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**Local quantum physics and beyond.**
*(English)*
Zbl 0843.46052

Araki, Huzihiro (ed.) et al., Quantum and non-commutative analysis. Past, present and future perspectives. Proceedings of the international Oji seminar on quantum analysis, Kyoto, Japan, June 25-29, 1992 and the symposium on non-commutative analysis, Kyoto, Japan, June 29-July 2, 1992 dedicated to Prof. Huzihiro Araki on the occasion of his 60th birthday. Dordrecht: Kluwer Academic Publishers. Math. Phys. Stud. 16, 3-10 (1993).

Summary: Local quantum physics concerns the synthesis of the principle of locality on the level of special relativity with quantum theory. The frame of the theory, including its physical interpretation, may be characterized by a net of algebras of local observables satisfying a few general principles. This offers a concise language and an efficient tool for the study of the anatomy of the theory and its qualitative physical consequences. The most pertinent results for physics are:

(i) particle structure and collision theory,

(ii) the theory of charge structure, exchange symmetry, global gauge groups,

(iii) characterization of thermal equilibrium, its relation to the mathematical theory of modular automorphisms, to stability and passivity and the rôle of the chemical potentials,

(iv) spontaneous breaking of symmetries..

There are many results on the mathematical structure and internal consistency, some of which will be mentioned. Some outstanding open problems in each of the areas (i) to (iv) will be pointed out. For a future theory – which includes the lessons from general relativity – rather radical changes of the frame are needed. We shall discuss a few hints in this context.

For the entire collection see [Zbl 0833.00043].

(i) particle structure and collision theory,

(ii) the theory of charge structure, exchange symmetry, global gauge groups,

(iii) characterization of thermal equilibrium, its relation to the mathematical theory of modular automorphisms, to stability and passivity and the rôle of the chemical potentials,

(iv) spontaneous breaking of symmetries..

There are many results on the mathematical structure and internal consistency, some of which will be mentioned. Some outstanding open problems in each of the areas (i) to (iv) will be pointed out. For a future theory – which includes the lessons from general relativity – rather radical changes of the frame are needed. We shall discuss a few hints in this context.

For the entire collection see [Zbl 0833.00043].

### MSC:

46L60 | Applications of selfadjoint operator algebras to physics |

46N50 | Applications of functional analysis in quantum physics |

81T20 | Quantum field theory on curved space or space-time backgrounds |