Related papers: Stochastic quantisation of locally supersymmetric …
Quantization of electromagnetic fields is investigated in the framework of stochastic variational method (SVM). Differently from the canonical quantization, this method does not require canonical form and quantization can be performed…
It is often stated that quantum mechanics only makes statistical predictions and that a quantum state is described by the various probability distributions associated with it. Can we describe a quantum state completely in terms of…
We construct a relativistically covariant stochastic model for systems of non-interacting spinless particles whose number undergoes random fluctuations. The model is compared with the canonical quantization of the free scalar field in the…
Quantum mechanics contains some strange unphysical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by complex vectors, superpositions of states, collapse of wave…
Quantum theory has the property of "local tomography": the state of any composite system can be reconstructed from the statistics of measurements on the individual components. In this respect the holism of quantum theory is limited. We…
The local volatility model is a widely used for pricing and hedging financial derivatives. While its main appeal is its capability of reproducing any given surface of observed option prices---it provides a perfect fit---the essential…
A supersymmetric relativistic quantum theory in the temporal domain is developed for bi-spinor fields satisfying the Dirac equation. The simplest time-domain supersymmetric theory can be postulated for fields with time-dependent mass,…
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
In quantizing gravity based on stochastic quantization method, the stochastic time plays a role of the proper time. We study 2D and 4D Euclidean quantum gravity in this context. By applying stochastic quantization method to real symmetric…
We describe a measurement device principle based on discrete iterations of Bayesian updating of system state probability distributions. Although purely classical by nature, these measurements are accompanied with a progressive collapse of…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
Tracking the behaviour of stochastic systems is a crucial task in the statistical sciences. It has recently been shown that quantum models can faithfully simulate such processes whilst retaining less information about the past behaviour of…
The paper gives a systematic review of the basic ideas of (non-relativistic) quantum mechanics including all changes that result from previous work of the authors. This shows that the new theory is self-consistent and (in certain sense)…
The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either…
A new proposal for a Lorentz-invariant spontaneous localization theory is presented. It is based on the choice of a suitable set of macroscopic quantities to be stochastically induced to have definite values. Such macroscopic quantities…
Stochastic processes are shown to emerge from the time evolution of complex quantum systems. Using parametric, banded random matrix ensembles to describe a quantum chaotic environment, we show that the dynamical evolution of a particle…
The set of continuous norm-preserving stochastic Schrodinger equations associated with the Lindblad master equation is introduced. This set is used to describe the localization properties of the state vector toward eigenstates of the…
We study the statistical mechanics of a general Hamiltonian system in the context of symplectic structure of the corresponding phase space. This covariant formalism reveals some interesting correspondences between properties of the phase…
In this initial paper in a series, we first discuss why classical motions of small particles should be treated statistically. Then we show that any attempted statistical description of any nonrelativistic classical system inevitably yields…