$T$-products in Bogolubov's axiomatics

The obvious phenomenon in the classical mechanics, namely the distinction between Hamiltonian $H$ and (minus) Lagrangian $-L$, is described in quantum field theory by two distinct $T$-products. This distinction is reflected in two forms of $S$-matrix – the chronological exponentials, $T_D$ with $H$ and $T_W$ with $-L$ as generators, proposed by second author in 1961. The causal and unitary $S$-matrix requires resp. non-local and non-hermitian Lagrangian in the general type of régularisation. The distinction between $T_D$ and $T_W$, is also clearly seen in Green functions. The field Green functions depend on T-products only of the fields themselves when the classical examples of renormalisable theories are concerned. Generally the renormalisation of Green functions requires taking into consideration the higher field-like quasilocal operators.