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

  1. #1 Question on notation in "differential forms and connections" 
    Senior Member
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    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
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    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 ....
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    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.
    The most important thing to keep in mind is that you don't know everything and nobody else does either.
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  2. #2  
    Administrator Markus Hanke's Avatar
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    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.
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