Covariant Operator Formalism for Quantized Superfields

The Takahashi-Umezawa method of deriving the free covariant quantization relations from the linear equations of motion is extended to superfields. The Cauchy problem for free superfields is solved, and an expression for the time independent scalar product is given. For the case of interacting fields, we give the general Kallen-Lehmann spectral representation for the two-point superfield Green functions and, after the introduction of the asymptotic condition for superfields, we give the superfield extension of the Yang-Feldman equation. The case of the D = 2 real scalar superfield and the case of the D = 4 chiral superfield are discussed in detail.