# Generalization of Heisenberg uncertainty principle for strong interactions

## Abstract

We propose a unified form of possible generalizations of Heisenberg uncertainty principle for strong interactions, which is based on the product of the envelope of the dynamical equations representing wave packets under conditions of mutual overlapping and nonlocal non-Hamiltonian forces. For conventional associative products of operators, we recover the conventional Heisenberg relations for particles under long range electromagnetic interactions and no appreciable wave overlapping. For nonassociative Lie-admissible products of operators we have (a) a number of generalizations of Heisenberg's equations of increasing algebraic complexity; (b) the capability of representing a correspondingly progressive increase of conditions of wave overlapping and nonlocal, non-Hamiltonian forces; and (c) a corresponding, rather inevitable sequence of generalizations of Heisenberg uncertainty relations. All these possibilities are expressed in a unified way by postulating generalized uncertainty relations whereby the product of operators is that of the envelope of the dynamical equations. For conditions of minimal wave overlapping under strong interactions, such as in the nuclear structure, we expect a very small nonlocal non-Hamiltonian component of the force and a minimal departure from Heisenberg principle. For progressive increase of wave overlappings, such as in the structure of hadrons, or in the structure of stars undergoing gravitational collapse, we expectmore »

- Authors:

- Publication Date:

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

- OSTI Identifier:
- 6648552

- Alternate Identifier(s):
- OSTI ID: 6648552

- Report Number(s):
- CONF-8008162-

Journal ID: CODEN: HAJOD

- DOE Contract Number:
- AC02-80ER10651

- Resource Type:
- Conference

- Resource Relation:
- Journal Name: Hadronic J.; (United States); Journal Volume: 4:3; Conference: 3. workshop on Lie-admissible formulations, Boston, MA, USA, 4 Aug 1980

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; STRONG INTERACTIONS; UNCERTAINTY PRINCIPLE; HADRONS; LIE GROUPS; QUANTUM OPERATORS; STARS; WAVE EQUATIONS; WAVE PACKETS; BASIC INTERACTIONS; DIFFERENTIAL EQUATIONS; ELEMENTARY PARTICLES; EQUATIONS; INTERACTIONS; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS; SYMMETRY GROUPS 645204* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- Strong Interactions & Properties; 657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics

### Citation Formats

```
Santilli, R.M.
```*Generalization of Heisenberg uncertainty principle for strong interactions*. United States: N. p., 1981.
Web.

```
Santilli, R.M.
```*Generalization of Heisenberg uncertainty principle for strong interactions*. United States.

```
Santilli, R.M. Wed .
"Generalization of Heisenberg uncertainty principle for strong interactions". United States.
doi:.
```

```
@article{osti_6648552,
```

title = {Generalization of Heisenberg uncertainty principle for strong interactions},

author = {Santilli, R.M.},

abstractNote = {We propose a unified form of possible generalizations of Heisenberg uncertainty principle for strong interactions, which is based on the product of the envelope of the dynamical equations representing wave packets under conditions of mutual overlapping and nonlocal non-Hamiltonian forces. For conventional associative products of operators, we recover the conventional Heisenberg relations for particles under long range electromagnetic interactions and no appreciable wave overlapping. For nonassociative Lie-admissible products of operators we have (a) a number of generalizations of Heisenberg's equations of increasing algebraic complexity; (b) the capability of representing a correspondingly progressive increase of conditions of wave overlapping and nonlocal, non-Hamiltonian forces; and (c) a corresponding, rather inevitable sequence of generalizations of Heisenberg uncertainty relations. All these possibilities are expressed in a unified way by postulating generalized uncertainty relations whereby the product of operators is that of the envelope of the dynamical equations. For conditions of minimal wave overlapping under strong interactions, such as in the nuclear structure, we expect a very small nonlocal non-Hamiltonian component of the force and a minimal departure from Heisenberg principle. For progressive increase of wave overlappings, such as in the structure of hadrons, or in the structure of stars undergoing gravitational collapse, we expect a corresponding progressive replacement of Heisenberg principle with more general principles. The problem of the experimental resolution of the exact or only approximate validity of Heisenberg principle under strong interactions is considered for a more detailed treatment in a separate paper.},

doi = {},

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

number = ,

volume = 4:3,

place = {United States},

year = {Wed Apr 01 00:00:00 EST 1981},

month = {Wed Apr 01 00:00:00 EST 1981}

}