A Modefied Model of Euclidean Quantum Field Theory

Cover A Modefied Model of Euclidean Quantum Field Theory
A Modefied Model of Euclidean Quantum Field Theory
Kurt Symanzik
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) < fh^)^)- I 3gGQ(0)(h2)]. L:pg(V/) < exp [| (JGJ) ^- I 9g((h^ + G^(0))^) - 1_ /, 3v 1 -. _ o (o)(h?' o 1 - ^g (hp - i 5g G^(0)(hf)]. Since also differentiability v/ith respect to a in the sense of (111. 17b) is easily shown, NJa, Jv is an entire analytic functional of order at most four. To see this more explicitly, we also prove directly the absolute convergence of the Volterra series for a'G^'a < 00, v;hich implies that |hj is bounded. The sum of the absolute values of the terms of the series is bounded by 1 ] I rt oT lo r -jc. 69 + I 3g|((H'^)2h2)| + g|((H-^)h^)| + Jg|(h^)| + 1 ^_ r, /^^//. T, ^2. + g 3g G^^^COllH^)"^) + 3g G^(0)|((H-^)h)l + + I 3g 0^(0)|(h2)| + (JH^)] L^3(^» Writing g = g-, ^ + gg + g^i ^2 2 5 ^ *^' ^® '^^^^ B||, j; < exp[J gl(h^)! + I 3g G^(0)|(h^)|]- ' J exj) [- I (Vv) - ^ (gg + gj) ((H;/)^) + + (g"\^ + I 3g)((H-^)2ihr) + I 5g G^(0)((H^)^) + + g( |{H;;/)i(|h^! +3G^(0)|h|)) + {JHi»], i;pg(7;.

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