"Henrique de Andrade Gomes" <gomes.ha@gmail.com> wrote in message

news:mt2.1-11092-1228438182@argon.astro.indiana.edu...

.. . .

>

> I haven't read the whole paper with care, but your main equation

> stating that the curvature is the anti-symmetrized gauge exterior

> derivative of the connection seems wrong. For the gauge exterior

> derivative is already anti-symmetric on space-time indices, hence

> anti-

> symmetrization does not affect it. I.e. DA= Antisymmetrized (DA).

> Note that DA is NOT equal to F (even though the variation of F is

> equal to D of the variation of A). Basically, there is a 1/2 on the

> commutator of the connection forms that is not there in DA.

> Cheers,

> Henrique

> Jay R. Yablon wrote:

>> I have completed the "exercise" I have been working on the past few

>> weeks, on integrating-by-parts, the action in Yang-Mills Theory, and

>> posted this at:

>>

>> http://jayryablon.files.wordpress.co...s-paper-20.pdf

>>

>> I would like feedback on whether I have done this exercise correctly,

>> and to facilitate the learning that I am trying to do by way of this

>> exercise, of course would like to know if there are any erroneous

>> calculations and / or statements. . . .
It would help if you used an equation number rather than refer to "your

main equation."

But from what I can parse out of what you are saying, you are correct

that F=DA includes the antisymmetry in the spacetime indexes. But when

you "unpack" this to show explicit spacetime indexes, the antisymmetry

returns (see, e.g., my (2.1) and discussion in section 2). I believe I

have addressed this in the footnote at the bottom of page 2 including

the factor of 1/2. What I should have put in also for clarity, which I

will in the next draft, is that the differentiation of any p-form H is

specified by:

dH=(1/p!)d_vH_u1 u2 u3...dx^v dx^u1 dx^u2 dx^u3...

with dx^u dx^v = -dx^v dx^u.

The differentials are anticommuting Grassman variables (sometime wedge

products are shown but they just clutter up the page) and they naturally

carry the asymmetries you speak of, while the 1/p! =1/2 for p=2 is the

source of the 1/2 factor you speak of for the two-form F.

All of this, I believe, is correctly used in the "exercise" paper.

Cheers,

Jay.