Discussion Overview
The discussion revolves around the diffeomorphism invariance of the metric determinant, specifically the expression sqrt(-g) and its powers. Participants explore whether these quantities are invariant under diffeomorphisms, with implications for their use in action formulations in general relativity.
Discussion Character
- Exploratory, Technical explanation, Debate/contested
Main Points Raised
- One participant asserts that sqrt(-g) is diffeomorphism-invariant and questions if all powers of this expression are also invariant.
- Another participant suggests that using the term "scalar" is more straightforward than "diffeomorphism-invariant," stating that any function of a scalar is also a scalar.
- A later reply expresses gratitude for the clarification and proposes a specific action involving sqrt(-g) and a scalar field, seeking confirmation of its validity.
- Another participant challenges the notion that the metric determinant is a scalar, using the example of volume elements in different coordinate systems to illustrate their point.
- One participant acknowledges the correction regarding the validity of the proposed action, indicating that the second term does not work as initially thought.
- A participant admits to an error in their earlier post, indicating a lack of attention at the time of writing.
Areas of Agreement / Disagreement
The discussion contains multiple competing views regarding the invariance of the metric determinant and its powers, with no consensus reached on the validity of the proposed action involving these quantities.
Contextual Notes
Participants express uncertainty about the definitions and implications of diffeomorphism invariance and scalar quantities, highlighting the complexity of the topic.