Index gymnastics of electromagnetism quantities

Click For Summary

Discussion Overview

The discussion revolves around the appropriate use of metrics for raising and lowering indices of electromagnetic quantities, specifically in the context of a non-Minkowski metric. Participants explore the implications of using either the curved spacetime metric or the Minkowski metric in this process.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether to use the curved spacetime metric g or the Minkowski metric n when raising or lowering indices of the electromagnetic tensor F and vector potential A in a non-Minkowski setting.
  • Another participant asserts that the Minkowski metric is merely an approximation to the actual curved-spacetime metric.
  • A further response clarifies that coordinate indices should be raised and lowered using the curved metric g, while tetrad indices should be handled with the Minkowski metric η, regardless of the spacetime being curved or flat.

Areas of Agreement / Disagreement

The discussion contains competing views regarding the appropriate metric to use for raising and lowering indices, indicating that there is no consensus on the matter.

Contextual Notes

Participants have not fully resolved the implications of using different metrics for various types of indices, and there may be assumptions regarding the definitions of the metrics and their applicability in specific contexts.

coleman123
Messages
17
Reaction score
0
This bothers me, and the question is simple:

If am working with a non-minkowski metric g, when raising or lowering indexes of electromagnetism quantities, for example the electromagnetic tensor F, or the vector potential A, should I use my curved spacetime metric g or the minkowski metric n?
 
Last edited:
Physics news on Phys.org
The actual metric. The Minkowski metric is at best an approximation to the curved-spacetime metric.
 
  • Like
Likes   Reactions: 1 person
Thanks!
 
coleman123 said:
If am working with a non-minkowski metric g, when raising or lowering indexes of electromagnetism quantities, for example the electromagnetic tensor F, or the vector potential A, should I use my curved spacetime metric g or the minkowski metric n?

Coordinate indices are raised and lowered with ##g## but tetrad indices are raised and lowered using ##\eta##, be it curved space-time or flat space-time.
 
  • Like
Likes   Reactions: 1 person

Similar threads

  • · Replies 9 ·
Replies
9
Views
885
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 26 ·
Replies
26
Views
2K
  • · Replies 13 ·
Replies
13
Views
2K
  • · Replies 10 ·
Replies
10
Views
4K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K