For a rank (0,3) tensor, Aabc, without any constraint, degrees of freedom are 216, a,b,c = 0, ..., 6.
If this tensor is antisymmetric in the first 2 indices, degrees of freedom dicrease to 90.
If it is mixed symmetry, the number of constraint equations are:
\frac{n(n-1)(n-2)}{3!}...
How can I calculate degrees of freedom of a rank (o,3) tensor, Aabc, that is mixed symmetry and antisymmetric in the first 2 indices? By mixed symmetry I mean this:
Aabc+Acab+Abca=0.
Dear Bill_K and Matterwave
First of all, thank you so much for your time and attention. I value it a great deal.
Yes Bill_k, this is what I want to do. To be more precise I'm going to explain what exactly I want:
Consider the action
SM=(1/2k2)\int d^{D}x\sqrt{-g}{R-2\Lambda+\alpha...
Gauss-Bonnet term extrinsic curvature calculations?
In General Relativity if one wants to calculate the field equation with surface term, must use this equation:
S=\frac{1}{16\pi G}\int\sqrt{-g} R d^{4} x+\frac{1}{8\pi G}\int\sqrt{-h} K d^{3} x
The second term is so-called Gibbons-Hawking...
Can the relationship between the quantum mechanical path integral and
classical mechanics be stated as this?
A path integral involves an exponential of the action S.
Dear JustinLevy
Sorry for being late to answer your posts. I value your hard work to obtain this expression a great deal. Thank you very much for your time and care.
Thank you for your time and care, but I need to obtain this:
δR=Rμσ δg+gμσ δg^μσ -∇μ ∇σ δg^μσ
in f(R) gravity:
http://en.wikipedia.org/wiki/F(R)_gravity