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Produktbild: Introduction to Continuous Symmetries
- 12%

Introduction to Continuous Symmetries From Space-Time to Quantum Mechanics

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93,99 € UVP 108,00 €

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

16.08.2023

Abbildungen

100

Verlag

Wiley-VCH

Seitenzahl

576

Maße (L/B/H)

24,9/17,5/3,5 cm

Gewicht

1240 g

Auflage

1. Auflage

Übersetzt von

Nicole Ostrowsky + weitere

Sprache

Englisch

ISBN

978-3-527-41416-1

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

16.08.2023

Abbildungen

100

Verlag

Wiley-VCH

Seitenzahl

576

Maße (L/B/H)

24,9/17,5/3,5 cm

Gewicht

1240 g

Auflage

1. Auflage

Übersetzt von

  • Nicole Ostrowsky
  • Daniel Ostrowsky

Sprache

Englisch

ISBN

978-3-527-41416-1

Herstelleradresse

Wiley-VCH GmbH
Boschstraße 12
69469 Weinheim
DE

Email: wiley-vch@kolibri360.de

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  • Produktbild: Introduction to Continuous Symmetries
  • I Symmetry Transformations

    A Fundamental Symmetries

    B Symmetries in Classical Mechanics C Symmetries in Quantum Mechanics

    A_I Euler's and Lagrange's Views in Classical Mechanics

    1 Euler's Point of View

    2 Lagrange's Point of View

     

    II Notions on Group Theory

    A General Properties of Groups

    B Linear Representations of a Group

    A_II Residual Classes of a Subgroup; Quotient Group

    1 Residual Classes on the Left

    2 Quotient Group

     

    III Introduction to Continuous Groups and Lie Groups

    A General Properties B Examples

    C Galileo and Poincaré Groups

    A_III Adjoint Representation, Killing Form, Casimir Operator

    1 Representation Adjoint to the Lie Algebra

    2 Killing Form; Scalar Product and Change of Basis in L

    3 Totally Antisymmetric Structure Constants

    4 Casimir Operator

     

    IV Representations Induced in the State Space

    A Conditions Imposed on Transformations in the State Space

    B Wigner's Theorem

    C Transformations of Observables

    D Linear Representations in the State Space

    E Phase Factors and Projective Representations

    A_IV Finite-Dimensional Unitary Projective Representations of Related Lie Groups

    1 Case Where G is Simply Connected

    2 Case Where G is P-Connected

    B_IV Uhlhorn-Wigner Theorem

    1 Real Space

    2 Complex Space

     

    V Representations of the Galileo and Poincaré Groups: Mass, Spin and Energy

    A Galileo Group

    B Poincaré Group

    A_V Some Properties of the Operators S and W_2

    1 Operator S

    2 Eigenvalues of the Operator W_2

    B_V Geometric Displacement Group

    1 Reminders: Classical Properties of Displacements

    2 Associated Operators in the State Space

    C_V Clean Lorentz Group

    1 Link with the Group SL(2,C)

    2 Small Group Associated with a Four-Vector

    3 Operator W_2

    D_V Space Reflections (Parity)

    1 Action in Real Space

    2 Associated Operator in the State Space

    3 Retention of Parity

     

    VI Construction of State Spaces and Wave Equations

    A Galileo Group, Schrödinger Equation

    B Poincaré Group, Klein-Gordon and Dirac Equations

    A_VI Lagrangians of Wave Equations

    1 Lagrangian of a Field

    2 Schrödinger's Equation

    3 Klein-Gordon Equation

    4 Dirac's Equation

     

    VII Irreducible Representations of the Group of Rotations, Spinors

    A Irreducible Unitary Representations of the Group of Rotations

    B Spin 1/2 Particles; Spinors

    C Composition of the Kinetic Moments

    A_VII Homorphism Between SU(2) and Rotation Matrices

    1 Transformation of a Vector P Induced by an SU(2) Matrix

    2 The Transformation is a Rotation

    3 Homomorphism

    4 Link to the Reasoning of Chapter VII

    5 Link with Bivalent Representations

     

    VIII Transformation of Observables by Rotation

    A Vector Operators B Tensor Operators

    C Wigner-Eckart Theorem

    D Decomposition of the Density Matrix on Tensor Operators

    A_VIII Basic Reminders on Classical Tensors

    1 Vectors

    2 Tensors

    3 Properties

    4 Tensoriality Criterion

    5 Symmetric and Antisymmetric Tensors

    6 Special Tensors

    7 Irreducible Tensors

    B_VIII Second Order Tensor Operators

    1 Tensor Product of Two Vector Operators

    2 Cartesian Components of the Tensor in the General Case

    C_VIII Multipolar Moments

    1 Electrical Multipole Moments

    2 Magnetic Multipole Moments

    3 Multipole Moments of a Quantum System for a Given Kinetic Moment Multiplicity J

     

    IX Groups SU(2) and SU(3)

    A System of Discernible but Equivalent Particles

    B SU(2) Group and Isospin Symmetry

    C Symmetry SU(3)

    A_IX the Nature of a Particle Is Equivalent to an Internal Quantum Number

    1 Partial or Total Antisymmetrization of a State Vector

    2 Correspondence Between the States of Two Physical Systems

    3 Physical Consequences

    B_IX Operators Changing the Symmetry of a State Vector by Permutation

    1 Fermions

    2 Bosons

     

    X Symmetry Breaking

    A Magnetism, Breaking of the Rotation Symmetry

    B Some Other Examples

     

    APPENDIX

    I The Reversal of Time

    1 Time Reversal in Classical Mechanics

    2 Antilinear and Antiunitary Operators in Quantum Mechanics

    3 Time Reversal and Antilinearity

    4 Explicit Form of the Time Reversal Operator

    5 Applications