Related papers: A Local Gauge-Covariant Formulation of Classical D…

We present a theory for the construction of renormalized kinetic equations to describe the dynamics of classical systems of particles in or out of equilibrium. A closed, self-consistent set of evolution equations is derived for the…

The equations of relativistic hydrodynamics are transformed so that steps forward in time preserves local simultaneity. In these variables, the space-time coordinates of neighboring points on the mesh are simultaneous according to co-moving…

There exist instances of dynamical systems possessing symmetry transformations of which the conserved Noether charges generating these symmetries feature an explicit time dependence in their functional representation over phase space. The…

Assuming that Quantum Mechanics is universal and that it can be applied over all scales, then the Universe is allowed to be in a quantum superposition of states, where each of them can correspond to a different space-time geometry. How can…

General relativity allows for the existence of closed time-like curves, along which a material object could travel back in time and interact with its past self. This possibility raises the question whether certain initial conditions, or…

The automorphism invariant theory of Crawford[J. Math. Phys. 35, 2701 (1994)] has show great promise, however its application is limited by the paradigm to the domain of spin space. Our conjecture is that there is a broader principle at…

We have constructed a non-relativistic theory of quantum mechanics based on local modulus symmetry. The resulting connection in the covariant derivative is identified as the escape velocity of the gravitational field. A new real and…

Here we postulate three laws which form a mathematical framework to capture the essence of Darwinian evolutionary dynamics. The second law is most quantitative and is explicitly expressed by a unique form of stochastic differential…

We give an overview of some conceptual difficulties, sometimes called paradoxes, that have puzzled for years the physical interpetation of classical canonical gravity and, by extension, the canonical formulation of generally covariant…

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…

We introduce a new geometric framework for relativistic particle dynamics based on contact geometry and suitable for treating dissipative processes like particle decay. The dynamics is formulated on a nine--dimensional extended phase space…

We derive for generally covariant theories the generic dependency of observables on the original fields, corresponding to coordinate-dependent gauge fixings. This gauge choice is equivalent to a choice of intrinsically defined coordinates…

We describe in detail how to eliminate nonphysical degrees of freedom in the Lagrangian and Hamiltonian formulations of a constrained system. Two important and distinct steps in our method are the fixing of ambiguities in the dynamics and…

Governing equations are fundamental for describing and predicting dynamic urban geographic systems. Unlike physical systems guided by first principles, urban spatiotemporal phenomena emerge from coupled geographic processes that lack…

Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…

It is well known that the statistics of closed classical systems evolves according to the Liouville theorem. Here we study the dynamics of the marginal statistics of classical systems coupled to external degrees of freedom, by developing a…

Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Due to instabilities, small…

We study a class of theories in which space-time is treated classically, while interacting with quantum fields. These circumvent various no-go theorems and the pathologies of semi-classical gravity, by being linear in the density matrix and…

We study classical limit for quantum mechanics with two times and temperature, which describes a generalized dynamics of relativistic point mass. In this theory, thermodynamic time means a parameter of evolution, whereas geometric time is…

A nonlocal mass operator can be consistently set in local form through the introduction of a set of additional fields with geometrical appropriated properties. A local and polynomial gauge invariant action is thus identified. Equations…