Towards an axiomatic formulation of noncommutative quantum field theory. II. (English) Zbl 1472.81247
Summary: Classical results of the axiomatic quantum field theory – irreducibility of the set of field operators, Reeh and Schlieder’s theorems and generalized Haag’s theorem are proven in \(SO(1, 1)\) invariant quantum field theory, of which an important example is noncommutative quantum field theory. In \(SO(1, 3)\) invariant theory new consequences of generalized Haag’s theorem are obtained. It has been proven that the equality of four-point Wightman functions in two theories leads to the equality of elastic scattering amplitudes and thus the total cross-sections in these theories.
For Part I, see [the first author et al., J. Math. Phys. 52, No. 3, 032303, 13 p. (2011; Zbl 1315.81096)].
For Part I, see [the first author et al., J. Math. Phys. 52, No. 3, 032303, 13 p. (2011; Zbl 1315.81096)].
MSC:
| 81T75 | Noncommutative geometry methods in quantum field theory |
| 81T05 | Axiomatic quantum field theory; operator algebras |
| 53D55 | Deformation quantization, star products |
| 14D21 | Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) |
| 81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |
| 46L05 | General theory of \(C^*\)-algebras |
| 81U05 | \(2\)-body potential quantum scattering theory |
Citations:
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