Download Communications in Mathematical Physics - Volume 225 by M. Aizenman (Chief Editor) PDF

By M. Aizenman (Chief Editor)

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Mat. Fis. Milano 65, 9–22 (1995) 20. : Stabilization of statistical solutions of the Klein–Gordon equation. Mosc. Univ. Math. Bull. 41, no. 2, 72–75 (1986) 21. : Stabilisation of Statistical Solutions of Klein–Gordon Equations. PhD Thesis, Moscow State University, 1986 22. : Partial Differential Equations. Moscow: Mir, 1978 23. : Decay and scattering of solutions of a nonlinear relativistic wave equation. Comm. Pure Appl. Math. 25, 1–31 (1972) 24. : Limit Theorems of Probability Theory. Oxford: Clarendon Press, 1995 25.

5 in order to show the relevance of the algebraic operation • in the computation of n-point functions. Let us then first summarize the results of Sect. 4. We have constructed n-point functions Pn [F1 , . . , Fn ] which depend uniquely on the n − 3 conformal moduli of the insertion points τi of the functions Fi . In particular, the one-point function P1 , which we shall call P in the sequel, is a generalization of the trace, Tr, and is given by: P1 [F ] = P [F ] = Tr (F ) − 2i Habc Tr Xa X b X c F .

M, and m + 1, . . , n, respectively) lim Pn [F1 , . . , Fn ] ετi , τj ε→0 = Pn−m+1 Om [F1 , . . , Fm ] (τi ) , Fm+1 , . . , Fn 0, τj . (39) Nonassociative Star Product Deformations 55 For example, one can show that P [(F • G) • H ] = P [F • (G • H )] . This follows from applying (39) and recalling the fact that the three-point function P3 [F, G, H ] (τ1 , τ2 , τ3 ) is independent of the moduli. If one considers the two limits τ2 → τ1 and τ2 → τ3 , and uses factorization with O2 ∼ •, one quickly arrives at the above result.

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