Momentum-space integral ($\int d^{d}pf(p)$)

An integral over momentum space. For example, state counting in $d$ spatial dimensions uses a measure proportional to $d^{d}p/(2\pi \hslash {)}^d$, whereas a relativistic Feynman integral commonly uses $d^{d}p/(2\pi {)}^d$ in natural units. The convention and any regulator must be specified. Independent loop momenta supply separate integration variables in a loop Feynman diagram; ultraviolet divergences and infrared divergences can require different regularizations.