REDUCTION OF OPERATOR RINGS AND THE IRREDUCIBILITY AXIOM IN QUANTUM FIELD THEORY
The mathematical theory of the reduction of operator rings is used to investigate some structures that can occur in quantum field theory when the postulate that the field operators generate an irreducible ring is relaxed. In particular, it is shown that if a quantum field theory has a commutator that commutes with all field operators it is a direct integral of theories, in each of which the commutator is a scalar. If in addition the theory satisfies the postulates of Lorentz covariance, existence of an invariant vacuum, and mass and energy spectra, then the the theory is a direct integral of generalized free field theories, whenever the unitary representation of the Lorentz group can be constructed in terms of functions of the field operators and every state can be constructed by applying field operators on the vacuum. It is also shown that the latter two assumptions together with the requirement of a unique invariant vacuum state are sufficient to prove that the ring genei ated by the field operators is irreducible. In other words, under these conditions the irreducibility postulater is redundant. (auth)
- Research Organization:
- Univ. of Rochester, N.Y.
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-16-032195
- OSTI ID:
- 4784807
- Report Number(s):
- NYO-10032
- Journal Information:
- J. Math. Phys., Vol. Vol: 3; Other Information: NYO-10032. Orig. Receipt Date: 31-DEC-62
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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