×

zbMATH — the first resource for mathematics

Postulates of quantum field theory. (English) Zbl 0125.21903
Summary: We give a survey of the postulates which provide the framework of quantum field theory. Particular attention is given to the lesser known ones, namely, completeness requirements and “primitive causality.” Three field theoretical models are analyzed. These examples show that “primitive causality” is not a consequence of the commonly used postulates (which include the “causal commutation relations”). “Asymptotic completeness” is not assured by any of the other postulates listed. In the formulation and analysis the concept of operator rings associated with space-time regions is used extensively.

MSC:
81T05 Axiomatic quantum field theory; operator algebras
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1063/1.1724220 · Zbl 0132.43902 · doi:10.1063/1.1724220
[2] Licht A. L., Bull. Am. Phys. Soc. 6 pp 59– (1961)
[3] DOI: 10.1103/PhysRev.101.860 · Zbl 0074.22902 · doi:10.1103/PhysRev.101.860
[4] Haag R., Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd. 29 (12) (1955)
[5] DOI: 10.1007/BF02731765 · Zbl 0066.44006 · doi:10.1007/BF02731765
[6] DOI: 10.1103/PhysRev.112.669 · Zbl 0085.43602 · doi:10.1103/PhysRev.112.669
[7] DOI: 10.1007/BF02859796 · Zbl 0082.42104 · doi:10.1007/BF02859796
[8] DOI: 10.1103/PhysRev.111.995 · Zbl 0093.44407 · doi:10.1103/PhysRev.111.995
[9] DOI: 10.1007/BF02856049 · Zbl 0077.42403 · doi:10.1007/BF02856049
[10] DOI: 10.1007/BF02856049 · Zbl 0077.42403 · doi:10.1007/BF02856049
[11] DOI: 10.1007/BF02733373 · Zbl 0111.43204 · doi:10.1007/BF02733373
[12] DOI: 10.2307/1968823 · Zbl 0023.13303 · doi:10.2307/1968823
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.