How are renormalizability and locality connected?

[jakob1111]

In his paper Quantum Field Theory: renormalization and the renormalization group Zinn-Justin states:

Low energy physics does not depend on all the details of the microscopic model because some RG has an IR fixed point or at least a low dimension fixed surface. Of course at this stage the next more fundamental theory may still assume the form of a local quantum field theory, but ultimately locality will have to be abandoned.

Where does the connection between the fact that low energy physics does not depend on all details of the microscopic model and that "ultimately locality will have to be abandoned" come from?

 

[AndyW]

The connection between the fact that low energy physics does not depend on all details of the microscopic model and the idea that "ultimately locality will have to be abandoned" comes from the concept of renormalization and the renormalization group (RG) in quantum field theory.

Renormalization is a mathematical technique used to remove infinities that arise in quantum field theory calculations. It allows us to understand the behavior of a physical system at different energy scales, from the smallest scales (microscopic) to the largest scales (macroscopic). The RG is a method used to study how physical systems change as we move from one energy scale to another.

In quantum field theory, we know that at high energies, the interactions between particles are described by a local quantum field theory. However, as we move to lower energies, the effects of these interactions become less important and the physics can be described by an effective theory with fewer degrees of freedom. This effective theory is often referred to as a low-energy theory.

The idea that "ultimately locality will have to be abandoned" comes from the observation that at extremely high energies, the concept of locality breaks down. This is because at these energies, the effects of quantum fluctuations become significant and the spacetime structure itself becomes uncertain. This means that the concept of a local quantum field theory, which assumes a fixed spacetime structure, is no longer applicable.

The connection between the fact that low energy physics does not depend on all details of the microscopic model and the abandonment of locality is that the renormalization process allows us to understand how the low-energy behavior of a physical system is independent of the details of the underlying microscopic theory. This suggests that there may be a more fundamental theory at high energies that has a different description of spacetime and locality, and that this theory may ultimately replace our current understanding of physics.