# Thread: Question on notation in "differential forms and connections"

1. Can you please take a look at something for me? I'm having trouble understanding the notation in the book Differential Forms and Connections by R.W.R. Darling that a friend lent me. Here is what I don't understand so far; from page 2 section 1.1.2
--------------------------------------------
The description of for any 2 <= p <= n follows the same lines; is the set of formal sums

(1.7)

of “generators” , where each coefficient is indexed by a multi-index ); elements of are called “p-vectors,” and are subject to the rules ....
--------------------------------------------
For those of you not familiar with the subject is the wedge product (or exterior product) of the vectors u and v where u and v are vectors in the n-dimensional vector space V. I don’t understand what the functions are, mean or represent. What are they?

Note: The L's are supposed to be 's but for some reason I can't get the Latex to accept greek subscripts. Does anyone know why this is happening? I.e. what am I doing wrong?

Also I thought that a 3-vector was a regular Cartesian vector, i.e. R = (x, y, z) in R3 and 4-vectors were regular vectors/events X = (ct, x, y, x) in Minkowski spacetime M4. But this definition defines it differently. Is that the case?

Than you.

2. The L(k) aren't functions, they are multi-indices. The a represent a set of coefficients ( probably real numbers ), whereas the u would be generator functions - you'd need p of those for an exterior power of degree p.

 Posting Permissions
 You may not post new threads You may not post replies You may not post attachments You may not edit your posts   BB code is On Smilies are On [IMG] code is On [VIDEO] code is On HTML code is Off Trackbacks are Off Pingbacks are Off Refbacks are On Forum Rules