New D(2, 1; α) mechanics with spin variables

Pseudoclassical Mechanics for the Spin 0 and 1 Particles

We give an action for the massless spinning particle in pseudoclassical mechanics by using grassmann variables. The constructed action is invariant under τ-reparametrizations, local SUSY and O(N) transformations. After quantization, for the special case N = 2, we get an action which describes the spin 0, 1 particles and topological sectors of the massless DKP theory. A SUSY formulation of the g...

Complex Variables in Classical Hamiltonian Mechanics

Hidden Variables and Commutativity in Quantum Mechanics

This paper takes up a suggestion that the reason we cannot find hidden variable theories for quantum mechanics, as in Bell’s Theorem, is that we require them to assign joint probability distributions on incompatible observables; these joint distributions are empirically meaningless on one standard interpretation of quantum mechanics. Some have proposed to get around this problem by using genera...

Toy Quantum Mechanics Using Hidden Variables

It is used to state that no local theory assuming any kind of evolving-in-time physical field (hidden variables) can reproduce the same predictions as standard quantum mechanics. Bell formulated a corresponding theorem in [1]. An advanced variant of the theorem was proposed in [2]. Feynman, in [3], stated another but analogous idea: not any classical computational device (even when probabilisti...

Geometro-Stochastically Quantized Fields with Internal Spin Variables

The use of internal variables for the description of relativistic particles with arbitrary mass and spin in terms of scalar functions is reviewed and applied to the stochastic phase space formulation of quantum mechanics. Following Bacry and Kihlberg a four-dimensional internal spin space S̄ is chosen possessing an invariant measure and being able to represent integer as well as half integer spi...