# Status of the mathematical and physical studies on the Lie-admissible formulations on July 1979, with particular reference to the strong interactions

## Abstract

The first part of the paper presents a reveiw of the mathematical studies on Lie-admissible algebras conducted (a) via the theory of abstract algebras; (b) via a Lie-admissible generalization of Lie's theory, and (c) via a symplectic-admissible generalization of the symplectic geometry. The second part presents a review of the physical applications in: Newtonian mechanics; classical field theory; classical statistical mechanics; quantum mechanics; quantum field theory; and quantum statistical mechanics; with specific applications, such as: Bose-expansion theory in nuclear physics; renormalization theory; broken unitary symmetries for the classification of hadrons; etc. In the third part a number of open physical and mathematical problems are outlined.

- Authors:

- Publication Date:

- Research Org.:
- Harvard Univ., Cambridge, MA

- OSTI Identifier:
- 6760598

- Alternate Identifier(s):
- OSTI ID: 6760598

- Report Number(s):
- CONF-7908175-

Journal ID: CODEN: HAJOD

- Resource Type:
- Conference

- Resource Relation:
- Journal Name: Hadronic J.; (United States); Journal Volume: 2:6; Conference: 2. workshop on Lie-admissible formulations, Cambridge, MA, USA, 1 Aug 1979

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; LIE GROUPS; ALGEBRA; STRONG INTERACTIONS; CLASSICAL MECHANICS; FIELD THEORIES; GEOMETRY; HADRONS; NUCLEAR PHYSICS; QUANTUM MECHANICS; RENORMALIZATION; REVIEWS; STATISTICAL MECHANICS; SYMMETRY BREAKING; USES; BASIC INTERACTIONS; DOCUMENT TYPES; ELEMENTARY PARTICLES; INTERACTIONS; MATHEMATICS; MECHANICS; PHYSICS; SYMMETRY GROUPS 645204* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- Strong Interactions & Properties; 658000 -- Mathematical Physics-- (-1987); 645400 -- High Energy Physics-- Field Theory; 657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics

### Citation Formats

```
Santilli, R.M.
```*Status of the mathematical and physical studies on the Lie-admissible formulations on July 1979, with particular reference to the strong interactions*. United States: N. p., 1979.
Web.

```
Santilli, R.M.
```*Status of the mathematical and physical studies on the Lie-admissible formulations on July 1979, with particular reference to the strong interactions*. United States.

```
Santilli, R.M. Sat .
"Status of the mathematical and physical studies on the Lie-admissible formulations on July 1979, with particular reference to the strong interactions". United States.
doi:.
```

```
@article{osti_6760598,
```

title = {Status of the mathematical and physical studies on the Lie-admissible formulations on July 1979, with particular reference to the strong interactions},

author = {Santilli, R.M.},

abstractNote = {The first part of the paper presents a reveiw of the mathematical studies on Lie-admissible algebras conducted (a) via the theory of abstract algebras; (b) via a Lie-admissible generalization of Lie's theory, and (c) via a symplectic-admissible generalization of the symplectic geometry. The second part presents a review of the physical applications in: Newtonian mechanics; classical field theory; classical statistical mechanics; quantum mechanics; quantum field theory; and quantum statistical mechanics; with specific applications, such as: Bose-expansion theory in nuclear physics; renormalization theory; broken unitary symmetries for the classification of hadrons; etc. In the third part a number of open physical and mathematical problems are outlined.},

doi = {},

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

number = ,

volume = 2:6,

place = {United States},

year = {Sat Dec 01 00:00:00 EST 1979},

month = {Sat Dec 01 00:00:00 EST 1979}

}