Abstract:
We consider the infinite series in Wick powers of a generalized free field that are convergent under smoothing with analytic test functions and realize a nonlocal extension of the Borchers equivalence classes. The nonlocal fields to which the Wick power series converge are proved to be asymptotically commuting. This property serves as a natural generalization of the relative locality of the Wick polynomials. The proposed proof is based on exploiting the analytic properties of the vacuum expectation values in the x space and applying the Cauchy–Poincaré theorem.
Citation:
A. G. Smirnov, M. A. Soloviev, “Wick Power Series Converging to Nonlocal Fields”, TMF, 127:2 (2001), 268–283; Theoret. and Math. Phys., 127:2 (2001), 632–645
This publication is cited in the following 5 articles:
Soloviev M.A., “Reconstruction in quantum field theory with a fundamental length”, J Math Phys, 51:9 (2010), 093520
Soloviev, MA, “Quantum field theory with a fundamental length: A general mathematical framework”, Journal of Mathematical Physics, 50:12 (2009), 123519
Albeverio, S, “HIDA DISTRIBUTION CONSTRUCTION OF NON-GAUSSIAN REFLECTION POSITIVE GENERALIZED RANDOM FIELDS”, Infinite Dimensional Analysis Quantum Probability and Related Topics, 12:1 (2009), 21
Soloviev, MA, “Failure of microcausality in noncommutative field theories”, Physical Review D, 77:12 (2008), 125013
Soloviev, MA, “Noncommutativity and theta-locality”, Journal of Physics A-Mathematical and Theoretical, 40:48 (2007), 14593