Use of the density function in physics

Click For Summary

Discussion Overview

The discussion revolves around the application of density functions in the context of continuous groups within physics, particularly how these mathematical concepts can be utilized in physical theories or models. Participants are exploring the theoretical implications and seeking examples to clarify the concepts presented.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant introduces the idea of using a density function for an invariant measure when summing over group elements, suggesting potential applications in physics.
  • Several participants express the need for more specific information and examples to understand the initial claim better.
  • Another participant suggests that the discussion relates to Group Theory and its connection to Hilbert spaces, indicating that these areas are significant in physics.
  • A request is made for examples or calculations from the original mathematical text to illustrate the concepts being discussed.

Areas of Agreement / Disagreement

Participants generally agree that more information and examples are necessary to clarify the initial question. However, there is no consensus on specific applications or examples related to the use of density functions in physics.

Contextual Notes

Limitations include a lack of specific examples or calculations from the referenced mathematical text, which may hinder a deeper understanding of the concepts discussed.

kent davidge
Messages
931
Reaction score
56
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?
 
Physics news on Phys.org
Your are very vague. Don't be lazy, give some more information and/or examples.
 
  • Like
Likes   Reactions: jim mcnamara
martinbn said:
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.
 
Ok, but it is not clear what you are talking about. Can you at least tell us which book?
 
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.
 

Similar threads

Undergrad Density fluctuations and the color of the sky
  • · Replies 0 ·
Replies
0
Views
2K
Graduate QFT for the gifted amateur: translation of prob. density
  • · Replies 23 ·
Replies
23
Views
3K
Undergrad Density Operators of Pure States
  • · Replies 21 ·
Replies
21
Views
3K
Probability density for observable with continuous Spectrum
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Born rule as an axiom or as a theorem?
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad The initial density of an object and its compression into a black hole
  • · Replies 17 ·
Replies
17
Views
6K
Undergrad The electron as a smeared charge density
  • · Replies 13 ·
Replies
13
Views
3K
Undergrad Probability Density Function of the Product of Independent Variables
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Obtain the Density of State using the Green function
  • · Replies 12 ·
Replies
12
Views
3K
Insights Lie Algebras: A Walkthrough - The Basics
  • · Replies 8 ·
Replies
8
Views
3K