Discussion Overview
The discussion revolves around a problem encountered while solving an example related to differential forms, specifically focusing on discrepancies in results derived from two different sources. Participants explore the implications of factors such as ##1/p!## and the treatment of anti-symmetry in the context of forms and vectors.
Discussion Character
- Debate/contested
- Technical explanation
- Conceptual clarification
Main Points Raised
- One participant notes a divergence in results when applying the definition of a p-form from one source compared to another, leading to confusion about the correct answer.
- Another participant identifies that the discrepancy arises from the presence of a factor of ##1/p!## in one pdf but not in the other, resulting in an answer that is off by a factor of ##1/2##.
- There is a suggestion that the need for a factor of ##1/2## may depend on whether one is considering the anti-symmetric part of the expression or a different formulation involving two forms.
- A later reply indicates that the original poster may have overlooked summing over all components, which contributed to their incorrect result.
- One participant expresses frustration regarding the clarity of the original poster's questions and suggests a lack of foundational understanding in the subject matter.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the correct approach or resolution to the problem. There are multiple competing views regarding the necessity of the factor of ##1/2## and the handling of anti-symmetry in the calculations.
Contextual Notes
Limitations include potential missing assumptions regarding the definitions of forms and the treatment of anti-symmetry, as well as unresolved mathematical steps in the calculations presented by the original poster.
given in this pdf https://www.rose-hulman.edu/~bryan/lottamath/difform.pdf. According to it, the answer is that on the image above. But when I tried to solve this same example by following the expression for ##w## given in this pdf http://www.bose.res.in/~amitabha/diffgeom/chap13.pdf, namely that a p-form ##w## can be written as $$\frac{1}{p!}w_{\mu_1 ... \mu_p}dx^{\mu_1} \wedge \ ... \ \wedge dx^{\mu_p}$$ and that ##w##, in this case, applied to two vectors ##v_{(1)}## and ##v_{(2)}## is ##w_{i j}v_{(1)}^i v_{(2)}^j##, the answer that I'm getting diverges from that given in the other pdf. What is wrong?