,notBold,notItalic,open,FitWidth,-1
	5.2 Partitions and Young Diagrams/85,Black,notBold,notItalic,open,FitWidth,-1
	5.3 Symmetrizers and Anti-Symmetrizers of Young Tableaux/87,Black,notBold,notItalic,open,FitWidth,-1
	5.4 Irreducible Representations of Sₙ/88,Black,notBold,notItalic,open,TopLeftZoom,684,191,0.0
	5.5 Symmetry Classes of Tensors/90,Black,notBold,notItalic,open,FitWidth,-1
	Problems/98,Black,notBold,notItalic,open,FitWidth,-1
CHAPTER 6: ONE-DIMENSIONAL CONTINUOUS GROUPS/100,Black,notBold,notItalic,open,FitWidth,-1
	6.1 The Rotation Group SO(2)/101,Black,notBold,notItalic,open,FitWidth,-1
	6.2 The Generator of SO(2)/103,Black,notBold,notItalic,open,FitWidth,-1
	6.3 Irreducible Representations of SO(2)/104,Black,notBold,notItalic,open,FitWidth,-1
	6.4 Invariant Integration Measure, Orthonorrnality and Completeness Relations/106,Black,notBold,notItalic,open,FitWidth,-1
	6.5 Multi-Valued Representations/108,Black,notBold,notItalic,open,FitWidth,-1
	6.6 Continuous Translational Group in One Dimension/109,Black,notBold,notItalic,open,FitWidth,-1
	6.7 Conjugate Basis Vectors/111,Black,notBold,notItalic,open,FitWidth,-1
	Problems/113,Black,notBold,notItalic,open,FitWidth,-1
CHAPTER 7: ROTATIONS IN THREE-DIMENSIONAL SPACE-THE GROUP SO(3)/114,Black,notBold,notItalic,open,FitWidth,-1
	7.1 Description of the Group SO(3)/114,Black,notBold,notItalic,open,FitWidth,-1
		7.1.1 The Angle-and-Axis Parameterization/116,Black,notBold,notItalic,open,FitWidth,-1
		7.1.2 The Euler Angles/117,Black,notBold,notItalic,open,FitWidth,-1
	7.2 One Parameter Subgroups, Generators, and the Lie Algebra/119,Black,notBold,notItalic,open,FitWidth,-1
	7.3 Irreducible Representations of the SO(3) Lie Algebra/122,Black,notBold,notItalic,open,FitWidth,-1
	7.4 Properties of the Rotational Matrices Dʲ(α,β,γ)/127,Black,notBold,notItalic,open,FitWidth,-1
	7.5 Application to Particle in a Central Potential/129,Black,notBold,notItalic,open,FitWidth,-1
		7.5.1 Characterization of States/130,Black,notBold,notItalic,open,FitWidth,-1
		7.5.2 Asymptotic Plane Wave States/131,Black,notBold,notItalic,open,FitWidth,-1
		7.5.3 Partial Wave Decomposition/131,Black,notBold,notItalic,open,FitWidth,-1
		7.5.4 Summary/132,Black,notBold,notItalic,open,FitWidth,-1
	7.6 Transformation Properties of Wave Functions and Operators/132,Black,notBold,notItalic,open,FitWidth,-1
	7.7 Direct Product Representations and Their Reduction/137,Black,notBold,notItalic,open,FitWidth,-1
	7.8 Irreducible Tensors and the Wigner-Eckart Theorem/142,Black,notBold,notItalic,open,FitWidth,-1
	Problems/143,Black,notBold,notItalic,open,FitWidth,-1
CHAPTER 8: THE GROUP SU(2) AND MORE ABOUT SO(3)/145,Black,notBold,notItalic,open,FitWidth,-1
	8.1 The Relationship between SO(3) and SU(2)/145,Black,notBold,notItalic,open,FitWidth,-1
	8.2 Invariant Integration/149,Black,notBold,notItalic,open,FitWidth,-1
	8.3 Orthonormality and Completeness Relations of Dʲ/153,Black,notBold,notItalic,open,FitWidth,-1
	8.4 Projection Operators and Their Physical Applications/155,Black,notBold,notItalic,open,FitWidth,-1
		8.4.1 Single Particle State with Spin/156,Black,notBold,notItalic,open,FitWidth,-1
		8.4.2 Two Particle States with Spin/158,Black,notBold,notItalic,open,FitWidth,-1
		8.4.3 Partial Wave Expansion for Two Particle Scattering with Spin/160,Black,notBold,notItalic,open,FitWidth,-1
