By O.I. Zavialov
`In the reviewer's opinion, this e-book is unquestionably some of the most beneficial monographs on quantum box conception in contemporary years.'
Mathematical Reviews, 91k, 1991
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Additional info for Renormalized Quantum Field Theory
The function Dret(x - y) vanishes if Xo < YO· Therefore, when t = Xo 4 ~ the domain which gives non-zero contribution to the integral lation - ~(x) So the field =_4> (x) + ~(x) other hand, when JDret(x - JDret (x - y)J(y) - J D(x dy becomes smaller and smaller. should asymptotically approach the free one. on the ret the function D (x - y) coincides with D(x - y) Xo > Yo and at asymptotically large t = to 4>(x) + y)j(y) dy in the Yang-Feldman re- Xo 4 ~ the field ~(x) should be close - y)j(y) dy.
In the domain Xo > 0 it coincides with the commutation function D(x). Since 2 ret . r(x) • )~(x) In terms of the current, the causality condition takes the form o 3 . 2. Connection Between Two systems of Axioms Now we sketch the proof that the interpolating field ¢(x) - constructed according to relations (74) and (75) - satisfies the Wightman conditions 1-5. rent J(x) is Hermitean: j+(x) = j(x) . Take the derivative in $ of both sides of the unitarity condition (72): OS+ 6f(XT S + S ® + oS ® 6~ (x) = O.
Ambiguity in the Choice of Chronological Products The coefficient functions of the last three diagrams on Figure I-2, and of the last two diagrams on Figure I-3, contain some powers of the regularized Green function DC(x). Since DC(x) tends to the distribution r r DC(X) when the intermediate regularization is taken away, the very existence of the limiting value (as r ~ 0) is at least not obvious. A simple calculation shows that in this limit the coefficient functions of these diagrams are really divergent.
Renormalized Quantum Field Theory by O.I. Zavialov