Hi all. I have a simple question on methodology for counting graphs explicitely. I am trying to find all trees of the complete graph K_5. I know that the answer is 5^(5-2)=125 and that each should have only four of the ten edges. I am trying to understand how I would draw them down by hand...
Firstly after some studying the fermionic operators are Z2-graded (even-odd rank for a differential form) differential operators, and s here was a left such derivative. That means that depending on the grade of the two forms a,b in s(ab) the sign is decided as + if a is of even rank and - if...
Do you think we can start from identifying what mathematical objects are the things that are here?
For starters
e^{\pm} are the two components of a one-form
\omega is a one form
\xi^{\alpha} are the components of a fermionic vector field, so each one is a fermionic variable
what...
I am happy to see that you are interested! My main problem too is indeed intuition as you have well identified. In the meantime I have made progress with the algebra and solved some of my questions. I have to harry up with the calculations since I am doing this as part of a project. When you are...
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...
Hello I am new in string theory and I am wrestling with a paper in Beltrami parametrization. Although I have spend time studying ghosts, brs symmetry etc my knowledge in differential geometry is very limited (for string theory). My question is how do I count practically the grading of an object...
in varying an action like Polyakov's action with respect to the metric on the world sheet we have to consider the variation of the square root of the determinant. I have not found how to express the variation of the determinant of the metric. From reverse engineering I found that
\delta(h)=2...
ok I am getting really confused.
A is grassmann (fermionic field). So A^2=0. For a derivation operator acting "normally"
d(A^2)=dA A + A dA =0 thus dA A=-A dA which is a property of grassmann numbers (see http://www.mathematics.thetangentbundle.net/wiki/Grassmann_number" )
but if I...
Thanks, so let me see if I got it right. When I wrote
s^2 \Omega = \xi^\beta \xi^\alpha_{,\beta} \Omega_{,\alpha} + \xi^\alpha \xi^\beta_{,\alpha} \Omega_{,\beta} +\xi^\alpha \xi^\beta \Omega_{,\beta \alpha}
the two plus signs would be minus signs. So the first two terms cancel out...
bigubau please bare with me I do not want spoon feeding.
This is my first time with grassmann numbers but so far it goes like this
s \Omega = \xi^\alpha \Omega_{,\alpha}
s^2 \Omega = s (\xi^\alpha) \Omega_{,\alpha} + \xi^\alpha (s \Omega )_{,\alpha}
I am assuming here that the partial...
Hi, I am learning what is going on with ghost fields in string theory. Does anyone know where I can find the basics for the brs (brst) operator? Specifically I need help with the following calculation. I have for the action of the brs operator on a ghost field and on the metric
s \xi^\alpha =...
TheTankEngine you should keep in mind that we have absolutely no idea what an electron actually is. We have several frameworks to think of what it does wrt other stuff. If you want a better understanding you should think of all these theories as models that stick because they work. What I tried...
how about going polar in this sense (x,y)=( r cos(u),r sin(u) )|-> ( r' cos (u') /r'^2 , rsin(u')/ r'^2 ) and solving for r',u' ? This gives you two equations write them both down.