6 papers
Temporal-Plane Carroll--Schrödinger Dynamics and Vortex Sectors in (2,2) Klein Space
José Rojas, Melvin Arias
Motivated by the temporal dynamics identified in the Carroll-Schrödinger theory, we derive a post-Carrollian Schrödinger dynamics in flat Klein space with signature $(2,2…
Probability Conservation, Liouville Measure, and the Symplectic Origin of Hamiltonian Dynamics
Enmanuel RodrÃguez-Brea, Melvin Arias
Liouville's theorem -- the preservation of phase-space volume -- is often presented as a corollary of Hamilton's canonical equations. Here we adopt an ensemble-first viewpoint in w…
On the Dynamics of Multiparticle Carroll-Schrdinger Quantum Systems
José Rojas, Melvin Arias
We study the dynamics of multiparticle Carroll-Schrödinger (CS) quantum systems in dimensions, where acts as the evolution variable and as the configuration coordi…
An Algebraic-Recursive Approach to Generate Higher-Order Symmetry Operators for Schrödinger and Klein-Gordon equations
Enrique Casanova, Melvin Arias
This article explores an algebraic-recursive approach to construct differential operators that commute with a central operator in quantum mechanics. Starting from the Sch…
On the Schrödinger and Carroll Schrödinger Equations: Dualities and Applications
José Rojas, Enrique Casanova, Melvin Arias
We investigate precise structural relations between the standard Schrödinger equation and its Carrollian analogue-the Carroll-Schrödinger equation-in 1+1 dimensions, with emphasi…
On the Derivation of Equations of Motion from Symmetries in Quantum-Mechanical Systems via Heisenberg's Uncertainty
Enrique Casanova, José Rojas, Melvin Arias
We propose the construction of equations of motion based on symmetries in quantum-mechanical systems, using Heisenberg's uncertainty principle as a minimal foundation. From canonic…