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Modern methods in quantum field theory
Work with controlled expansions, spectral and effective descriptions, quantum information, amplitudes, and nonperturbative consistency constraints.
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Module 01 research
Modern methods in quantum field theory
Work with controlled expansions, spectral and effective descriptions, quantum information, amplitudes, and nonperturbative consistency constraints.
- 01
Spectral representations and unitarity
Derive positive spectral weights from physical intermediate states and use a Euclidean correlator to test their consequences.
32 min - 02
Wilsonian matching and power counting
Integrate out a Gaussian heavy scalar, determine the effective interaction's sign, and measure the accuracy of its derivative expansion.
33 min - 03
Large-N expansions and saddle points
Compute a controlled saddle correction, distinguish fluctuation width from observable errors, and connect the calculation to large-component field theories.
34 min - 04
The epsilon expansion and critical exponents
Locate the Wilson–Fisher fixed point near four dimensions and compute a consistently ordered correlation-length exponent.
35 min - 05
Instantons and semiclassical saddles
Derive the action of a double-well instanton and distinguish tunneling amplitudes, energy splittings, and false-vacuum decay rates.
36 min - 06
Functional renormalization and truncations
Read the exact effective-average-action flow, identify the approximation introduced by a truncation, and interpret infrared stability with a stated scale convention.
36 min - 07
Schwinger–Keldysh and open quantum fields
Build a normalized closed-time-contour generating functional and use an exactly solvable dephasing channel to distinguish unitary evolution from reduced dynamics.
37 min - 08
Entanglement entropy and area laws
Calculate entropy from Schmidt probabilities and distinguish finite quantum-information measures from regulator-dependent field-theory entanglement.
35 min - 09
Bootstrap crossing and positivity
Translate conformal crossing into a positive-coefficient consistency problem and understand what a numerical exclusion certificate proves.
38 min - 10
Analyticity, dispersion, and positivity bounds
Relate a pole-subtracted low-energy scattering coefficient to a positive dispersive moment with explicit assumptions.
39 min