Euclidean Quantum Field Theory I Equations for a Scalar Model

Kurt Symanzik

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12) S + g S - a S = xS X XXX X The change in the KS and MM equations is the same as that described for (3. 11), and the discussion of (12) leads in every detail to similar results as were obtained for (1) .
The model (1) stands in the relation described in appendix A to the model given by H = 1/2 V a'^a"'"aa, [a, a''"] = 1 The "n-particle distribution function" is p^(6) = [Tr exp(-6H+6yN)] ^Tr{ (a'*')"a" exp(-3H+3tjN) } where N = a a. The generating function is v\ S (x) = I (nl) x^ (6) = p n n=...o + C Trfexp (-eH+3yN)e^^ e^} which is easily calculated to be -43- S (x) = C' I dz{l-exp[3M+ J BV+izCeV)"""'^]} ''" . Exp{- -| z^+x[-H- exp(-3iJ-l/2?V-iz(3V)-'-'^] "*■} The substitution corresponding to (A. 4), (A. 6) and (A. 7) V = - 6g, x =(1/2) BU, y = -1/2 + a/2 leads, with C ^ 6, for 8 -^ to (3) % -44- Appendlx C. D = 1: The Anharmonic Oscillator For d = 1, (2. 1) becomes (C. L) L = b'''b - in^B"'"B - 1/2 g(B"'"B)^ + a b"^B.
With B = r exp(i(j)), B = r esp(-i(|)) the Hamiltonian becomes (C.

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