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Non-Abelian gauge fields and quantization
Develop Yang-Mills dynamics, gauge fixing, ghosts, identities, and physical-state constraints while distinguishing perturbative machinery from strong-coupling conclusions.
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Module 01 research
Non-Abelian gauge fields and quantization
Develop Yang-Mills dynamics, gauge fixing, ghosts, identities, and physical-state constraints while distinguishing perturbative machinery from strong-coupling conclusions.
- 01
Yang–Mills curvature and covariant derivatives
Fix a non-Abelian convention and compute curvature arising from both spatial variation and noncommuting potentials.
32 min - 02
Gauge transformations and parallel transport
Track endpoint covariance and path ordering for finite matrix-valued transport in a fixed convention.
32 min - 03
Yang–Mills classical equations and conserved currents
Derive covariant field equations and test a homogeneous nonlinear solution ansatz without promoting it to quantum dynamics.
32 min - 04
Faddeev–Popov determinant and ghost action
Interpret gauge-fixing Jacobians and Grassmann determinants within a local perturbative patch.
32 min - 05
Covariant-gauge propagators and gauge parameters
Invert the free Euclidean gauge-field kernel and isolate the gauge-dependent longitudinal sector.
32 min - 06
BRST transformations and nilpotent charge
Use a graded differential to encode gauge algebra and define physical equivalence within its perturbative domain.
32 min - 07
Slavnov–Taylor identities
Translate BRST invariance into constraints on full Green functions and renormalization constants.
32 min - 08
Background-field gauge and renormalization
Preserve background covariance while integrating quantum fluctuations and interpret the domain of one-loop running.
32 min - 09
Gribov copies and global gauge fixing
Distinguish local Faddeev-Popov invertibility from global orbit uniqueness and interpret restricted gauge regions carefully.
32 min - 10
Gauge-invariant observables and physical-state space
Define representation-specific Wilson loops and physical-state conditions while separating Higgs and confinement statements from gauge choices.
32 min