The Axial Anomaly in D=3+1 Light-Cone QED

الأصل · EN

We consider (3+1)-dimensional, Dirac electrons of arbitrary mass, propagating in the presence of electric and magnetic fields which are both parallel to the x³ axis. The magnetic field is constant in space and time whereas the electric field depends arbitrarily upon the light-cone time parameter x+ = (x⁰ + x³)/√2. We present an explicit solution to the Heisenberg equations for the electron field operator in this background. The electric field results in the creation of electron-positron pairs. We compute the expectation values of the vector and axial vector currents in the presence of a state which is free vacuum at x+ = 0. Both current conservation and the standard result for the axial vector anomaly are verified for the first time ever in (3+1)-dimensional light-cone QED. An interesting feature of our operator solution is the fact that it depends in an essential way upon operators from the characteristic at x- = -L, in addition to the usual dependence upon operators at x+ = 0. This dependence survives even in the limit of infinite L. Ignoring the x- operators leads to a progressive loss of unitarity, to the violation of current conservation, to the loss of renormalizability, and to an incorrect result for the axial vector anomaly.