Mathematical Quantum Field Theory - Spacetime - Comments

[Urs Schreiber]

Greg Bernhardt submitted a new PF Insights post

Mathematical Quantum Field Theory - Spacetime

Continue reading the Original PF Insights Post.

 

[jedishrfu]

Thanks for writing this excellent article.

 

[Greg Bernhardt]

17 more parts to enjoy coming soon! :)

 

[dextercioby]

A minor note: Urs, I imagine you being more of a geometer than an analyst, so I would say: Relativistic field theory takes place on spacetime. ("on" in the exact sense of fiber bundle theory, in which the Minkowski spacetime - or a curved version of it - is the basis manifold of the fiber bundles which accommodate matter fields and gauge fields, thus, technically, one has fields "living" in their own spaces, not in spacetime.

Another note is that the metric tensor on the generic spacetime $\eta$ is nowhere explicitely defined as diag (-++...+) and the benefit of using it compared to the "West Coast" version diag (+--..-).

 

[strangerep]

Typo in proof of example 2.23: "hatv".

 

[Urs Schreiber]

Typo in proof of example 2.23: "hatv".

Thanks! Fixed now.

 

[Urs Schreiber]

A minor note: Urs, I imagine you being more of a geometer than an analyst, so I would say: Relativistic field theory takes place on spacetime.

Okay, I changed it. But I wasn't meaning to be speaking with any mathematical perspective at this point, but instead to first say something intuitive. I suppose we all feel that we live "in" spacetime, not "on" it. No?

But anyway, I should not be using parenthetical remarks in an expositional paragraph. So I changed it to "on".

Another note is that the metric tensor on the generic spacetime $\eta$ is nowhere explicitely defined as diag (-++...+) and the benefit of using it compared to the "West Coast" version diag (+--..-).

I did say what the norm-square is supposed to be, but you are right that I never made explicit the induced Minkowski inner product. I have expanded now def. 2.15 to make it more explicit. Then I also added a remark 2.16 on how the metric encodes length and what this means for units of length (this will be needed later in chapter 5 to understand why mass terms come with the Compton wavelength.)

Thanks for the feedback!