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__how do I count practically the grading of an object (it is defined as it's ghost number plus form degree).__

Do I read this from the Lagrangian?

Second question: Where can I find the full Lagrangian with terms for antighosts?

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- Thread starter christodouloum
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- #1

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Do I read this from the Lagrangian?

Second question: Where can I find the full Lagrangian with terms for antighosts?

- #2

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What is the paper? This will be easier to answer if I can see what you're reading.

- #3

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Hi, thanks for the interest! The paper is Physics Letters 196B, 142 (1987) by L.Baulieu and M.Bellon.

In trying to reproduce the calculations I see that I am definitely missing something. I believe I do not understand how to use the graded commutation and derivation correctly.

Specifically I do not understand:

1. how in equation (11) the plus and minus components of d from (8a) mix with those of lambda. The calculation should be straightforward from (8a) , (10) and the zero torsion condition after (11).

2. what exactly is meant by__symmetrical product of forms__ which is mentioned in (7). I can see that in (7) it means to change the index signs in the right parenthesis before doing the multiplication.

3. if the spin connection omega is even or odd graded. From calculations I did I see that it must probably be graded even but I do not understand how I can tell from my equations.

Any help much appreciated since very few people can help me with this

In trying to reproduce the calculations I see that I am definitely missing something. I believe I do not understand how to use the graded commutation and derivation correctly.

Specifically I do not understand:

1. how in equation (11) the plus and minus components of d from (8a) mix with those of lambda. The calculation should be straightforward from (8a) , (10) and the zero torsion condition after (11).

2. what exactly is meant by

3. if the spin connection omega is even or odd graded. From calculations I did I see that it must probably be graded even but I do not understand how I can tell from my equations.

Any help much appreciated since very few people can help me with this

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- #6

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For starters

[tex]e^{\pm}[/tex] are the two components of a one-form

[tex]\omega[/tex] is a one form

[tex]\xi^{\alpha}[/tex] are the components of a fermionic vector field, so each one is a fermionic variable

what confuses me is the zweibein. From what I knew so far I thought it should be a basis of vector fields and being the components of a one form here confuses me.

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But I don't understand the complex coordinates. I have the usual beginner's trouble with thinking of [tex]z[/tex] and [tex]\bar{z}[/tex] as independent variables, but OK, maybe if I think about it for long enough, I'll get used to it. However, what I'm really not getting is the association between the frame vectors and the complex coordinates. Is [tex]e^+[/tex] supposed to depend only on [tex]z[/tex], and [tex]e^-[/tex] only on [tex]\bar{z}[/tex]?

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