Physics: theory survey

The Many-Body Problem in Quantum Mechanics

  • many many-body systems
  • even a proton can be viewed as a many-body system: of quarks and gluons
  • even 0-body, i.e. the vacuum, is a many-body system

Many-Body Systems

  • condensed matter systems: electron gas, phonons, etc.
  • nuclear matter
  • quark (and gluon) matter: HICs and neutron stars

Recurrent Concepts

  • quasi-particles: mass spectrum and width
  • in-medium effects and collective excitations
  • statistical mechanics
  • partition functions
  • kinetic theory and transport
  • symmetry and its spontaneous breaking (hiding)
  • phase transitions

Theoretical Methods

  • Feynman diagrams and perturbation theory
  • field theoretical techniques, self-consistent equations
  • scattering theory and dispersion relations
  • approximation methods
    • saddle-point approximation and beyond
    • expansion in (coupling, N, densities, etc.)
  • group theory and angular momenta
  • effective models, potential models, matrix models, etc.

our approach in this course

  • find the stupidest example in a physics topic / method
  • check to see whether the ability to numerically compute things could improve our understanding
  • numerical exploration of some math. problems: visualize, algorithm

an example

1+2+3+…=−112=ζ(−1)\begin{aligned} 1 + 2 + 3 + \ldots = -\frac{1}{12} = \zeta(-1) \end{aligned}

  • Can we teach the computer to understand this?
  • And more importantly, can we learn something from it?

THE END