Induced representations of groups and quantum mechanics

Robert D. Richtmyer

Teturô Inui, Yukito Tanabe, Yositaka Onodera

Lochlainn O'Raifeartaigh

Sujeewa Wickramasekara, Arno Böhm

In this paper we study how differentiable representations of certain subsemigroups of the Weyl–Heisenberg group may be obtained in suitably constructed rigged Hilbert spaces. These semigroup representations are induced from a continuous unitary representation of the Weyl–Heisenberg group in a Hilbert space. Aspects of the rigged Hilbert space formulation of time asymmetric quantum mechanics are also investigated within the context of the results developed here.

Emmanuel G. Floratos, I. Tsohantjis

Abstract Following the method of induced group representations of Wigner-Mackay, the explicit construction of all the unitary irreducible representations of the discrete finite Heisenberg-Weyl group $$HW_{2^{s}}$$ H W 2 s over the discrete phase space lattice $$\mathbb {Z}_{2^{s}}\otimes $$ Z 2 s ⊗ $$\mathbb {Z}_{2^{s}}$$ Z 2 s is presented. We explicitly determine their characters and their fusion rules. We discuss possible physical applications for finite quantum mechanics and quantum computation.

Hermann Weyl