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Quantum mechanics and quantum field theory by Jonathan Dimock in 2011

I. Non-relativistic

1. Mathematical prelude

  • 1.1 Bounded operators
  • 1.2 Unbounded operators
  • 1.3 Self-adjoint operators
  • 1.4 Compact operators

2. Classical mechanics

  • 2.1 Hamiltonian mechanics
  • 2.2 Examples
  • 2.3 Canonical transformations
  • 2.4 Symmetries

3. Quantum mechanics

  • 3.1 Principles of quantum mechanics
  • 3.2 Canonical quantization
  • 3.3 Symmetries
  • 3.4 Perspectives and problems

4. Single particle

  • 4.1 Free particle
  • 4.2 Particle in a potential
  • 4.3 Spectrum
  • 4.4 The harmonic oscillator
  • 4.5 Scattering
  • 4.6 Spin

5. Many particles

  • 5.1 Two particles
  • 5.2 Identical particles
  • 5.3 n-particles
  • 5.4 Fock space

6. Statistical mechanics

  • 6.1 Mixed states
  • 6.2 Equilibrium states
  • 6.3 Free boson gas
  • 6.4 Free fermion gas
  • 6.5 Interacting bosons
  • 6.6 Further developments

II. Relativistic

7. Relativity

  • 7.1 Principles of relativity
  • 7.2 Minkowski space
  • 7.3 Classical free fields
  • 7.4 Interacting classical fields
  • 7.5 Fundamental solutions

8. Scalar particles and fields

  • 8.1 Scalar particles
  • 8.2 Scalar fields
  • 8.3 Charged scalar field

9. Electrons and photons

  • 9.2 Electrons
  • 9.3 Dirac fields
  • 9.4 Photons
  • 9.5 Electromagnetic field

10. Field theory on a manifold

  • 10.1 Lorentzian manifolds
  • 10.2 Classical fields on a manifold
  • 10.3 Quantum fields on a manifold

III. Probabilistic methods

11. Path integrals

  • 11.1 Probability
  • 11.2 Gaussian processes
  • 11.3 Brownian motion
  • 11.4 The Feynman-Kac formula
  • 11.5 Oscillator process
  • 11.6 Application: ground states

12. Fields as random variables

  • 12.1 More on Gaussian processes
  • 12.2 The Schrodinger representation
  • 12.3 Path integrals * free fields
  • 12.4 Vacuum correlation functions
  • 12.5 Thermal correlation functions

13. A nonlinear field theory

  • 13.1 The model
  • 13.2 Regularization
  • 13.3 Infinite volume
  • 13.4 Path integrals * interacting fields
  • 13.5 A reformulation

Appendices

A. Normed spaces

B. Tensor product

C. Distributions

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