What is the Wedge Product in Theoretical Physics?

Marin
Messages
192
Reaction score
0
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! :)
 
Physics news on Phys.org
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.
 

Thread 'Trouble understanding an online solution to an exercise in Dummit & Foote'

##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Thread 'Decomposition into irreps of compact Lie group'

When decomposing a representation ##\rho## of a finite group ##G## into irreducible representations, we can find the number of times the representation contains a particular irrep ##\rho_0## through the character inner product $$ \langle \chi, \chi_0\rangle = \frac{1}{|G|} \sum_{g\in G} \chi(g) \chi_0(g)^*$$ where ##\chi## and ##\chi_0## are the characters of ##\rho## and ##\rho_0##, respectively. Since all group elements in the same conjugacy class have the same characters, this may be...
View full post »

Similar threads

Is Wedge Product the Same as Cross Product?
Replies
6
Views
5K
Can one do mathematical physics and theoretical physics at the same time?
Replies
8
Views
2K
Other Need advice regarding choosing my master's research project in theoretical physics and applied maths
Replies
6
Views
2K
What sparked my passion for theoretical physics?
Replies
1
Views
344
Calculus Should I read Spivak's Calculus as an undergrad in theoretical physics?
Replies
2
Views
4K
What is the focus of my research in theoretical physics?
Replies
1
Views
390
Other Potential Effects of Recent AI Developments on Physics?
Replies
15
Views
2K
I can't find a PhD in theoretical physics after 6 months of trying
Replies
37
Views
6K
Studying Sophomore Undergrad Feeling Hopeless
Replies
9
Views
1K
I How Can Wedge Products Be Used in Differential Geometry?
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top