Related papers: Pseudodynamical evolution and path integral in qua…
We introduce two new integral transforms of the quantum mechanical transition kernel that represent physical information about the path integral. These transforms can be interpreted as probability distributions on particle trajectories…
The Entropic Dynamics reconstruction of quantum mechanics is extended to quantum field theory in curved space-time. The Entropic Dynamics framework, which derives quantum theory as an application of the method of maximum entropy, is…
The dynamical equations which are basic for the description of the dynamics of quantum felds in arbitrary space--time geometries, can be derived from the requirements of a unique deterministic evolution of the quantum fields, the…
In this paper, the projective geometry is used to describe the features of spherical manifold and discreteness in quantum evolution. As a system evolves in time the state vector changes and it traces out a curve in Hilbert space.…
The concept of phase space distribution functions and their evolution is used in the case of en enlarged phase space. In particular, we include the intrinsic spin of particles and present a quantum kinetic evolution equation for a scalar…
A quantum version of the action principle in a simple covariant dynamical theory of two relativistic particles is formulated. The central object of this new formulation of quantum theory is a stationary eigenvalue of the quantum action.…
In this contribution a path integral approach for the quantum motion on three-dimensional spaces according to Koenigs, for short``Koenigs-Spaces'', is discussed. Their construction is simple: One takes a Hamiltonian from three-dimensional…
A method is presented which restricts the space of paths entering the path integral of quantum mechanics to subspaces of $C^\alpha$, by only allowing paths which possess at least $\alpha$ derivatives. The method introduces two external…
En nous laissant guider par la notion de champ qui en fait domine toute la physique nous d\'efinissons la nature physique d'un syst\`eme, ses propri\'et\'es et ses \'etats possibles. Nous proposons alors un cadre tr\`es g\'en\'erale…
The path integral formulation in quantum mechanics corresponds to the first quantization since it is just to rewrite the quantum mechanical amplitude into many dimensional integrations over discretized coordinates $x_n$. However, the path…
We analyze the problem of one dimensional quantum particle falling in a constant gravitational field, also known as the {\it bouncing ball}, employing a semiclassical approach known as momentous effective quantum mechanics. In this…
A new dynamical paradigm merging quantum dynamics with cosmology is discussed. Time evolution involves a genuine passage of time, which distinguishes the formalism from those where dynamics in space is equivalent to statics in space-time.…
The formulation of quantum mechanics within the framework of entropic dynamics is extended to the domain of relativistic quantum fields. The result is a non-dissipative relativistic diffusion in the infinite dimensional space of field…
We introduce a framework for non-linear time evolution in quantum mechanics as a natural non-linear generalization of the Schrodinger equation. Within our framework, we derive simple toy models of dynamical geometry on finite graphs. Along…
We have developed a proper path integral formalism consistent with the deformed version of the quantum mechanics which contains a maximum observable length scale at the order of the Cosmological particle horizon, existing in cosmology.…
Several years ago the so-called quantum geometrodynamics in extended phase space was proposed. The main role in this version of quantum geometrodynamics is given to a wave function that carries information about geometry of the Universe as…
The Moran process is one of an basic mathematical structure in the evolutionary game theory. In this work, we introduce the formulation of the path integral approach for evolutionary game theory based on the Moran process. We derive the…
In the geometry of quantum evolutions, a geodesic path is viewed as a path of minimal statistical length connecting two pure quantum states along which the maximal number of statistically distinguishable states is minimum. In this paper, we…
In quantum mechanics, outcomes of measurements on a state have a probabilistic interpretation while the evolution of the state is treated deterministically. Here we show that one can also treat the evolution as being probabilistic in nature…
The issue of field redefinition invariance of path integrals in quantum field theory is reexamined. A ``paradox'' is presented involving the reduction to an effective quantum-mechanical theory of a $(d+1)$-dimensional free scalar field in a…