	8.5 Differential Equations Satisfied by the Dʲ-Functions/161,Black,notBold,notItalic,open,FitWidth,-1
	8.6 Group Theoretical Interpretation of Spherical Harmonics/163,Black,notBold,notItalic,open,FitWidth,-1
		8.6.1 Transformation under Rotation/164,Black,notBold,notItalic,open,FitWidth,-1
		8.6.2 Addition Theorem/165,Black,notBold,notItalic,open,FitWidth,-1
		8.6.3 Decomposition of Products of Yₗₘ With the Same Arguments/165,Black,notBold,notItalic,open,TopLeftZoom,433,191,0.0
		8.6.4 Recursion Formulas/165,Black,notBold,notItalic,open,FitWidth,-1
		8.6.5 Symmetry in m/166,Black,notBold,notItalic,open,TopLeftZoom,342,191,0.0
		8.6.6 Orthonormality and Completeness/166,Black,notBold,notItalic,open,FitWidth,-1
		8.6.7 Summary Remarks/166,Black,notBold,notItalic,open,TopLeftZoom,593,191,0.0
	8.7 Multipole Radiation of the Electromagnetic Field/167,Black,notBold,notItalic,open,FitWidth,-1
	Problems/170,Black,notBold,notItalic,open,FitWidth,-1
CHAPTER 9: EUCLIDEAN GROUPS IN TWO- AND THREE-DIMENSIONAL SPACE/172,Black,notBold,notItalic,open,FitWidth,-1
	9.1 The Euclidean Group in Two-Dimensional Space E₂/174,Black,notBold,notItalic,open,TopLeftZoom,297,191,0.0
	9.2 Unitary Irreducible Representations of E₂ — the Angular-Momentum Basis/176,Black,notBold,notItalic,open,FitWidth,-1
	9.3 The Induced Representation Method and the Plane-Wave Basis/180,Black,notBold,notItalic,open,FitWidth,-1
	9.4 Differential Equations, Recursion Formulas, and Addition Theorem of the Bessel Function/183,Black,notBold,notItalic,open,FitWidth,-1
	9.5 Group Contraction — SO(3) and E₂/185,Black,notBold,notItalic,open,FitWidth,-1
	9.6 The Euclidean Group in Three Dimensions: E₃/186,Black,notBold,notItalic,open,FitWidth,-1
	9.7 Unitary Irreducible Representations of E₃ by the Induced Representation Method/188,Black,notBold,notItalic,open,FitWidth,-1
	9.8 Angular Momentum Basis and the Spherical Bessel Function/190,Black,notBold,notItalic,open,FitWidth,-1
	Problems/191,Black,notBold,notItalic,open,FitWidth,-1
CHAPTER 10: THE LORENTZ AND POINCARÉ GROUPS, AND SPACE-TIME SYMMETRIES/193,Black,notBold,notItalic,open,FitWidth,-1
	10.1 The Lorentz and Poincaré Groups/193,Black,notBold,notItalic,open,FitWidth,-1
		10.1.1 Homogeneous Lorentz Transformations/194,Black,notBold,notItalic,open,FitWidth,-1
		10.1.2 The Proper Lorentz Group/197,Black,notBold,notItalic,open,FitWidth,-1
		10.1.3 Decomposition of Lorentz Transformations/199,Black,notBold,notItalic,open,FitWidth,-1
		10.1.4 Relation of the Proper Lorentz Group to SL(2)/200,Black,notBold,notItalic,open,FitWidth,-1
		10.1.5 Four-Dimensional Translations and the Poincaré Group/201,Black,notBold,notItalic,open,FitWidth,-1
	10.2 Generators and the Lie Algebra/202,Black,notBold,notItalic,open,FitWidth,-1
	10.3 Irreducible Representations of the Proper Lorentz Group/207,Black,notBold,notItalic,open,FitWidth,-1
		10.3.1 Equivalence of the Lie Algebra to SU(2)×SU(2)/207,Black,notBold,notItalic,open,FitWidth,-1
		10.3.2 Finite Dimensional Representations/208,Black,notBold,notItalic,open,FitWidth,-1
		10.3.3 Unitary Representations/209,Black,notBold,notItalic,open,FitWidth,-1
	10.4 Unitary Irreducible Representations of the Poincaré Group/211,Black,notBold,notItalic,open,FitWidth,-1
		10.4.1 Null Vector case (Pµ = 0)/212,Black,notBold,notItalic,open,FitWidth,-1
		10.4.2 Time-Like Vector Case (c₁ > 0)/212,Black,notBold,notItalic,open,FitWidth,-1
