Friday, January 15, 2016

soft question - Why is the dx right next to the integral sign in QFT literature?


I've noticed that in QFT literature, integrals are usually written as dx f(x) instead of f(x)dx. Why?



Answer



IMHO, the notation badxf(x) is much cleaner than baf(x)dx, because the integration variable (x) and its associated integral range (ba) are kept together. This is particularly important in lengthy and multi-dimensional integrals. Consider Υpq(k)=0dxβ(x)0dy10dt0dηdκf(x,y,t)ei[kxx+kyy]ηtΘpq(κ,ηk)

as opposed to Υpq(k)=0β(x)0100f(x,y,t)ei[kxx+kyy]ηtΘpq(κ,ηk)dκdηdtdydx.


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