Supersymmetric methods in quantum, statistical and solid state physics /

As with the earlier edition, this book provides an accessible introduction to supersymmetric quantum mechanics and its applications in quantum, statistical and solid state physics. Building on the earlier edition it now encapsulates the substantial developments that have been made in supersymmetric...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Junker, Georg, 1961- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2019]
Edición:Enlarged and revised edition.
Colección:IOP (Series). Release 6.
IOP expanding physics.
Temas:
Supersymmetry.
Quantum theory.
Statistical physics.
Quantum physics (quantum mechanics & quantum field theory).
SCIENCE / Physics / Quantum Theory.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 1. Introduction
  • 2. Supersymmetric quantum mechanics
  • 2.1. Definition of SUSY quantum mechanics
  • 2.2. Properties of N = 2 SUSY quantum mechanics
  • 2.3. Problems
  • 3. The Witten model
  • 3.1. Witten's model and its modification
  • 3.2. Witten parity and SUSY transformation
  • 3.3. The SUSY potential and zero-energy states
  • 3.4. Broken versus good SUSY
  • 3.5. SUSY transformations for continuum states
  • 3.6. Examples
  • 3.7. Problems
  • 4. One-dimensional quantum systems
  • 4.1. Supersymmetrisation of one-dimensional systems
  • 4.2. Shape-invariance and exact solutions
  • 4.3. The Darboux transformation method
  • 4.4. A SUSY-partner family for the harmonic oscillator
  • 4.5. Classical fields in (1 + 1) dimensions
  • 4.6. Problems
  • 5. Supersymmetric classical mechanics
  • 5.1. Pseudoclassical models
  • 5.2. A supersymmetric classical model
  • 5.3. The classical dynamics
  • 5.4. Discussion of the fermionic phase
  • 5.5. Quantisation
  • 5.6. Problems
  • 6. Quasi-classical approximation
  • 6.1. The path-integral formalism
  • 6.2. Quasi-classical quantisation conditions
  • 6.3. Quasi-classical eigenfunctions
  • 6.4. Discussion of the results
  • 6.5. Problems
  • 7. Supersymmetry in classical stochastic dynamics
  • 7.1. Langevin and Fokker-Planck equation
  • 7.2. Supersymmetry of the Fokker-Planck equation
  • 7.3. Supersymmetry of the Langevin equation
  • 7.4. Implications of supersymmetry
  • 7.5. Continuous stationary Markov processes
  • 7.6. Problems
  • 8. Supersymmetric Pauli Hamiltonians
  • 8.1. Electrons in an external magnetic field
  • 8.2. Pauli paramagnetism of non-interacting electrons
  • 8.3. Electrons in a spherically symmetric scalar field
  • 8.4. Problems
  • 9. Supersymmetric Dirac Hamiltonians
  • 9.1. The Dirac Hamiltonian and SUSY
  • 9.2. The free Dirac Hamiltonian in three dimensions
  • 9.3. The two-dimensional Dirac Hamiltonian with magnetic field
  • 9.4. Dirac Hamiltonians with a Lorentz-scalar potential
  • 9.5. Dirac electrons in spherical symmetric potentials
  • 9.6. Supersymmetry of the Dirac Coulomb Hamiltonian
  • 9.7. The relativistic Witten model
  • 9.8. Problems
  • 10. Concluding remarks and overview.

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