Download Communications In Mathematical Physics - Volume 273 by M. Aizenman (Chief Editor) PDF

By M. Aizenman (Chief Editor)

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Causal independence and the energy level density of states in local quantum field theory. Commun. Math. Phys. 106, 321 (1986) 8. : Some exact results for N -point massive Feynman integrals. J. Math. Phys 32, 1052– 1060 (1991) 36 S. Hollands 9. : A Compact expression for the scalar one loop four point function. Nucl. Phys. B 367, 637 (1991) 10. : Radiation Damping In: A Gravitational Field. Annals Phys. 9, 220 (1960) 11. : A local (perturbative) construction of observables in gauge theories: the example of QED.

To get the desired representer C IT provided by Theorem 2, we again use the definitions Eqs. (90) and (91) corresponding to our choice δ = 0. Thus, we must compose C I with ψT (ε), take a Mellin transform, and extract the residue at 0, −i, −2i in the complex z-plane. To do the Mellin transform (90), we perform first a short distance expansion of the integrand in (114) around x3 , using the corresponding expansions [10] of the quantities σ, vn present in H, ri . This short distance expansion will lead to a sum of terms, each of which is a curvature polynomial at x3 , times a Minkowski distribution in ξ1 , ξ2 and the Riemannian normal coordinates of y.

N−1 ). (104) = a,b However, since this holds for all metrics, Eq. (95) follows. 32 S. Hollands Using the definition of W a just given, item 4) immediately follows from the fact that C I has an expansion of the form (89), and that C IT ∼δ,T C I . 5. Example We now illustrate our general method for computing the OPE in curved spacetime by an example. Let us summarize again the steps needed in this computation. 1. Fix a desired accuracy, δ, of the OPE, and determine as in Theorem 1. 2. Identify the retarded products in Eq.

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