Quaternionic quantum mechanics in real Hilbert space

Gianni Cassinelli, Piero Truini

Matthew A. Graydon

Sergio Giardino

The second quantization of the quaternionic fermionic field is undertaken using the real Hilbert space approach to quaternionic quantum mechanics ([Formula: see text]QM). The solution responds to an open problem of quaternionic quantum theory, and launches the basis to the development of the quaternionic interaction theory.

Sergio Giardino

The Dirac delta function potential is considered within the real Hilbert space approach for complex wave functions, as well as quaternionic wave functions. As has been previously determined, the real Hilbert space approach enables the possibility of self-interacting physical systems. The self-interaction precludes confining states, and also imposes non-stationary quantum states, both of them representing novel situations that cannot be observed in terms of quantum wave functions. These results remark the differences between quaternionic quantum mechanics ($\mathbbm H$QM) and complex quantum mechanics ($\mathbbm C$QM), and also establish a method of solving the wave equation that may be applied to a variety of different cases.

František Jenč

Steven P. Brumby, Gayatri Joshi