CLASSIC & QUANT MECH LIE..(2ND ED)

This book offers a fresh approach towards introducing three major topics in physics: quantum mechanics, classical mechanics and special relativity. These topics are then unified in terms of their joint mathematical framework: Lie algebras and their theory. This way, the material flows smoothly from algebraic tools only, avoiding heavy analysis.

Each chapter concludes with a substantial set of engaging exercises, complete with solutions, designed to introduce new material step by step. The only prerequisites are linear algebra and calculus. The required background is covered throughout the book, and especially in the appendix, which may serve as a point of reference.

This new edition features major revisions throughout the book (notably in Parts II, IV–V, VIII, and more), along with two new chapters on Feynman diagrams, the Killing form, spin, and polarization.

Contents:

• Introduction to Newtonian Physics:
  • Introduction to Newtonian Mechanics
  • Angular Momentum and Inertia
  • Geometrical Optics and Its Stability
• Stability in Classical Mechanics:
  • Poincaré Stability
  • Chaos and Stability
• Towards Quantum Statistical Mechanics:
  • Newton's Binomial and Brownian Motion
  • Applications in Quantum Statistical Mechanics
• Introduction to Special Relativity:
  • Introduction to Special Relativity
• Introduction to Quantum Mechanics:
  • Introduction to Quantum Mechanics
  • Angular Momentum
  • Spin and Pauli Matrices
  • Spin and Polarization
• Quantum Chemistry: Electronic Structure:
  • Background: Determinant
  • The Hartree-Fock System
• Introduction to Lie Algebras:
  • The Jordan Form for Matrices/Algebras
  • Design Your Lie Algebra
  • Ideals and Isomorphism Theorems
  • Solvability and Nilpotency
  • Nilpotency and Engel's Theorems
  • Weight Space and Lie's Lemma and Theorem
  • Cartan's Criterion for Solvability
  • The Killing Form and The Simple-Ideal Decomposition
• Lie Groups/Algebras: Applications:
  • Hamiltonian Mechanics: Energy and Angular Momentum
  • Lie Groups/Algebras in Quantum Mechanics and Special Relativity
  • Feynman Diagrams and The Killing Form
• Appendix: Background in Calculus:
  • Functions and Their Derivatives
  • Polynomials and Partial Derivatives
  • Matrix and Its Eigenvalues
• References
• Index

Readership: Undergraduate and graduate students, researchers in Mathematics, Physics, and Chemistry.