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· 분류 : 외국도서 > 경제경영 > 무역
· ISBN : 9781420078749
· 쪽수 : 256쪽
· 출판일 : 2010-03-16
목차
Symmetries and Conservation Laws
Lagrangian and Hamiltonian Mechanics
Quantum Mechanics
Coupled Oscillators: Normal Modes
One-Dimensional Fields: Waves
The Final Step: Lagrange?Hamilton Quantum Field Theory
Quantum Angular Momentum
Index Notation
Quantum Angular Momentum
Result
Matrix Representations
Spin 1/2
Addition of Angular Momenta
Clebsch?Gordan Coefficients
Matrix Representation of Direct (Outer, Kronecker) Products
Change of Basis
Tensors and Tensor Operators
Scalars
Scalar Fields
Invariant Functions
Contravariant Vectors (t →index at top)
Covariant Vectors (Co = Goes Below)
Notes
Tensors
Rotations
Vector Fields
Tensor Operators
Connection with Quantum Mechanics
Specification of Rotations
Transformation of Scalar Wave Functions
Finite Angle Rotations
Consistency with the Angular Momentum Commutation Rules
Rotation of Spinor Wave Function
Orbital Angular Momentum (x × p)
The Spinors Revisited
Dimensions of Projected Spaces
Connection between the "Mixed Spinor" and the Adjoint (Regular) Representation
Finite Angle Rotation of SO(3) Vector
Special Relativity and the Physical Particle States
The Dirac Equation
The Clifford Algebra: Properties of γ Matrices
Structure of the Clifford Algebra and Representation
Lorentz Covariance of the Dirac Equation
The Adjoint
The Nonrelativistic Limit
Poincare Group: Inhomogeneous Lorentz Group
Homogeneous (Later Restricted) Lorentz Group
Poincare Algebra
The Casimir Operators and the States
Internal Symmetries
Lie Group Techniques for the Standard Model Lie Groups
Roots and Weights
Simple Roots
The Cartan Matrix
Finding All the Roots
Fundamental Weights
The Weyl Group
Young Tableaux
Raising the Indices
The Classification Theorem (Dynkin)
Result
Coincidences
Noether’s Theorem and Gauge Theories of the First and Second Kinds
Basic Couplings of the Electromagnetic, Weak, and Strong Interactions
Spontaneous Symmetry Breaking and the Unification of the Electromagnetic and Weak Forces
The Goldstone Theorem and the Consequent Emergence on Nonlinear Transforming Massless Goldstone Bosons
The Higgs Mechanism and the Emergence of Mass from Spontaneously Broken Symmetries
Lie Group Techniques for beyond the Standard Model Lie Groups
The Simple Sphere
Beyond the Standard Model
Massive Case
Massless Case
Projection Operators
Weyl Spinors and Representation
Charge Conjugation and Majorana Spinor
A Notational Trick
SL(2, C) View
Unitary Representations
Supersymmetry: A First Look at the Simplest (N = 1) Case
Massive Representations
Massless Representations
Superspace
Three Dimensional Euclidean Space (Revisited)
Covariant Derivative Operators from Right Action
Superfields
Supertransformations
The Chiral Scalar Multiplet
Superspace Methods
Covariant Definition of Component Fields
Supercharges Revisited
Invariants and Lagrangians
Superpotential
References and Problems appear at the end of each chapter.
