Related papers: Lorentz covariant physical Brownian motion: Classi…
A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical three-body system in one space dimension, comprised of one photon and two identical massive spin one-half Dirac particles, which can be thought of as two…
The recent analysis on noncommutative geometry, showing quantization of the volume for the Riemannian manifold entering the geometry, can support a view of quantum mechanics as arising by a stochastic process on it. A class of stochastic…
A relativistic kinetic Fokker-Planck equation that has been recently proposed in the physical literature is studied. It is shown that, in contrast to other existing relativistic models, the one considered in this paper is invariant under…
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…
A Lorentz and general co-ordinate co-variant form of canonical gravity, using Ashtekar's variables, is investigated. A co-variant treatment due to Crnkovic and Witten is used, in which a point in phase space represents a solution of the…
Consider a worldline of a pointlike particle parametrized by polynomial functions, together with the light cone ("retardation") equation of an inertially moving observer. Then a set of apparent copies, R- or C-particles, defined by the…
While it has often been proposed that, fundamentally, Lorentz-invariance is not respected in a quantum theory of gravity, it has been difficult to reconcile deviations from Lorentz-invariance with quantum field theory. The most commonly…
A fairly general Lorentz-covariant quark model of mesons is constructed. It has several versions whose nonrelativistic limit corresponds to the well-known Isgur, Scora, Grinstein, and Wise model. In the heavy-quark limit, the covariant…
We study the peculiar motion of non-relativistic matter in a fully covariant way. The exact nonlinear equations are derived and then applied to the case of pressure-free matter, moving relatively to a quasi-Newtonian Eulerian frame. Our…
Statistical invariance of Wiener increments under SO(n) rotations provides a notion of gauge transformation of state-dependent Brownian motion. We show that the stochastic dynamics of non gauge-invariant systems is not unambiguously…
Implementing Poincar\'e's `geometric conventionalism' a scalar Lorentz-covariant gravity model is obtained based on gravitationally modified Lorentz transformations (or GMLT). The modification essentially consists of an appropriate…
We investigate the profound relation between the equations of biological evolution and quantum mechanics by writing a biologically inspired equation for the stochastic dynamics of an ensemble of particles. Interesting behavior is observed…
Recently the general form of a translation-covariant quantum Boltzmann equation has been derived which describes the dynamics of a tracer particle in a quantum gas. We develop a stochastic wave function algorithm that enables full…
We consider the problem of whether there are deterministic theories describing the evolution of an individual physical system in terms of the definite trajectories of its constituent particles and which stay in the same relation to Quantum…
We present a systematic study of the cosmological dynamics resulting from an effective Hamiltonian, recently derived in loop quantum gravity using Thiemann's regularization and earlier obtained in loop quantum cosmology (LQC) by keeping the…
We investigate what can be concluded about a quantum system when sequential quantum measurements of its observable -- a prominent example of the so-called quantum stochastic process -- fulfill the Kolmogorov consistency condition and thus…
For linear bose field theories, I show that if a classical Hamiltonian function is strictly positive, then there is a canonical transformation making the evolution orthogonal. This structure theorem is used to analyze the corresponding…
It is possible to implement a certain form of modified gravity inspired by loop quantization through non-bijective canonical transformations. The canonical nature might suggest that such modifications are guaranteed to preserve general…
The special relativity laws emerge as one-parameter (light speed) generalizations of the corresponding laws of classical physics. These generalizations, imposed by the Lorentz transformations, affect both the definition of the various…
Classical Hamiltonian systems with balanced loss and gain are considered in this review. A generic Hamiltonian formulation for systems with space-dependent balanced loss and gain is discussed. It is shown that the loss-gain terms may be…