		10.4.3 The Second Casimir Operator/215,Black,notBold,notItalic,open,FitWidth,-1
		10.4.4 Light-Like Case (c₁ = 0)/216,Black,notBold,notItalic,open,FitWidth,-1
		10.4.5 Space-Like Case (c₁ < 0)/219,Black,notBold,notItalic,open,FitWidth,-1
		10.4.6 Covariant Normalization of Basis States and Integration Measure/220,Black,notBold,notItalic,open,FitWidth,-1
	10.5 Relation Between Representations of the Lorentz and Poincaré Groups - Relativistic Wave Functions, Fields, and Wave Equations/222,Black,notBold,notItalic,open,FitWidth,-1
		10.5.1 Wave Functions and Field Operators/222,Black,notBold,notItalic,open,FitWidth,-1
		10.5.2 Relativistic Wave Equations and the Plane Wave Expansion/223,Black,notBold,notItalic,open,FitWidth,-1
		10.5.3 The Lorentz-Poincaré Connection/226,Black,notBold,notItalic,open,FitWidth,-1
		10.5.4 \"Deriving\" Relativistic Wave Equations/228,Black,notBold,notItalic,open,FitWidth,-1
	Problems/230,Black,notBold,notItalic,open,FitWidth,-1
CHAPTER 11: SPACE INVERSION INVARIANCE/232,Black,notBold,notItalic,open,FitWidth,-1
	11.1 Space Inversion in Two-Dimensional Euclidean Space/232,Black,notBold,notItalic,open,FitWidth,-1
		11.1.1 The Group O(2)/233,Black,notBold,notItalic,open,FitWidth,-1
		11.1.2 Irreducible Representations of O(2)/19,Black,notBold,notItalic,open,FitWidth,-1
		11.1.3 The Extended Euclidean Group Ẽ₂ and its Irreducible Representations/238,Black,notBold,notItalic,open,FitWidth,-1
	11.2 Space Inversion in Three-Dimensional Euclidean Space/241,Black,notBold,notItalic,open,FitWidth,-1
		11.2.1 The Group O(3) and its Irreducible Representations/241,Black,notBold,notItalic,open,FitWidth,-1
		11.2.2 The Extended Euclidean Group Ẽ₃ and its Irreducible Representations/243,Black,notBold,notItalic,open,FitWidth,-1
	11.3 Space Inversion in Four-Dimensional Minkowski Space/247,Black,notBold,notItalic,open,FitWidth,-1
		11.3.1 The Complete Lorentz Group and its Irreducible Representations/247,Black,notBold,notItalic,open,FitWidth,-1
		11.3.2 The Extended Poincaré Group and its Irreducible Representations/251,Black,notBold,notItalic,open,FitWidth,-1
	11.4 General Physical Consequences of Space Inversion/257,Black,notBold,notItalic,open,FitWidth,-1
		11.4.1 Eigenstates of Angular Momentum and Parity/258,Black,notBold,notItalic,open,FitWidth,-1
		11.4.2 Scattering Amplitudes and Electromagnetic Multipole Transitions/260,Black,notBold,notItalic,open,FitWidth,-1
	Problems/263,Black,notBold,notItalic,open,FitWidth,-1
CHAPTER 12: TIME REVERSAL INVARIANCE/265,Black,notBold,notItalic,open,FitWidth,-1
	12.1 Preliminary Discussion/265,Black,notBold,notItalic,open,FitWidth,-1
	12.2 Time Reversal Invariance in Classical Physics/266,Black,notBold,notItalic,open,FitWidth,-1
	12.3 Problems with Linear Realization of Time Reversal Transformation/267,Black,notBold,notItalic,open,FitWidth,-1
	12.4 The Anti-Unitary Time Reversal Operator/270,Black,notBold,notItalic,open,FitWidth,-1
	12.5 Irreducible Representations of the Full Poincaré Group in the Time-Like Case/271,Black,notBold,notItalic,open,FitWidth,-1
	12.6 Irreducible Representations in the Light-Like Case (c₁ = c₂ = 0)/274,Black,notBold,notItalic,open,FitWidth,-1
	12.7 Physical Consequences of Time Reversal Invariance/276,Black,notBold,notItalic,open,FitWidth,-1
		12.7.1 Time Reversal and Angular Momentum Eigenstates/276,Black,notBold,notItalic,open,FitWidth,-1
