Time-reversal violation as loop-antiloop symmetry breaking: the Bessel   equation, group contraction and dissipation
  We show that the Bessel equation can be cast, by means of suitable transformations, into a system of two damped/amplified parametric oscillator equations. The relation with the group contraction mechanism is analyzed and the breakdown of loop-antiloop symmetry due to group contraction manifests itself as violation of time-reversal symmetry. A preliminary discussion of the relation between some infinite dimensional loop-algebras, such as the Virasoro-like algebra, and the Euclidean algebras e(2) and e(3) is also presented. 
Eleonora Alfinito (INFM, Sezione di Lecce, Italy), Giuseppe Vitiello   (Dipartimento di Fisica "E.R.Caianiello", Universit\`...