Equivalence of stochastic and Klauder quantization and the concept of locality and nonlocality in quantum mechanics

A Geometrical Approach Towards Entanglement

“…The equivalence of this formalism with geometric quantization [4] has also been pointed out. Again, it has been shown [5,6] that this procedure has its relevance in stochastic quantization of a fermion when a spinning particle is endowed with an internal degree of freedom through a direction vector (vortex line) which is topologically equivalent to a magnetic flux line. So it is expected that entanglement of a two qubit system is related to this internal degree of freedom manifested through the magnetic flux line.…”

The geometric phase and the geometrodynamics of relativistic electron vortex beams

“…It has been shown in some earlier papers [10,11] that in Nelson's stochastic quantization procedure [12,13], the quantization of a fermion can be achieved when we introduce an internal variable that appears as a direction vector. This direction vector essentially gives rise to the spin degrees of freedom.…”

Fermion doubling on a lattice and topological aspects of chiral anomaly

“…In the complexified space-time having the coordinate z ϭx ϩi , a fermion ͑an-tifermion͒ is characterized by the domain such that belongs to the interior of the forward ͑backward͒ light cone and as such represents the upper ͑lower͒ half-plane. 11 In such a space one should take into account the polar coordinates r,, along with the angle specifying the rotational orientation around the ''direction vector'' . The eigenvalue of the operator ‫ץ/ץ‪i‬‬ given by just corresponds to the ''internal helicity.''…”

“…To be equivalent to the Feynman path integral we have to take into account complexified space-time when the coordinate is given by z ϭx ϩi where corresponds to the ''direction vector'' attached to the space-time point x . 11 Since for quantization we have to introduce Brownian motion process both in the external and internal space, after quantization, for an observational procedure, we can think of the mean position of the particle in the external observable space with a stochastic extension as determined by the internal stochastic variable. The nonrelativistic quantum mechanics is obtained in the sharp point limit.…”

“…The nonrelativistic quantum mechanics is obtained in the sharp point limit. 11 This analysis of the quantization procedure suggests that we can write the position and momentum variable of this extended body as…”