Abstract
A new, physical definition of the time elements is mathematically given. Their union constitutes a disconnected time topological space, [Formula: see text]. Based on the properties of this time–space and using the theory of random quantum fields previously developed, a nonunitary evolution operator, [Formula: see text], is derived. [Formula: see text] breaks down into two disjunct, spontaneously renormalized evolution operators by quantizing the random field action integral: one operator is unitary, [Formula: see text], and the other non-measure-preserving, [Formula: see text]. [Formula: see text] coincides, apart from the renormalization, with the evolution operator of the standard QFT. U ump (τ) breaks time symmetry in QFT. It reconciles the time reversal invariance of the basic equations of quantum theory with the irreversibility of the macroscopic, and some microscopic, phenomena. It provides a basis for the CP violation in the neutral K0 meson decay. Functional integrals arising in the theory have in the limit countably additive measures.
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