Unitarity of the Wick $T$-exponent

The unitarity of the regularized $S$ matrix written as a Wick time-ordered exponential is proved; the proof also applies when derivatives are present in the interaction. The combinatorial part of the proof is carried out in the language of functional integration. First, formal unitarity is proved for the nonregularized $S$ matrix and then a regularization of the Pauli–Villars type is introduced (with this regularization the Wick and the Dyson chronological products of operators are identical [1]), and the unitarity of the regularized $S$ matrix is proved in each perturbation order.