What Does the Dirac Delta Function Look Like in Curved Spacetime?

[friend]

Does anyone know what the Dirac delta function would look like in a space with curvature and torsion? The Dirac delta function is a type of distribution. But that distribution might look differently in curved spacetime than in flat spacetime. I wonder what it would look like in curved spacetime. Any help? Thanks.

 

[HallsofIvy]

The Dirac delta function is a distribution as you say. The definition of any function or distribution has nothing to do with "curved" or flat space. Perhaps you mean something else.

 

[friend]

The Dirac delta function is a distribution as you say. The definition of any function or distribution has nothing to do with "curved" or flat space. Perhaps you mean something else.

I suppose that being a distribution really doesn't matter. I was thinking that a distribution might help with visualizing physically on the situation.

Where I am going is that I have seen where the path integral of quantum mechanics is developed from the definition of the Dirac delta functin. This development is in flat spacetime. So I wonder if a similar development can be done in curved spacetime. Any help would be appreciated. Thanks.

 

[Pere Callahan]

Try the book on Path Integrals by Hagen Kleinert. He treats path integrals in spaces with curvature and torsion.

 

[friend]

Try the book on Path Integrals by Hagen Kleinert. He treats path integrals in spaces with curvature and torsion.

Yes, Kleinert has an on-line presentation of this at:

http://www.physik.fu-berlin.de/~kleinert/kleiner_re252/node11.html

I can follow it until about equation 115 where he got and complex exponential for the Jacobian.

 

[Pere Callahan]

I cannot follow Kleinert's presentation at all. I have his book and I once took two courses on path integrals taught by him, but his way of doing things is just too different from mine.
Still the book is a great resource if you're prepared for pages and pages of weird and seemingly unmotivated/unjustified calculations (only my opinion)

 

[friend]

I cannot follow Kleinert's presentation at all. I have his book and I once took two courses on path integrals taught by him, but his way of doing things is just too different from mine.
Still the book is a great resource if you're prepared for pages and pages of weird and seemingly unmotivated/unjustified calculations (only my opinion)

Does he use a lot of differential form notation, etc? Hagen Kleinert's name comes up a lot when researching path integrals in curved spacetime. But I wish there were more agreement that his treatment is acceptable. And it would be nice if there were an expanded version of his derivations for us dummies. As it is, he mentions things like "nonholomorphic" and expects everyone to automatically know what he is talking about when there is not even any reference to it on Wikipedia, etc.