Appendix D Problems

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Table of Contents

Basic

• B-1. Additive Group of Integers
• B-2. Multiplicative Group of Positive Real Numbers
• B-3. Multiplication of Integers Does Not Form a Group
• B-4. Group Conditions of \(U(1)\)
• B-5. 3-Dimensional \(z\)-Axis Rotation
• B-6. Commutation Relation of Pauli Matrices \([\sigma_1, \sigma_2]\)
• B-7. Commutation Relations of Pauli Matrices (All Pairs)
• B-8. Antisymmetry of Commutation Relations
• B-9. Eigenvalues and Eigenvectors of Spin 1/2

Medium

• M-1. Exponential Representation of \(SU(2)\) Elements
• M-2. Jacobi Identity (Verification with Pauli Matrices)
• M-3. Parameter Count of \(SU(N)\)

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Basic

B-1. Additive Group of Integers

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B-2. Multiplicative Group of Positive Real Numbers

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B-3. Multiplication of Integers Does Not Form a Group

Lie Groups

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B-4. Group Conditions of \(U(1)\)

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B-5. 3-Dimensional \(z\)-Axis Rotation

Lie Algebra

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B-6. Commutation Relation of Pauli Matrices \([\sigma_1, \sigma_2]\)

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B-7. Commutation Relations of Pauli Matrices (All Pairs)

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B-8. Antisymmetry of Commutation Relations

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B-9. Eigenvalues and Eigenvectors of Spin 1/2

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Medium

M-1. Exponential Representation of \(SU(2)\) Elements

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M-2. Jacobi Identity (Verification with Pauli Matrices)

Representation and Physics

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M-3. Parameter Count of \(SU(N)\)

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