A question about causality in physics

Question

The concept of causality lies at the root of all modern physics, e.g. consideration of it lead to special relativity and in quantum field theory it is also fundamental, although you wouldn't be able to tell from most text books. In fact, hardly any even have a single reference to it in their index. With the exceptions of Dirac, Sakurai, and Jackson, I can not find any references anywhere in any of the books I have; not even in Feynman's Lectures. Why is this? Specifically, what troubles me is that some particles are described by nonlinear wave equations, such as the Higgs particle; how can you be sure that such equations don't have solutions that violate the causality principle?

Answer 1

For most of science, it's taken for granted and not necessary to mention.  It's the same reason they don't mention the details of arithmetic.  Causality violation is contemplated with certain hypothetical structures with 'closed timelike curves' in general relativity.  I would conclude from this that it's not expected to happen in any real physical situation.

One problem with the equations with which we express our theories is that they allow an incredible number of solutions which violate all manner of things.  Renormalization is one approach to avoiding solutions with infinities.

Answer 2

The thing to check is that the correlation function between any two points in space/time is zero if they are separated by a space-like interval.  This is the case in QED (and I think the entire standard model).  If a theory is not well-behaved, that is a good indicator that it is, at best, an effective theory that gets superceded at some energy levels.

I don't have my library in front of me, so I can't give you a reference, but I'm pretty sure Peskin & Schroder do the calculation.  Another book to check is Anthony Zee's field theory book.  Between those two books, you have most of what you need in QFT.  Reading Zee is good to learn ABOUT field theory.  P&S is the best book to learn to DO field theory.