## Abstract

We solve the relativistic two-body bound state problem with O(3,1) invariant direct action potentials in the framework of a manifestly covariant canonical quantum theory. The solutions are representations of the Lorentz group in Gel'fand's principal series. The spectra and wave functions have the correct nonrelativistic limit. For the relativistic oscillator, we obtain a positive definite spectrum without subsidiary conditions or ghosts.

Original language | English |
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Pages (from-to) | 123-128 |

Number of pages | 6 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 128 |

Issue number | 3-4 |

DOIs | |

State | Published - 28 Mar 1988 |

Externally published | Yes |

### Bibliographical note

Funding Information:* Supported in part by the US—Israel Binational Science Foundation, Jerusalem, Israel. ~ A preliminary version ofthis work was reported in “Proceedingsofthe Workshop on Constraint’s theory and relativistic dynamics” (World Scientific, Singapore, 1987). It was alsopresentedby L.P. Horwitz at the Workshop on Lorentztransformations and spacetime geometry, University of Maryland, College Park, Maryland, 27—30 May, 1987.

### Funding

* Supported in part by the US—Israel Binational Science Foundation, Jerusalem, Israel. ~ A preliminary version ofthis work was reported in “Proceedingsofthe Workshop on Constraint’s theory and relativistic dynamics” (World Scientific, Singapore, 1987). It was alsopresentedby L.P. Horwitz at the Workshop on Lorentztransformations and spacetime geometry, University of Maryland, College Park, Maryland, 27—30 May, 1987.

Funders | Funder number |
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US-Israel Binational Science Foundation |