Anomalous Ward Identities in Spinor Field Theories
1969/08/25 by William A. Bardeen · 1,105 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Classical mechanics #Coupling (piping) #Divergence (linguistics) #Field (mathematics) #Geometry #High-pressure geophysics and materials #Laser-Plasma Interactions and Diagnostics #Magnetic field #Mathematical physics #Mathematics #Meson #Physics #Pseudoscalar #Pseudovector #Pure mathematics #Quantum and Classical Electrodynamics #Quantum electrodynamics #Quantum mechanics #Scalar (mathematics) #Solenoidal vector field #Spinor #Vector Laplacian #Vector field #Vector operator #Vector potential
paper · doi:10.1103/physrev.184.1848
published in Physical Review 184(5), 1848-1859 (American Institute of Physics)
openalex publication_date 1969/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Abstract
We consider the model of a spinor field with arbitrary internal degrees of freedom having arbitrary nonderivative coupling to external scalar, pseudoscalar, vector, and axial-vector fields. By carefully defining the S matrix in the interaction picture, the vector and axial-vector currents associated with the external vector and axial-vector fields are found to satisfy anomalous Ward identities. If we require that the vector currents satisfy the usual Ward identities, the divergence of the axial-vector current contains well-defined anomalous terms. These terms are explicitly calculated.
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