Recent content by ssamsymn

okay, I am thinking on it. thank you.

They can be, yes, but I also need to know their boundary term in terms of volume element. Is there a rule to generalise any kind of fractal object to d-dimension? Because I may try to apply, I remember I found a fractal with boundary term with dimension less than 3. thank you very much.

For my work, I need to check my calculations with an example of a fractal object. I searched on the internet, there are some examples of fractals with their hausdorff dimensions, but no boundary terms related. Also found some 1-d examples, but I need d>3 dimensional objects since my calculations...

Correction: I was trying to ask is there a matrix which includes all the "four vector information" in itself and we can act it on salt \vec{v} 's as (c, \vec{v} ) (not a four velocity but still) Maybe it seems meaningless but I was confused with all the γ factors because I couldn't find...

I didn't encounter the matrix anywhere, they always use the addition of the velocities, so I wasn't sure. I think I should construct on my own that matrix. Thank you

Can Lorentz Transformation be applied directly to a four velocity vector? I mean let v_{α} be a four velocity vector. Is there a form of Lorentz tfm matrix such that: v^{'}_{α} = \Lambda^{β}_{α}v_{β} ?

n_x , n_y , n_z are your quantum numbers, they describe your state, when you solve the Schr. Eqn. for ψ's, which are sinusoidal functions as mentioned below, n_x,y,z will appear in the energy values.

Thank you very much. Yes I rewrited everything with g lower index. I am not sure about that symmetry: R^{αβ}_{αβ}= - R^{βα}_{βα} But I feel I am close to it. Thank you again.

Ok here is my thoughts, I try to stay away from the connection coefficients. So, I don't write the R tensors in form of \Gamma's. So I am trying: R= g^{αβ} R_{αβ} = g^{αβ} R^{c}_{αcβ} = g^{αβ} g^{αb} R_{bαcβ} but now I can't have the R_{αβαβ} form. Since it is 2-d, I put α=1 and...

I am asked to show it by the symmetries of the Riemann tensor by the way.

Where should I start from to show that curvature scalar (RiemannScalar) is 2\frac{R_1212}{det (g_μ√)} ?

Yes, thank you very much. I thought that my function such as 2n+1/2 should be valid for any real number but I think the remaining non-integers from half integers are included in f(x)=x otherwise case. thank you

thank you very much. I am trying to figure out Cantor's method. I think I should construct disjoint one countable and one uncountable sets and their union should be real numbers.

thank you very much. I don't fully understant how I can pick real numbers with n indices. I am not familiar with the notation, I need a valid function to show this map is one to one and onto. my real numbers set is non countable, non integers set is also.I thought the function can be...

I came up with some idea but not sure. I can only map all the real numbers to (0,1) interval. And then try to enlarge it to (n,n+1) where n goes to infinity. Is it valid?