Green Function approach is more physical?

[robousy]

Hey folks,

I'm not really sure which forum to put this question in but I figured this was probably the best as it deals with issues of regularization.

I'm reading Miltons 'The Casimir Effect'. In chapter one he derives the Casimir energy for a massless scalar field by employing dimensional regularization. He then goes on in the next section to derive the same result using a Green function approach which he claims is "...a physical and rigorous approach".

From this sentence it appears that he favors the Green function approach over Dim reg. Is this a general 'feeling' in the physics community? That Green functions are somehow superior to Dim Reg? Also, why should this be 'physical'?

I hope this question makes sense.

Rich

 

[CompuChip]

I do have the feeling that Greens functions are more physical than dimensional regularization. That is, I can very well imagine the physical meaning of a propagator, but I don't really have intuition for $4 + \epsilon$ dimensions with $\epsilon \in \mathbb{C}$.
I can't remember seeing Greens functions being used for regularization though.

 

[sir-pinski]

Hi Rich,

The Green function approach is often considered to be more physical because it is based on the concept of a propagator, which describes how a field evolves in time and space. This approach is more closely related to the physical processes that are happening in a system, such as the interaction between particles.

On the other hand, dimensional regularization is a mathematical technique used to remove divergences in calculations, but it may not have a direct physical interpretation. It is a useful tool for obtaining finite results, but it may not provide as much insight into the underlying physics as the Green function approach.

In general, the choice of approach may depend on the specific problem at hand and personal preferences of the physicist. Some may find the Green function approach more intuitive and physically meaningful, while others may prefer the mathematical simplicity of dimensional regularization. Both approaches have their advantages and limitations, and it is important to understand when and how to use them appropriately.

I hope this helps to answer your question. Happy studying!