• Support PF! Buy your school textbooks, materials and every day products Here!

Symplectic notation

  • Thread starter aaaa202
  • Start date
  • #1
1,170
3
The attached is a section of the derivation of canonical transformation from the symplectic formulation. I tend to get very confused by the subscripts i and j. For me they both run from 1 to 2n and can be used interchangeably. But of course that is not the case since equation (9.53) on the attached picture specifically instructs you to transpose the matrix described by (9.51). Can someone explain what is wrong with just changing the indices in a pedagogic way - an example would be lovely too.
 

Attachments

Answers and Replies

  • #2
gabbagabbahey
Homework Helper
Gold Member
5,002
6
The attached is a section of the derivation of canonical transformation from the symplectic formulation. I tend to get very confused by the subscripts i and j. For me they both run from 1 to 2n and can be used interchangeably. But of course that is not the case since equation (9.53) on the attached picture specifically instructs you to transpose the matrix described by (9.51). Can someone explain what is wrong with just changing the indices in a pedagogic way - an example would be lovely too.
I'm not sure exactly what you are asking. Can you give a specific example of the equation where you think you can't transpose i & j?
 
  • #3
191
8
Well, the indices do run from 1 to 2n, and there is no deep physics hidden in calling the indices i and j, specifically. Could be any letter or symbol, really. However, the order is important.

Changing the order of the indices for a matrix actually is the same as taking the transpose. Think of i as a row index and j as a column index. Just make up some old matrix and try it out.
 
  • #4
1,170
3
perhaps I wasn't clear enough. My frustation is actually due to not being able to see why the order of i and j is important - it's probably trivial but I don't see it.
 
  • #5
gabbagabbahey
Homework Helper
Gold Member
5,002
6
My frustation is actually due to not being able to see why the order of i and j is important
In what term/equation?
 

Related Threads on Symplectic notation

  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
7
Views
1K
Replies
1
Views
856
Replies
2
Views
6K
  • Last Post
Replies
6
Views
669
  • Last Post
2
Replies
28
Views
7K
Replies
1
Views
551
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
4
Views
5K
  • Last Post
Replies
2
Views
1K
Top