dorsal/arxiv
View SchemaTowards an Autonomous Formalism for Quantum Mechanics
| Authors | Tulsi Dass |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0207104 |
| URL | https://arxiv.org/abs/quant-ph/0207104 |
Abstract
A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as the basic feature of quantum theory. Arguments are given to show that when such a unification is attempted at the configuration space level, the wave funtions of Schr$\ddot{o}$dinger theory appear as the natural candidates for the desired unification. A *-algebra $\mathcal{A}_{Q}$ of (not necessarily bounded) linear operators acting on an appropriate dense set of these wave functions appears as the arena for quantum kinematics. A simple generalization of an existing formalism in noncommutative geometry is employed to develop the notion of generalized algebraic symplectic structure (GASS) which can accomodate classical and quantum symplectic structures as special cases. Quantum kinematics and dynamics is developed in in the framework of a noncommutative Hamiltonian system employing an appropriate GASS based in $ \mathcal{A}_{Q}$. The Planck constant is introduced at only one place -- in the quantum symplectic form; its appearance at conventional places is then automatic. Unitary Wigner symmetries appear as canonical transformations in the noncommutative Hamiltonian system. A straightforward treatment of quantum - classical correspondence is given in terms of appropriate GASSes.
{
"annotation_id": "86d4dc0d-edf5-4418-9db6-991dc0c2fdf9",
"date_created": "2026-03-02T18:01:52.301000Z",
"date_modified": "2026-03-02T18:01:52.301000Z",
"file_hash": "f1896054a2f90bf1a8bf1a19d3491b4bc0fbd422fcd12afe49dd1b0eb274d4e4",
"private": false,
"record": {
"abstract": "A formalism is presented in which quantum particle dynamics can be developed\non its own rather than `quantization\u0027 of an underlying classical theory. It is\nproposed that the unification of probability and dynamics should be considered\nas the basic feature of quantum theory. Arguments are given to show that when\nsuch a unification is attempted at the configuration space level, the wave\nfuntions of Schr$\\ddot{o}$dinger theory appear as the natural candidates for\nthe desired unification. A *-algebra $\\mathcal{A}_{Q}$ of (not necessarily\nbounded) linear operators acting on an appropriate dense set of these wave\nfunctions appears as the arena for quantum kinematics. A simple generalization\nof an existing formalism in noncommutative geometry is employed to develop the\nnotion of generalized algebraic symplectic structure (GASS) which can\naccomodate classical and quantum symplectic structures as special cases.\nQuantum kinematics and dynamics is developed in in the framework of a\nnoncommutative Hamiltonian system employing an appropriate GASS based in $\n\\mathcal{A}_{Q}$. The Planck constant is introduced at only one place -- in the\nquantum symplectic form; its appearance at conventional places is then\nautomatic. Unitary Wigner symmetries appear as canonical transformations in the\nnoncommutative Hamiltonian system. A straightforward treatment of quantum -\nclassical correspondence is given in terms of appropriate GASSes.",
"arxiv_id": "quant-ph/0207104",
"authors": [
"Tulsi Dass"
],
"categories": [
"quant-ph"
],
"title": "Towards an Autonomous Formalism for Quantum Mechanics",
"url": "https://arxiv.org/abs/quant-ph/0207104"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "ca6c8559-9b55-4725-9ab4-424da313e317",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}