Renormalization in Minkowski space-time

TL;DR

This paper explores the application of renormalization group methods to four-dimensional scalar theories in Minkowski space-time, highlighting the importance of subtraction point choices and the complexities introduced by mass-shell contributions.

Contribution

It demonstrates how renormalization techniques differ in Minkowski space compared to Euclidean space, emphasizing the significance of subtraction point selection and complex parameter flows.

Findings

Subtraction point choice is more critical in Minkowski space.

Renormalization group flow is more complex due to mass-shell effects.

Parameters become complex, affecting the flow dynamics.

Abstract

The multiplicative and the functional renormalization group methods are applied for the four dimensional scalar theory in Minkowski space-time. It is argued that the appropriate choice of the subtraction point is more important in Minkowski than in Euclidean space-time. The parameters of the cutoff theory, defined by a subtraction point in the quasi-particle domain, are complex due to the mass-shell contributions and the renormalization group flow becomes much more involved than its Euclidean counterpart.