phy2403

New aggregate collection of class notes for phy2403: up to lecture 17.

November 14, 2018 phy2403 No comments

I’ve now uploaded a new version of my class notes for PHY2403, the UofT Quantum Field Theory I course, taught this year by Prof. Erich Poppitz.

This version includes the following chapters, roughly one per lecture, plus some extras

  • Introduction
  • Units, scales, and Lorentz transformations.
  • Lorentz transformations and a scalar action.
  • Scalar action, least action principle, Euler-Lagrange equations for a field, canonical quantization.
  • Klein-Gordon equation, SHOs, momentum space representation, raising and lowering operators.
  • Canonical quantization, Simple Harmonic Oscillators, Symmetries
  • Symmetries, translation currents, energy momentum tensor.
  • 1st Noether theorem, spacetime translation current, energy momentum tensor, dilatation current.
  • Unbroken and spontaneously broken symmetries, Higgs Lagrangian, scale invariance, Lorentz invariance, angular momentum quantization
  • Lorentz boosts, generator of spacetime translation, Lorentz invariant field representation.
  • Microcausality, Lorentz invariant measure, retarded time SHO Green’s function.
  • Klein-Gordon Green’s function, Feynman propagator path deformation, Wightman function, Retarded Green’s function.
  • Forced Klein-Gordon equation, coherent states, number density, time ordered product, perturbation theory, Heisenberg picture, interaction picture, Dyson’s formula
  • Time evolution, Hamiltonian pertubation, ground state
  • Perturbation ground state, time evolution operator, time ordered product, interaction
  • Differential cross section, scattering, pair production, transition amplitude, decay rate, S-matrix, connected and amputated diagrams, vacuum fluctuation, symmetry coefficient
  • Scattering, decay, cross sections in a scalar theory.
  • Problem Set 1.
  • Problem Set 2.
  • Independent study problems
  • Useful formulas and review.
  • Momentum of scalar field.
  • Index
  • Bibliography

Problem set 1-2 solutions are redacted.  If you aren’t a UofT student taking PHY2403, feel free to contact me for an un-redacted copy.

New aggregate notes collection for UofT phy2403 Quantum Field Theory I

October 21, 2018 phy2403 No comments , ,

I’ve uploaded a new aggregate notes collection of my UofT phy2403 Quantum Field Theory I class notes (taught by Prof. Erich Poppitz), which now includes up to Wed Oct 17th’s lecture 11 (but doesn’t have my problem set I solution)

  • 1 Introduction
  • 1.1 What is a field?
  • 1.2 Scales.
  • 1.2.1 Bohr radius
  • 1.2.2 Compton wavelength.
  • 1.2.3 Relations.
  • 2 Units, scales, and Lorentz transformations.
  • 2.1 Natural units.
  • 2.2 Gravity.
  • 2.3 Cross section.
  • 2.4 Lorentz transformations.
  • 3 Lorentz transformations and a scalar action.
  • 3.1 Determinant of Lorentz transformations.
  • 3.2 Field theory.
  • 3.3 Actions.
  • 3.4 Problems.
  • 4 Scalar action, least action principle, Euler-Lagrange equations for a field, canonical quantization.
  • 4.1 Principles cont.
  • 4.2 d = 2 .
  • 4.3 d = 3 .
  • 4.4 d = 4 .
  • 4.5 d = 5 .
  • 4.6 Least action principle (classical field theory)
  • 4.7 Canonical quantization.
  • 5 Klein-Gordon equation, SHOs, momentum space representation, raising and lowering operators.
  • 5.1 Canonical quantization.
  • 5.2 Momentum space representation.
  • 6 Canonical quantization, Simple Harmonic Oscillators, Symmetries
  • 6.1 Quantization of Field Theory.
  • 6.2 Free Hamiltonian.
  • 6.3 QM SHO review.
  • 6.4 Discussion.
  • 6.5 Switching gears: Symmetries.
  • 7 Symmetries, translation currents, energy momentum tensor.
  • 7.1 Symmetries.
  • 7.2 Spacetime translation.
  • 8 1st Noether theorem, spacetime translation current, energy momentum tensor, dilatation current.
  • 8.1 1st Noether theorem.
  • 8.2 Unitary operators.
  • 8.3 Continuous symmetries.
  • 8.4 Classical scalar theory.
  • 9 Unbroken and spontaneously broken symmetries, Higgs Lagrangian, scale invariance, Lorentz invariance, angular momentum quantization
  • 9.1 Last time.
  • 9.2 Examples of symmetries.
  • 9.3 Scale invariance.
  • 9.4 Lorentz invariance.
  • 10 Lorentz boosts, generator of spacetime translation, Lorentz invariant field representation.
  • 10.1 Lorentz transform symmetries.
  • 10.2 Transformation of momentum states.
  • 11 Microcausality, Lorentz invariant measure, retarded time SHO Green’s function.
  • 11.1 Relativistic normalization.
  • 11.2 Spacelike surfaces.
  • 11.3 Condition on microcausality.
  • 11.4 Harmonic oscillator.
  • 11.5 Field theory (where we are going).
  • 12 Independent study problems
  • Appendices
  • A Useful formulas and review
  • Index
  • Bibliography