No grad should be pre-empted from going into high-energy theory simply because he didn't get an advanced undergraduate education (or even a Master's degree, like many before they come here). Students must be ready to start preparation for research in the middle of the second year (so by the end of that year they can take an oral to prove they're ready).
Modifying the structure or timing of only the theory courses would require consensus among just theorists, and not an entire department (although it might encourage them to do so later). The plan would then be:
- 1st semester: (“core”) courses "required" of all physics grad students.
- 2nd semester: courses specialized for theorists, but accessible to others for breadth requirements (“core theory”). Squeezed out (for @ least a year) are 2nd-semester E&M (mostly wave guides & other inessentials) and 2nd-semester QM (mostly atomic physics & stuff redundant to advanced theory courses, such as Dirac equation, QED, S-matrix; but not necessarily, depending on instructor).
- 3rd semester: advanced, specialized courses for theorists, intended as preparation for research, but accessible to all theory students.
- 4th semester: while beginning research in preparation for an oral exam, remaining courses not directly required for research (lab, breadth, "required" 2nd semester courses inessential for research, etc.).
Field theory & strings can also be divided into classical (“phenomenological”) and quantum, so each 2-semester course can be taken in parallel, rather than series; the classical halves can then also be taken by non-specialists.
For example, for someone planning on going into strings (non-string theory students would modify the 3rd semester):
- Dirac & Weyl equations
- group theory, Yang-Mills
- spontaneous breakdown, Higgs
- supersymmetry, superspace (might go below)
- GUTs, cosmology
- some trees, via classical field theory or Feynman heuristics
|Quantum field theory
- second quantization: path integrals
- BRST: special gauges
- more trees: spinor helicity
- loops: 1/N, β, renormalons, anomalies
||Supergravity & branes
- general relativity: local Lorentz, Weyl scale
- supergravity: D=2,4,5,10,11
- S- & T-duality
- compactification, Calabi-Yau
- branes, flux compactification
- 2D quantization: spectrum, BRST
- 2D CFT
- trees, loops, anomalies
- nonperturbative approaches
- preparation for oral
- lab, breadth, 2nd-semester remainders
Other specialized 3rd-semester courses would include “Advanced” courses in Particle Physics, Field Theory, & Statistical Mechanics.
(Presently, the only viable plan for students of string theory is to take quantum field theory in their first and second semesters, so they can take string theory in their third and fourth.)
*Ultimately the 1st-year courses could also use some improvement: In particular, there is considerable overlap between conventional "Classical electrodynamics" and "Quantum mechanics" courses, as both are mostly about solving wave equations (linear in the wave function, in fixed backgrounds, including boundaries). A better dichotomy might be:
- equations: Schrödinger, Klein-Gordon, Dirac, Maxwell; integral forms
- backgrounds: potentials, media/conductors
- actions, symmetries, conservation laws: current density, energy-momentum tensor
- Galilean & Poincaré: angular momentum, spin, multipoles (spherical harmonics)
- Green functions, perturbation, scattering
- exact solutions with symmetry: static, 1D, 2D, spherical, H atom
- variational, eikonal
- Hilbert space: observables, preparation & measurement
- dynamics: Hamiltonians, pictures
- semiclassical: correspondence principle, JWKB
- path integrals
- particle, oscillator
- anticommuting c-numbers
- multiparticle, statistics