The math is real.

All details of the analysis have a physical meaning and should be interpretable for the physicist.

If there was some detail in a mathematical expression – any factor, any exponentiation, addition or whatever, that detail has a specific physical meaning. If it didn’t matter, there wouldn’t be any reason for it to be there, and you are using an analysis with superfluous detail. If it has to be there to get the answer that matches experiment, then it has meaning…

Sometimes I will hear that one thing or another is “just a mathematical thing”, but that is clearly not so. I think sometimes we give up on doing physics and just start doing math, but if we really are physicists we can’t give up on understanding our equations. Shankar has already said very similar things.