# The Integration In Quantum Field Theory

I struggle with integral notation in Quantum Field Theory , I see integrals like d4k/(2pi)^4 , but I dont know how to evaluate it! I think it will be good if I can understand the sign d4k and how to evaluate simple integrals in 4-dimension like in the picture

• See in which reference? Which page? Sep 21, 2017 at 17:32
• Peskin (Introduction to Quantum Field Theory) Sep 21, 2017 at 17:45

It's because you're integrating a multivariate function: The function is defined not on a line (like, for example, the function $f(x) = x^2$), but on a four-dimensional space, like $g(x,y,z,t) = x^2 + y^2 + z^2 - ct^2$.
That little $d^4 k$ is the volume element. Without getting too much into the weeds, this means that you break the entire space you're integrating over down into little four-dimensional cubes of dimensions $dk \times dk \times dk \times dk$, evaluate the function in the center of each of these cubes, and sum the whole thing up. Then you take the limit as $dk \to 0$ and hope the answer converges.