The starting point for Feynman’s trick of ‘differentiating under the integral sign,’ mentioned at the end of Chap. 1, is Leibniz’s formula. If we have the integral ααααI(α)=∫a(α)b(α)f(x,α) dxwhere α is the so-called parameter of the integral (not the dummy variabl...
The trick of inverting Feynman’s trick by integrating the integral of interest to make a double integral and then reversing the order of integration is introduced. The Cauchy-Schlӧmilch transformation is stated, derived, and used to evaluate some interesting variations of the probability integral...
Note also that for increasing orders of , each integral operator gets a di¤erent dummy integration variable. But that's just the beginning. To see the e¤ect of the interaction on particle creation and annihilation, we'll have to take even more di¤erentials as required by the n-point ...
2.3. Integration on supermanifolds 7 2.4. Divisors 8 3. Supermanifolds from graphs 8 3.1. Feynman’s trick and Schwinger parameters 8 3.2. The case of Grassmann variables 10 3.3. Graphs with fermionic legs 12 3.4. Graph supermanifolds 16 3.5. Examples from Feynman graphs 17 3.6. The univers...