MARKOV DIFFUSIONS IN COMOVING COORDINATES AND STOCHASTIC QUANTIZATION OF THE FREE RELATIVISTIC SPINLESS PARTICLE

A Suggested Answer To Wallstrom's Criticism: Zitterbewegung Stochastic Mechanics I

Wallstrom's criticism of existing formulations of stochastic mechanics is that they fail to derive the empirical predictions of orthodox quantum mechanics because they require an ad hoc quantization condition on the postulated velocity potential, \emph{S}, in order to derive Schrödinger wave functions. We propose an answer to this criticism by modifying the Nelson-Yasue formulation of non-relativistic stochastic mechanics for a spinless particle with the following hypothesis: a spinless Nelson-Yasue particle of rest mass $m$ continuously undergoes a driven steady-state oscillation of `zitterbe…

A New Derivation of the Propagator's Path Integral for Spinless Elementary Particles

We introduce a notion of isolated units, elementary particles or more general physical phenomena that do not significantly affect their surrounding environment, and we build a primitive ontology to describe their evolution and interaction. We further introduce a notion of indistinguishability of distinct spacetime paths of a unit, for which the evolution of the state variables of the unit is the same, and a generalization of the equivalence principle based on indistinguishability. Under a time invertibility condition on the whole set of indistinguishable paths of a unit, we show that the quant…

无自旋量子力学中的挠率驱动非线性

Torsion-Driven Nonlinearity in Spinless Quantum Mechanics

本文研究带挠率空间中无自旋非相对论粒子的量子动力学，提出适配一般坐标系的随机变分方法，推导得挠率大小上界，揭示挠率影响量子系统的新机制。

Semi-relativistic wave-phase approximation for two-body spinless bound states in 1+1 dimensions

An approximate quantum-mechanical two-body equation for spinless particles incorporating relativistic kinematics is derived. The derivation is based on the relativistic energy-momentum relation $mc^{2}+ε= \sqrt{m^{2}c^{4}+p^{2}c^{2}}+V$ for each single particle, where $mc^2$ is the particle rest mass energy, $p$ its linear momentum, $ε$ its dynamical energy, and $V$ being the time-like vector interaction potential. The resulting two-body equation assumes rapid wave oscillations in a single, slowly varying potential well. A Bohr-Sommerfeld-type quantization condition is obtained. The approximat…

Deformation Quantization of Geometric Quantum Mechanics

Second quantization of a classical nonrelativistic one-particle system as a deformation quantization of the Schrodinger spinless field is considered. Under the assumption that the phase space of the Schrodinger field is $C^{\infty}$, both, the Weyl-Wigner-Moyal and Berezin deformation quantizations are discussed and compared. Then the geometric quantum mechanics is also quantized using the Berezin method under the assumption that the phase space is $CP^{\infty}$ endowed with the Fubini-Study Kahlerian metric. Finally, the Wigner function for an arbitrary particle state and its evolution equati…

Massive conformal particles with non-Abelian charges from free U(2N,2N)-twistor dynamics: quantization and coherent states

The inclusion of non-Abelian U(N) internal charges (other than the electric charge) into Twistor Theory is accomplished through the concept of "colored twistors" (ctwistors for short) transforming under the colored conformal symmetry U(2N,2N). In particular, we are interested in 2N-ctwistors describing colored spinless conformal massive particles with phase space U(2N,2N)/[U(2N)xU(2N)]. Penrose formulas for incidence relations are generalized to N>1. We propose U(2N)-gauge invariant Lagrangians for 2N-ctwistors and we quantize them through a bosonic representation, interpreting quantum states …