Related papers: Poisson spaces with a transition probability
A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as…
The Bohmian formulation of quantum mechanics is used in order to describe the measurement process in an intuitive way without a reduction postulate in the framework of a deterministic single system theory. Thereby the motion of the hidden…
On a cotangent bundle $T\sp*G$ of a Lie group $G$ one can describe the standard Liouville form $\theta$ and the symplectic form $d \theta$ in terms of the right Maurer Cartan form and the left moment mapping (of the right action of $G$ on…
The widely accepted approach to the foundation of quantum mechanics is that the Poisson bracket, governing the non-commutative algebra of operators, is taken as a postulate with no underlying physics. In this manuscript, it is shown that…
In this paper we introduce the notion of a smooth structure on a stratified space, the notion of a Poisson smooth structure and the notion of a weakly symplectic smooth structure on a stratified symplectic space, refining the concept of a…
We construct a family of Poisson structures of hydrodynamic type on the loop space of $\mathbb{C} P^{n-1}$. This family is parametrized by the moduli space of elliptic curves or, in other words, by the modular parameter $\tau$. This family…
We study the relation between a given set of equations of motion in configuration space and a Poisson bracket. A Poisson structure is consistent with the equations of motion if the symplectic form satisfy some consistency conditions. When…
Let $G$ be a semisimple Lie group, ${\frak g}$ its Lie algebra. For any symmetric space $M$ over $G$ we construct a new (deformed) multiplication in the space $A$ of smooth functions on $M$. This multiplication is invariant under the action…
It is well known that both the symplectic structure and the Poisson brackets of classical field theory can be constructed directly from the Lagrangian in a covariant way, without passing through the non-covariant canonical Hamiltonian…
The quantum mechanical transition probability is symmetric. A probabilistically motivated and more general quantum logical definition of the transition probability was introduced in two preceding papers without postulating its symmetry, but…
Given a Lie group G whose Lie algebra is endowed with a nondegenerate invariant symmetric bilinear form, we construct a Poisson algebra of continuous functions on a certain open subspace R of the space of representations in G of the…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
Symplectic and Poisson structures of certain moduli spaces/Huebschmann,J./ Abstract: Let $\pi$ be the fundamental group of a closed surface and $G$ a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a…
The space of time-like geodesics on Minkowski spacetime is constructed as a coset space of the Poincar\'e group in (3+1) dimensions with respect to the stabilizer of a worldline. When this homogeneous space is endowed with a Poisson…
An extension of the Born rule, the {\it quantum typicality rule}, has recently been proposed [B. Galvan: Found. Phys. 37, 1540-1562 (2007)]. Roughly speaking, this rule states that if the wave function of a particle is split into…
We introduce a general framework for analysing general probabilistic theories, which emphasises the distinction between the dynamical and probabilistic structures of a system. The dynamical structure is the set of pure states together with…
Quantum mechanics is essentially a statistical theory. Classical mechanics, however, is usually not viewed as being inherently statistical. Nevertheless, the latter can also be formulated statistically. Furthermore, a statistical…
Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of…
The paper provides an introduction into p-mechanics, which is a consistent physical theory suitable for a simultaneous description of classical and quantum mechanics. p-Mechanics naturally provides a common ground for several different…
In quantum theory, the modulus-square of the inner product of two normalized Hilbert space elements is to be interpreted as the transition probability between the pure states represented by these elements. A probabilistically motivated and…