An application of half-order differential operators to four-dimensional off-shell super Yang-Mills theory

Abstract A method which represents bosonic fields in the form of spinors is applied to both the gauge vector and the auxiliary scalar bosons in (1 + 3)-dimensional N = 2 off-shell super Yang-Mills theory. It utilizes the half-order differential operators, which are nothing but Abel's integral transformation and its inverse. The one-loop Klein-Gordon action for these bosonic fields around the classical monopole or antimonopole solution is expressed in the same form as the Dirac one up to surface terms and the remaining N = 1 SUSY can be made manifest. Cancellation of the one-loop quantum corrections, between bosons and fermions, to the mass of these classical solutions becomes manifest and the Witten-Olive conjecture on the saturation of the Bogomolny bound is reconfirmed. Lorentz transformation properties of these “spinorized” bosonic fields are also discussed.