On Conservation of the axial current in massless electrodynamics
Sep, 197116 pages
Published in:
- Nucl.Phys.B 27 (1971) 525-540
- Published: 1971
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Abstract: (Elsevier)
Conservation of the axial current in massless electrodynamics is considered in connection with the existence of the so-called anomalous terms in the equation for the divergence of the axial current. It is shown that in the limit of vanishing electron mass m transitions forbidden by γ 5 invariance give a non-vanishing contribution to the imaginary part of the triangle graph. This phenomenon is analogous in some respect to the breaking of the formal consequences from γ 5 invariance for the probability of the transition between electrons with right and left helicity through the emission of a photon. As was noticed by Lee and Nauenberg, this probability does not vanish in the limit of m =0. In this respect the appearance of an ultraviolet divergence in the triangle graph is irrelevant to the breaking of γ 5 invariance. We give some examples of well defined loop graphs and tree graphs which nevertheless violate conservation of the axial current at m =0 for some particular configuration of external momenta. We consider also another limiting procedure when m is chosen to be equal to zero from the very beginning but the photon mass is chosen to be finite. It then becomes possible to construct a conserved axial current but the matrix element associated with the triangle graph proves to be singular in the photon mass.References(21)
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