		12.7.2 Time-Reversal Symmetry of Transition Amplitudes/277,Black,notBold,notItalic,open,FitWidth,-1
		12.7.3 Time Reversal Invariance and Perturbation Amplitudes/279,Black,notBold,notItalic,open,FitWidth,-1
	Problems/281,Black,notBold,notItalic,open,FitWidth,-1
CHAPTER 13: FINITE-DIMENSIONAL REPRESENTATIONS OF THE CLASSICAL GROUPS/282,Black,notBold,notItalic,open,FitWidth,-1
	13.1 GL(m): Fundamental Representations and The Associated Vector Spaces/283,Black,notBold,notItalic,open,FitWidth,-1
	13.2 Tensors in V×Ṽ, Contraction, and GL(m) Transformations/285,Black,notBold,notItalic,open,FitWidth,-1
	13.3 Irreducible Representations of GL(m) on the Space Of General Tensors/289,Black,notBold,notItalic,open,FitWidth,-1
	13.4 Irreducible Representations of Other Classical Linear Groups/297,Black,notBold,notItalic,open,FitWidth,-1
		13.4.1 Unitary Groups U(m) and U(m₊,m₋)/297,Black,notBold,notItalic,open,FitWidth,-1
		13.4.2 Special Linear Groups SL(m) and the Special Unitary Groups SU(m₊,m₋)/300,Black,notBold,notItalic,open,FitWidth,-1
		13.4.3 The Real Orthogonal Group O(m₊,m₋; R) and the Special Real Orthogonal Group SO(m₊,m₋; R)/303,Black,notBold,notItalic,open,TopLeftZoom,593,191,0.0
	13.5 Concluding Remarks/309,Black,notBold,notItalic,open,FitWidth,-1
	Problems/310,Black,notBold,notItalic,open,FitWidth,-1
APPENDIX I: NOTATIONS AND SYMBOLS/312,Black,notBold,notItalic,open,FitWidth,-1
	I.1 Summation Convention/312,Black,notBold,notItalic,open,FitWidth,-1
	I.2 Vectors and Vector Indices/312,Black,notBold,notItalic,open,FitWidth,-1
	I.3 Matrix Indices/313,Black,notBold,notItalic,open,FitWidth,-1
APPENDIX II: SUMMARY OF LINEAR VECTOR SPACES/315,Black,notBold,notItalic,open,FitWidth,-1
	II.1 Linear Vector Space/19,Black,notBold,notItalic,open,FitWidth,-1
	II.2 Linear Transformations (Operators) on Vector Spaces/317,Black,notBold,notItalic,open,FitWidth,-1
	II.3 Matrix Representation of Linear Operators/319,Black,notBold,notItalic,open,FitWidth,-1
	II.4 Dual Space, Adjoint Operators/321,Black,notBold,notItalic,open,FitWidth,-1
	II.5 Inner (Scalar) Product and Inner Product Space/322,Black,notBold,notItalic,open,FitWidth,-1
	II.6 Linear Transformations (Operators) on Inner Product Spaces/324,Black,notBold,notItalic,open,FitWidth,-1
APPENDIX III: GROUP ALGEBRA AND THE REDUCTION OF REGULAR REPRESENTATION/327,Black,notBold,notItalic,open,FitWidth,-1
	III.1 Group Algebra/327,Black,notBold,notItalic,open,FitWidth,-1
	III.2 Left Ideals, Projection Operators/328,Black,notBold,notItalic,open,FitWidth,-1
	III.3 Idempotents/329,Black,notBold,notItalic,open,FitWidth,-1
	III.4 Complete Reduction of the Regular Representation/332,Black,notBold,notItalic,open,FitWidth,-1
APPENDIX IV: SUPPLEMENTS TO THE THEORY OF SYMMETRIC GROUPS Sₙ/334,Black,notBold,notItalic,open,FitWidth,-1
APPENDIX V: CLEBSCH-GORDAN COEFFICIENTS AND SPHERICAL HARMONICS/338,Black,notBold,notItalic,open,FitWidth,-1
APPENDIX VI: ROTATIONAL AND LORENTZ SPINORS/340,Black,notBold,notItalic,open,FitWidth,-1
APPENDIX VII: UNITARY REPRESENTATIONS OF THE PROPER LORENTZ GROUP/348,Black,notBold,notItalic,open,FitWidth,-1
APPENDIX VIII: ANTI-LINEAR OPERATORS/351,Black,notBold,notItalic,open,FitWidth,-1
REFERENCES AND BIBLIOGRAPHY/355,Black,notBold,notItalic,open,FitWidth,-1
INDEX/358,Black,notBold,notItalic,open,FitWidth,-1




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