## Abstract

We carry out a quantization of a classical relativistic particle dynamics, that is, a theory of N spinless point masses in mutual interaction. It is of Hamiltonian form, manifestly covariant, and involves N first-class constraints. In the resultant relativistic quantum dynamics these constraints are N invariant simultaneous "Schrödinger equations" involving N invariant time parameters (a=1,N). Since the interaction functions (relativistic "potential energies") can have a complicated momentum dependence, these equations do not become second-order equations in the representation pa=-iqa. The integrability condition ensures the existence of a unitary operator that "propagates" the system from one point to another in N-dimensional space independent of the path. Møller operators and the scattering operator are defined and the limits a'± are studied. It is demonstrated how the separability of the interaction functions leads to a factorization of the S matrix (cluster decomposition).

Original language | English |
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Pages (from-to) | 1528-1542 |

Number of pages | 15 |

Journal | Physical Review D |

Volume | 24 |

Issue number | 6 |

DOIs | |

State | Published - 1981 |

Externally published | Yes |