Virial theorem and generalized momentum in quaternionic quantum mechanics

Geometric Phase in Quaternionic Quantum Mechanics

Quaternion quantum mechanics is examined at the level of unbroken SU(2) gauge symmetry. A general quaternionic phase expression is derived from formal properties of the quaternion algebra. pacs 03.65.Bz, 03.65.Ca,11.15.Kc, 02.30.+g 1 Quaternion Quantum Mechanics Quantum mechanics defined over general algebras have been conjectured since 1934 [1]. In 1936 Birkoff and von Neumann noted that the p...

Alternative Descriptions in Quaternionic Quantum Mechanics

We characterize the quasianti-Hermitian quaternionic operators in QQM by means of their spectra; moreover, we state a necessary and sufficient condition for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian with respect to a uniquely defined positive scalar product in a infinite dimensional (right) quaternionic Hilbert space. According to such results we obtain two altern...

Half-whole Dimensions in Quaternionic Quantum Mechanics

Quaternionic Quantum Mechanics and Noncommutative Dynamics

In this talk I shall first make some brief remarks on quaternionic quantum mechanics, and then describe recent work with A.C. Millard in which we show that standard complex quantum field theory can arise as the statistical mechanics of an underlying noncommutative dynamics. In quaternionic quantum mechanics, the Dirac transition amplitudes 〈ψ|φ〉 are quaternion valued, that is, they have the for...

Angular Momentum in Quantum Mechanics

We begin with a review of the basic concepts involved in the quantum mechanical description of physical systems and the notation we will use in the lectures. The notes in this Section are not intended to provide an introductory course on Quantum Mechanics. They assume the reader has had at least a first course at undergraduate physics level that covers some historical background and reviews the...