# Foundations of the hadronic generalization of the atomic mechanics. I. Generalization of Heisenberg's and Schroedinger's representations

## Abstract

This paper deals with the part of of the Hadronic Mechanics called of Lie-isotopic type, which: (1) is conceived for the exterior strong non-Hamiltonian treatment; (2) is based on the isotopic generalization of the associative algebra of operators on a Hilbert space; and (3) admits as a classical limit the recently achieved Birkhoffian generalization of the Hamiltonian Mechanics. We first review the Hadronic-isotopic covering of Heisenberg's representation with particular reference to the generalization of: Heisenberg's equations; canonical commutation rules; canonical quantization; Heisenberg's uncertainty principle; Planck's constant; Galilei's relativity; and the representation theory. A possible, single, unifying postulate for the covering theory is introduced. We then pass to the construction of the corresponding generalization of Schroedinger's representation. For this purpose, we first construct the Birkhoffian generalization of the Hamilton-Jacobi theory for local non-Hamiltonian systems. We then show that the latter theory admits a consistent quantization into a generalization of Schroedinger's equations. Some essential properties of the emerging hadronic generalization of the atomic wave theory, are presented. In particular, we identify the general solution of the hadronic wave packets under the most general possible local Hamiltonian and non-Hamiltonian forces, which has no counterpart in the Atomic Mechanics.

- Authors:

- Publication Date:

- Research Org.:
- Inst. for Basic Research, Cambridge, MA

- OSTI Identifier:
- 6296839

- Report Number(s):
- CONF-820136-

Journal ID: CODEN: HAJOD

- DOE Contract Number:
- AC02-80ER10651

- Resource Type:
- Conference

- Resource Relation:
- Journal Name: Hadronic J.; (United States); Journal Volume: 5:4; Conference: 1. international conference on non-potential interactions and their Lie-admissible treatment, Orleans, France, 5 Jan 1982

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; STRONG INTERACTIONS; QUANTUM MECHANICS; CLASSICAL MECHANICS; HADRONS; HAMILTONIANS; HEISENBERG PICTURE; LIE GROUPS; REVIEWS; SCHROEDINGER EQUATION; STATISTICAL MECHANICS; SYMMETRY BREAKING; BASIC INTERACTIONS; DIFFERENTIAL EQUATIONS; DOCUMENT TYPES; ELEMENTARY PARTICLES; EQUATIONS; INTERACTIONS; MATHEMATICAL OPERATORS; MECHANICS; PARTIAL DIFFERENTIAL EQUATIONS; QUANTUM OPERATORS; SYMMETRY GROUPS; WAVE EQUATIONS; 645204* - High Energy Physics- Particle Interactions & Properties-Theoretical- Strong Interactions & Properties

### Citation Formats

```
Santilli, R.M.
```*Foundations of the hadronic generalization of the atomic mechanics. I. Generalization of Heisenberg's and Schroedinger's representations*. United States: N. p., 1982.
Web.

```
Santilli, R.M.
```*Foundations of the hadronic generalization of the atomic mechanics. I. Generalization of Heisenberg's and Schroedinger's representations*. United States.

```
Santilli, R.M. Tue .
"Foundations of the hadronic generalization of the atomic mechanics. I. Generalization of Heisenberg's and Schroedinger's representations". United States.
doi:.
```

```
@article{osti_6296839,
```

title = {Foundations of the hadronic generalization of the atomic mechanics. I. Generalization of Heisenberg's and Schroedinger's representations},

author = {Santilli, R.M.},

abstractNote = {This paper deals with the part of of the Hadronic Mechanics called of Lie-isotopic type, which: (1) is conceived for the exterior strong non-Hamiltonian treatment; (2) is based on the isotopic generalization of the associative algebra of operators on a Hilbert space; and (3) admits as a classical limit the recently achieved Birkhoffian generalization of the Hamiltonian Mechanics. We first review the Hadronic-isotopic covering of Heisenberg's representation with particular reference to the generalization of: Heisenberg's equations; canonical commutation rules; canonical quantization; Heisenberg's uncertainty principle; Planck's constant; Galilei's relativity; and the representation theory. A possible, single, unifying postulate for the covering theory is introduced. We then pass to the construction of the corresponding generalization of Schroedinger's representation. For this purpose, we first construct the Birkhoffian generalization of the Hamilton-Jacobi theory for local non-Hamiltonian systems. We then show that the latter theory admits a consistent quantization into a generalization of Schroedinger's equations. Some essential properties of the emerging hadronic generalization of the atomic wave theory, are presented. In particular, we identify the general solution of the hadronic wave packets under the most general possible local Hamiltonian and non-Hamiltonian forces, which has no counterpart in the Atomic Mechanics.},

doi = {},

journal = {Hadronic J.; (United States)},

number = ,

volume = 5:4,

place = {United States},

year = {Tue Jun 01 00:00:00 EDT 1982},

month = {Tue Jun 01 00:00:00 EDT 1982}

}