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Anomalies, consistency, and topology in fields
Trace quantum anomalies through several derivations and applications, emphasizing which symmetries can be anomalous and which gauge inconsistencies must cancel.
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Module 01 research
Anomalies, consistency, and topology in fields
Trace quantum anomalies through several derivations and applications, emphasizing which symmetries can be anomalous and which gauge inconsistencies must cancel.
- 01
Preserve the vector current and expose the axial anomaly
Relate the triangle Ward identities to spectral flow with explicit current, charge, and unit conventions.
36 min - 02
Find the anomaly in the fermion measure
Use Grassmann Jacobians and a gauge-covariant heat-kernel regulator while distinguishing finite mode counting from a local quantum anomaly.
37 min - 03
Descend from a characteristic polynomial to a Ward variation
Track form degree, normalization, and the distinction between consistent and covariant anomalies in an explicit Abelian example.
39 min - 04
Audit a chiral spectrum for gauge consistency
Convert every fermion to an all-left-handed convention and check independent gauge and mixed gravitational anomaly coefficients.
37 min - 05
Detect a sign invisible to local anomaly polynomials
Use the ordinary SU(2) global anomaly to distinguish infinitesimal consistency from determinant holonomy under large transformations.
38 min - 06
Allocate a mixed anomaly without erasing its class
Use two background connections to distinguish exact global symmetries, dynamical gauge consistency, and counterterm-dependent Ward representatives.
39 min - 07
Carry an exact global-symmetry anomaly into the infrared
Use background response to reject incomplete infrared spectra while keeping anomaly constraints distinct from a dynamical solution.
38 min - 08
Track theta phases through topology and mass redefinitions
Separate integer-sector interference, the invariant strong-CP angle, and illustrative finite-sector models from full QCD dynamics.
39 min - 09
Read the index without overcounting zero modes
Connect smooth gauge topology to a chiral kernel difference and separate protected index data from determinant powers and boundary corrections.
39 min - 10
Cancel a boundary anomaly with bulk inflow
Match a Chern–Simons boundary variation to edge anomaly data while keeping consistent Ward identities distinct from physical Hall charge transport.
40 min