Related papers: Deterministic Quantization by Dynamical Boundary C…
We study the nonlinear realization of supersymmetry in a dynamical/cosmological background in which derivative terms like kinetic terms are finite. Starting from linearly realized theories, we integrate out heavy modes without neglecting…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
We study two-dimensional classically integrable field theory with independent boundary condition on each end, and obtain three possible generating functions for integrals of motion when this model is an ultralocal one. Classically…
We discuss in some generality aspects of noncommutative differential geometry associated with reality conditions and with differential calculi. We then describe the differential calculus based on derivations as generalization of vector…
We study dynamics in a neighborhood of a nonhyperbolic fixed point or an irreducible homoclinic tangent point. General type conditions for the existence of infinite sets of periodic points are obtained. A new method, based on the study of…
The development of last years in quantum geometrodynamics highlights new problems which were not obvious in its first formulation proposed by Wheeler and DeWitt. At the first stage the main task was to apply known quantization schemes to…
It is shown that quantum mechanics on noncommutative spaces (NQM) can be obtained by the canonical quantization of some underlying second class constrained system formulated in extended configuration space. It leads, in particular, to an…
In the present paper, a discrete differential calculus is introduced and used to describe dynamical systems over arbitrary graphs. The discretization of space and time allows the derivation of Heisenberg-like uncertainty inequalities and of…
We review realistic models that reproduce quantum theory in some limit and yield potentially new physics outside that limit. In particular, we consider deterministic hidden-variables theories (such as the pilot-wave model) and their…
A theory which claims to describe all the universe is advanced. It unifies general relativity, quantum field theory, and indeterministic conception. Basic entities are: classical metric tensor $g$, cosmic reference frame (including cosmic…
Two-dimensional matterless dilaton gravity with arbitrary dilatonic potential can be discussed in a unitary way, both in the Lagrangian and canonical frameworks, by introducing suitable field redefinitions. The new fields are directly…
We describe a method, using periodic points and determinants, for giving alternative expressions for dynamical quantities (including Lyapunov exponents and Hausdorff dimension of invariant sets) associated to analytic hyperbolic systems.…
Using the parametrized relativistic particle we obtain the noncommutative Snyder space-time. In addition, we study the consistency conditions between the boundary conditions and the canonical gauges that give origin to noncommutative…
We give an overview of the two different methods that have been introduced in order to describe the dynamics of constrained quantum systems; the symplectic formulation and the metric formulation. The symplectic method extends the work of…
Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such…
Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in…
A phase space treatment of special relativity of quantum systems is developed. In this approach a quantum particle remains localized if subject to inertial transformations, the localization occurring in a finite phase space area. Unlike…
We introduce a novel conditional stochastic interpolant framework for generative modeling of three-dimensional shapes. The method builds on a recent LDDMM-based registration approach to learn the conditional drift between geometries. By…
A new formulation of relativistic quantum mechanics is proposed in the framework of the rest-frame instant form of dynamics with its instantaneous Wigner 3-spaces and with its description of the particle world-lines by means of derived…
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…