A theory of spontaneous T violation

A theory of spontaneous T violation is presented.The total Lagrangian Is assumed to be invariant under the time reversal T and a gauge transformation (e.g., the hypercharge gauge), but-the physical solutions are not.In addition to the spin 1 gauge field and the knc:fwn matter fields, in its si!Tiplest form the theory consis!s of two complex spin 0 fields.Through the spontaneous symmetry breaking mechanism of Goldstone and Higgs, the vacuum expectation values of these two .spin 0 fields can be characterized by the shape of a triangle and their quantum fluctuations by its vibrational modes, just like a triangular molecule.T violations \ ' can be produced 9mong the known particles through virtual excitations of the vibrational modes of the triangle which has a built-in T violating phase angle.Examples of both Abelian and non-Abelian gauge groups are discussed.For renormalizable theories, all spontaneously T violating ~ffeds are finite.It is found that at low energy, below the threshold of producing these vibrational quanta, T violation is always quite small . 2.This gives then a well-defined difference between T and either CT or CPT.Since T is an anti-unitary operator, we can always choose the phase of k such that (3)To avoid irrelevant complications, we assume the theory not to be symmetric under any linear transformation which mixes q, 1 and q, 2 , so that.theright-hand side of (3) must remain k.