Physics / research
Quantum fields at temperature and out of equilibrium
Connect imaginary-time and real-time formalisms to thermal spectra, kinetic response, transport coefficients, and controlled approximations for evolving quantum fields.
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Module 01 research
Quantum fields at temperature and out of equilibrium
Connect imaginary-time and real-time formalisms to thermal spectra, kinetic response, transport coefficients, and controlled approximations for evolving quantum fields.
- 01
Identify thermal equilibrium through correlations
Derive KMS detailed balance from the Gibbs trace while keeping real-time Fourier conventions and bosonic versus fermionic Green-function signs explicit.
39 min - 02
Resolve a thermal circle into Matsubara modes
Derive periodic and antiperiodic imaginary-time frequencies and evaluate a convergent thermal sum without confusing imaginary time with dissipative real-time evolution.
38 min - 03
Separate spectral support from thermal occupation
Define a commutator spectral density and retarded sign convention, recover thermal Wightman weights, and demonstrate the Euclidean continuation for a free mode.
40 min - 04
Reorganize perturbation theory for soft thermal modes
Derive a leading scalar thermal mass with an explicit coupling convention and explain why soft propagators require resummation and subtraction even at weak coupling.
39 min - 05
Close the time contour without doubling the physics
Construct forward and backward evolution from an initial density matrix, explain the four contour correlators, and use unitarity to check source normalization.
39 min - 06
Separate causal response from statistical fluctuations
Define retarded, advanced, and symmetrized bosonic functions, derive their equilibrium fluctuation relation, and test noncommuting hydrodynamic limits.
41 min - 07
Extract transport from a low-frequency response
Normalize a shear-viscosity Kubo limit, connect its classical noise floor to fluctuation–dissipation, and identify why collisionless and hydrodynamic limits need different resummations.
41 min - 08
Derive a kinetic approximation from two-time dynamics
Separate exact memory evolution from Wigner and quasiparticle approximations, track a first gradient sign, and identify which assumptions make a Boltzmann equation meaningful.
42 min - 09
Resolve the scales in a weakly coupled plasma
Explain how hard thermal particles generate soft gauge response, compute leading Debye scales, and distinguish static electric screening, collective propagation, and ultrasoft magnetic limits.
41 min - 10
Test what has actually thermalized
Distinguish stationary, prethermal, and Gibbs behavior, reconcile local relaxation with closed-system unitarity, and audit the time and occupation limits of field-theory approximations.
41 min