Use of the density function in physics

[kent davidge]

For continuos groups one introduces a density function for an invariant measure when summing over the group elements.

I learned a little about these concepts in a pure mathematical book.

I was thinking about their utility in physics.. I know they probably do.. What physical areas could these concepts be used in?

 

[martinbn]

Your are very vague. Don't be lazy, give some more information and/or examples.

 

[kent davidge]

Your are very vague. Don't be lazy, give some more information and/or examples.

but I really don't know of any examples, that's why I'm asking for them.

 

[martinbn]

Ok, but it is not clear what you are talking about. Can you at least tell us which book?

 

[RPinPA]

I think you're asking a question about Group Theory and I suspect that there may be an answer to your question in connection with Hilbert spaces, which are very important in physics.

An example of a group you've been given, and an invariant measure, and what a "sum over the group elements" entails, would be useful. Surely some example was given in your textbook. Surely they actually did a calculation when they introduced these things. So show us that calculation.