New answers tagged regularization
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The $i \epsilon$ part is introduced in order to define in what direction you go around the pole at $k^2 = m^2$. The choice of $+ i \epsilon$ corresponds to going above the pole at $k_0 = -\sqrt{\mathbf k^2 + m^2}$ and below the pole at $k_0 = +\sqrt{\mathbf k^2 + m^2}$ in the complex plane (where $\mathbf k$ is the trhee-vector part of $k_\mu$).
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Firstly, if I'm correct in understanding your question, you are asking why one needs to regulate field theories since we renormalize them anyway?
Assuming this, here's my understanding:
Quantum field theory in general has several divergences, which we must deal with. We get around such divergences by dealing with renormalized quantities. But how does one ...
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