| _version_ | 1866901260005801984 |
|---|---|
| author | Allaghi, Sami |
| author_facet | Allaghi, Sami |
| contents | <p>We investigate the semiclassical limit of the q-deformed algebra associated with the M=576 finite monoid extension. We analyze the transition from the discrete non-commutative regime to the continuum limit.</p> <p>This document establishes the recovery of classical dynamics from the algebraic substrate:</p> <ol> <li> <p><strong>Deformation Quantization:</strong> We define a deformation bracket <span>$[A, B]_q$</span> that interpolates between the fermionic anticommutator (at q = -1) and the standard Lie bracket.</p> </li> <li> <p><strong>Poisson Limit:</strong> We demonstrate that in the continuum limit (lattice scaling <span>$\epsilon \to 0$</span> and <span>$q \to 1$</span>), the algebraic commutator converges to the classical Poisson Bracket <span>$\{A, B\}$</span>, inducing a symplectic structure on the state space.</p> </li> <li> <p><strong>Hamiltonian Dynamics:</strong> The time evolution of observables is shown to satisfy the Hamilton-Jacobi equations in the smooth limit, interpreting the geodesic flow on the graph as a Principle of Least Action.</p> </li> </ol> <p>This work proposes that classical smooth manifolds can be derived as the thermodynamic limit of the discrete <span>$M_{ext}$</span> algebra.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18305694 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Mathematical Curiosity — VIII Emergence of Symplectic Structure from Discrete Commutators Allaghi, Sami <p>We investigate the semiclassical limit of the q-deformed algebra associated with the M=576 finite monoid extension. We analyze the transition from the discrete non-commutative regime to the continuum limit.</p> <p>This document establishes the recovery of classical dynamics from the algebraic substrate:</p> <ol> <li> <p><strong>Deformation Quantization:</strong> We define a deformation bracket <span>$[A, B]_q$</span> that interpolates between the fermionic anticommutator (at q = -1) and the standard Lie bracket.</p> </li> <li> <p><strong>Poisson Limit:</strong> We demonstrate that in the continuum limit (lattice scaling <span>$\epsilon \to 0$</span> and <span>$q \to 1$</span>), the algebraic commutator converges to the classical Poisson Bracket <span>$\{A, B\}$</span>, inducing a symplectic structure on the state space.</p> </li> <li> <p><strong>Hamiltonian Dynamics:</strong> The time evolution of observables is shown to satisfy the Hamilton-Jacobi equations in the smooth limit, interpreting the geodesic flow on the graph as a Principle of Least Action.</p> </li> </ol> <p>This work proposes that classical smooth manifolds can be derived as the thermodynamic limit of the discrete <span>$M_{ext}$</span> algebra.</p> |
| title | A Mathematical Curiosity — VIII Emergence of Symplectic Structure from Discrete Commutators |
| url | https://doi.org/10.5281/zenodo.18305694 |