Related papers: A Variational Formulation of Symplectic Noncommuta…
There ought to exist a description of quantum field theory which does not depend on an external classical time. To achieve this goal, in a recent paper we have proposed a non-commutative special relativity in which space-time and matter…
We review opportunities for stochastic geometric mechanics to incorporate observed data into variational principles, in order to derive data-driven nonlinear dynamical models of effects on the variability of computationally resolvable…
The structure of the state-vector space of identical bosons in noncommutative spaces is investigated. To maintain Bose-Einstein statistics the commutation relations of phase space variables should simultaneously include…
In the last years noncommutative quantum mechanics has been investigated intensively. We consider the influence of magnetic field on decoherence of a system in the noncommutative quantum plane. Particularly, we point out a model in which…
A mathematical notion of interaction is introduced for noncommutative dynamical systems, i.e., for one parameter groups of *-automorphisms of $\Cal B(H)$ endowed with a certain causal structure. With any interaction there is a well-defined…
A comparison between the two possible variational principles for the study of a free falling spinless particle in a space-time with torsion is noted. It is well known that the autoparallel trajectories can be obtained from a variational…
From the principle that there is no absolute description of a physical state, we advance the approach according to which one should be able to describe the physics from the perspective of a quantum particle. The kinematics seen from this…
This work reflects on mechanics as an epistemological framework on the state of a physical system to regard dynamics as the distribution of mechanical properties over spacetime coordinates. The resulting distribution is taken to be the…
An explicit dynamical model for non relativistic quantum mechanics with an effective gravitational interaction is proposed, which, as being well defined, allows in principle for the evaluation of every physical quantity. Its non unitary…
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…
This textbook introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general relativity and quantum field theory as limiting…
The Nelson stochastic mechanics is derived as a consequence of the basic physical principles such as the principle of relativity of observations and the invariance of the action quantum. The unitary group of quantum mechanics is represented…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
A fractional generalization of variations is used to define a stability of non-integer order. Fractional variational derivatives are suggested to describe the properties of dynamical systems at fractional perturbations. We formulate…
We propose the difference discrete variational principle in discrete mechanics and symplectic algorithm with variable step-length of time in finite duration based upon a noncommutative differential calculus established in this paper. This…
This is a general description of a probabilistic formalism of mechanics, i.e., an extension of the Newtonian mechanics principles to the systems undergoing random motion. From an analysis of the induction procedure from experimental data to…
Classical dynamical laws are conventionally formulated as closed evolution equations defined on fixed geometric backgrounds and a global time parameter. We develop a formulation in which neither prescribed evolution laws nor an external…
Classical mechanics for individual physical systems and quantum mechanics of non-relativistic particles are shown to be exceptional cases of a generalized dynamics described in terms of maps between two manifolds, the source being…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
The variational principle for linear stability of three-dimensional, inhomogenious, compressible, moving magnetized plasma is suggested. The principle is ``softer'' (easier to be satisfied) than all previously known variational stability…