Calculating Determinants of Operators

[jarowit]

how to calculate determinant of $$\frac{\partial}{\partial t} \delta (t-\tau)$$?

 

[weejee]

Maybe this came from a path integral? I think you should use the discretized version of this operator.

 

[jarowit]

Maybe this came from a path integral? I think you should use the discretized version of this operator.

exactly, the source of this determinant is a path integral

is it possible that this det is a constant which can be absorbed by normalization ??

 

[jensa]

Depending on what you are calculating it is possible that it can be included in normalization. Are you looking to integrate out certain degrees of freedom to get an effective generating functional to evaluate correlation functions then I would say yes, it can be absorbed into normalization. On the other hand if you are calculating fluctuations around some classical path then this factor becomes important. The value of the determinant also depends on your boundary conditions, are you using periodic boundary condtions (thermal field theory)?

I think you may find some useful calculations H. Kleinert "Path integrals in quantum mechanics, Statistics, Polymer Physics and Financial markets" It is a great source of detailed calculations of this kind of stuff.

You can download up to 5 chapters from his homepage:

http://users.physik.fu-berlin.de/~kleinert/kleinert/?p=booklist