Mathematical method of quantum phase space is very useful in physical applications like quantum optics and non-relativistic quantum mechanics. However, attempts to generalize it for the relativistic case lead to some difficulties. One of problems is band structure of energy spectrum for a relativistic particle. This corresponds to an internal degree of freedom, socalled charge variable. In phys...

Quantum field theory is the usual solution to the problems inherent in melding quantum mechanics with special relativity. However, there has also been significant literature on an alternate presentation of relativistic quantum mechanics in terms of an “invariant fifth parameter” in addition to the usual four coordinates of spacetime. When this parameter is treated as parameterizing spacetime pa...

A thesis submitted in partial fulfilment of the requirements for the degree of

Relativistic quantum effects on physical observables of scalar charged particles are studied. Possible peculiarities of their behavior that can be verified in an experiment can confirm several fundamental conceptions of quantum mechanics. For observables independent of charge variable, we propose relativistic Wigner function formalism that contains explicitly the measurement device frame. This ...

This is an introduction to spacetime algebra (STA) as a unified mathematical language for physics. STA simplifies, extends and integrates the mathematical methods of classical, relativistic and quantum physics while elucidating geometric structure of the theory. For example, STA provides a single, matrixfree spinor method for rotational dynamics with applications from classical rigid body mecha...

The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic quantum mechanics algebra is also unstable. Its stabilization requires the non-commutativity of the space-time coordinates and the existence of a fundamental len...