# Null-plane invariance of Hamiltonian null-plane dynamics.

## Abstract

Relativistic Hamiltonian few-body dynamics [1,2] involves two unitary representations of the Poincare group on the Hilbert space H of physical states, with and without interactions. These two representations, U({Lambda}, a) and U{sub 0}({Lambda},a), coincide for a kinematic subgroup H. The ''Hamiltonians'' are the generators not in the Lie algebra of the kinematic subgroup. The kinematic subgroup of null-plane dynamics leaves the null-plane z {center_dot} x {triple_bond} x{sup 0} + x{sub 3} = 0 invariant. Few-body Hamiltonians satisfying the required commutation relations can be constructed as functions of a mass operator and kinematic quantities. For more than two particles there are nontrivial problems in satisfying cluster separability. [3] Consistency of electro-weak interactions with strong interactions also involves significant problems: Poincare covariance of current operators requires the construction of appropriate interaction currents.

- Authors:

- Publication Date:

- Research Org.:
- Argonne National Lab., IL (US)

- Sponsoring Org.:
- US Department of Energy (US)

- OSTI Identifier:
- 10905

- Report Number(s):
- ANL/PHY/CP-96947

TRN: US0103919

- DOE Contract Number:
- W-31109-ENG-38

- Resource Type:
- Conference

- Resource Relation:
- Conference: 16th European Conference on Few-Body Problems in Physics, Autrans (FR), 06/01/1998--06/06/1998; Other Information: PBD: 29 Jul 1998

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; COMMUTATION RELATIONS; HAMILTONIANS; HILBERT SPACE; POINCARE GROUPS; STRONG INTERACTIONS; MANY-BODY PROBLEM; WEAK INTERACTIONS

### Citation Formats

```
Coester, F.
```*Null-plane invariance of Hamiltonian null-plane dynamics.*. United States: N. p., 1998.
Web.

```
Coester, F.
```*Null-plane invariance of Hamiltonian null-plane dynamics.*. United States.

```
Coester, F. Wed .
"Null-plane invariance of Hamiltonian null-plane dynamics.". United States.
doi:. https://www.osti.gov/servlets/purl/10905.
```

```
@article{osti_10905,
```

title = {Null-plane invariance of Hamiltonian null-plane dynamics.},

author = {Coester, F.},

abstractNote = {Relativistic Hamiltonian few-body dynamics [1,2] involves two unitary representations of the Poincare group on the Hilbert space H of physical states, with and without interactions. These two representations, U({Lambda}, a) and U{sub 0}({Lambda},a), coincide for a kinematic subgroup H. The ''Hamiltonians'' are the generators not in the Lie algebra of the kinematic subgroup. The kinematic subgroup of null-plane dynamics leaves the null-plane z {center_dot} x {triple_bond} x{sup 0} + x{sub 3} = 0 invariant. Few-body Hamiltonians satisfying the required commutation relations can be constructed as functions of a mass operator and kinematic quantities. For more than two particles there are nontrivial problems in satisfying cluster separability. [3] Consistency of electro-weak interactions with strong interactions also involves significant problems: Poincare covariance of current operators requires the construction of appropriate interaction currents.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Wed Jul 29 00:00:00 EDT 1998},

month = {Wed Jul 29 00:00:00 EDT 1998}

}