Related papers: Symplectic Reduction of Classical Mechanics on Sha…
The modal analysis is revisited through the symplectic formalism, what leads to two intertwined eigenproblems. Studying the properties of the solutions, we prove that they form a canonical basis. The method is general and works even if the…
Classical Hamiltonian mechanics, characterized by a single conserved Hamiltonian (energy) and symplectic geometry, `hides' other invariants into symmetries of the Hamiltonian or into the kernel of the Poisson tensor. Nambu mechanics aims to…
The centuries-long practice of the teaching turned mechanics into an academic construct detached from its underlying science, the physics of macroscopic bodies. In particular, the regularities that delineate the scope of validity of…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
A calculus based on pointer-mark coincidences is proposed to define, in a mathematically rigorous way, measurements of space and time intervals. The connection between such measurements in different inertial frames according to the Galilean…
The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…
Classical mechanical systems are modeled by a symplectic manifold $(M,\omega)$, and their symmetries, encoded in the action of a Lie group $G$ on $M$ by diffeomorphisms that preserves $\omega$. These actions, which are called "symplectic",…
We propose a new systematic method of studying correlations between parameters that describe an astronomical (or any) physical system. We recall that behind Dimensionless scaling laws in complex, self-interacting physical objects lies a…
The absolute/relative debate on the nature of space and time is ongoing for thousands of years. Here we attempt to investigate space and time from the information theoretic point of view to understand spatial and temporal correlations under…
We show that an unification of quantum mechanics and general relativity implies that there is a fundamental length in Nature in the sense that no operational procedure would be able to measure distances shorter than the Planck length.…
The aim of this paper is to present a new logic-based understanding of the connection between classical kinematics and relativistic kinematics. We show that the axioms of special relativity can be interpreted in the language of classical…
Contrary to our immediate and vivid sensation of past, present, and future as continually shifting non-relational modalities, time remains as tenseless and relational as space in all of the established theories of fundamental physics. Here…
Constrained symplectic quantization is a functional formulation of quantum field theory in which quantum fluctuations are sampled through a deterministic Hamiltonian flow in an auxiliary intrinsic time $\tau$. In this paper we extend the…
Kendall's Similarity Shape Theory for constellations of points in the carrier space $\mathbb{R}^n$ was developed for use in Probability and Statistics. It was subsequently shown to reside within (Classical and Quantum) Mechanics'…
The main goal of these lectures is to introduce and review the Hamiltonian formalism for classical constrained systems and in particular gauge theories. Emphasis is put on the relation between local symmetries and constraints and on the…
Many important theories in modern physics can be stated using differential geometry. Symplectic geometry is the natural framework to deal with autonomous Hamiltonian mechanics. This admits several generalizations for nonautonomous systems,…
The objective of this work is twofold: First, we analyze the relation between the k-cosymplectic and the k-symplectic Hamiltonian and Lagrangian formalisms in classical field theories. In particular, we prove the equivalence between…
The notion of "reference frame" is a central theoretical construct for interpreting the physical implications of spacetime diffeomorphism invariance in General Relativity. However, the alternative formulation of classical General Relativity…
This thesis, explores the quantum entanglement and evolution through both a geometric and dynamical perspective. The first part focuses on classical phase space and its central role in Hamiltonian mechanics, emphasizing the importance of…
Particle-based simulations of the Vlasov equation typically require a large number of particles, which leads to a high-dimensional system of ordinary differential equations. Solving such systems is computationally very expensive, especially…