prof. dr hab. Henryk Arodź, UJ

On Relativistic Quantum Mechanics of the Majorana Particle

The Hilbert space of states of the relativistic Majorana particle consists of bispinors with real components. The usual momentum operator -i abla can not be defined in such space. Instead of it, we introduce the axial momentum operator p_5 = -i gamma_5 abla. It has rather intriguing properties. In particular, in the case of free massive particle there is an oscillating component, reminiscent of the Zitterbewegung. Next, we accordingly reformulate the plane wave expansion. The time evolution of the modes is given by an SO(4) matrix, which replaces the standard U(1) factor exp(-i E t)