What is the Wedge Product in Theoretical Physics?

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Discussion Overview

The discussion revolves around the concept of the "wedge product" as mentioned in a theoretical physics course. Participants explore its definition, applications, and contexts, including its relation to vectors and tensors, as well as its use in mathematical analysis.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on the wedge product after hearing it mentioned in class, indicating a lack of understanding.
  • Another participant asks for the context in which the wedge product was mentioned, questioning whether it relates to vectors or tensors.
  • A participant describes the wedge product as a generalization of the vector product.
  • It is suggested that the wedge product can be viewed as a dot product for functions rather than vectors, with a reference to Melnikov analysis as a relevant application.
  • Another participant recommends reading Spivak's "Calculus on Manifolds," explaining that the wedge product is a skew symmetric multiplication used in computing determinants.
  • There is a question raised about whether the meaning of the wedge product differs in Melnikov analysis compared to its geometric interpretation, indicating a potential misunderstanding or differing definitions.

Areas of Agreement / Disagreement

Participants express differing views on the definition and applications of the wedge product, with no consensus reached on its meaning across different contexts.

Contextual Notes

Some participants reference specific mathematical texts and concepts, but there are unresolved questions about the definitions and applications of the wedge product in various fields.

Marin
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Hi all!

The prof for "theoretical methods in physics" mentioned last week the term "wedge product" but it all remained very unclear to me. I read about it in Wikipedia, but couldn`t catch it at all, cause I`m doing in the first semester now.

Does anyone know where I could find it well explained?

Thanks in advance! :)
 
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In which context was it mentioned? Did it have to do with vectors? Or with tensors?
 
it´s was given as a generalisation of the vector product
 
Marin said:
Hi all!

The prof for "theoretical methods in physics" mentioned last week the term "wedge product" but it all remained very unclear to me. I read about it in Wikipedia, but couldn`t catch it at all, cause I`m doing in the first semester now.

Does anyone know where I could find it well explained?

Thanks in advance! :)

It's a dot product, but for functions rather than for vectors, it might help if you read upon melnikov analysis, a rather useful tool to analyse bifurcation boundaries on the parameter space, it involves the wedge product in its definition.
 
read spivak, calculus on manifolds, i think chapter 4. it is a skew symmetric multiplication, used to make determinants more routinely computational. i.e. the determinant of a matrix is essentially the wedge product of its rows. the wedge product of two n vectors, is a vector with n choose 2 entries, namely the 2by2 submatrices of the corresponding 2 by n matrix,..etc...

the wedge product of three n vectors is: guess what? oh there is also a variational version, wherein one takes the wedge product of vector fields and covector fields, etc...
 
TheIsingGuy said:
It's a dot product, but for functions rather than for vectors, it might help if you read upon melnikov analysis, a rather useful tool to analyse bifurcation boundaries on the parameter space, it involves the wedge product in its definition.

wait what? Is the meaning of wedge product different in melinov analysis as compared to geometry? ... This certainly isn't the meaning in geometry.
 

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