Let we have ##J_i \in{J_1,J_2,J_3}## ,and ##K_i \in{K_1,K_2,K_3}##, rotation and boost generators respectable .
##A_i=\cfrac{1}{2}(J_i+iK_i)##, and
##[A_i,A_j]=i\epsilon_{ijk}A_k##
##[K_i,K_j]=-i\epsilon_{ijk}J_k##
##[J_i,K_j]=-i\epsilon_{ijk}K_k##
How proof that ##(m,n)A_i=J^{(m)}_i\otimes...
How to prove that direct product of two rep of Lorentz group ##(m,n)⊗(a,b)=(m⊗a,n⊗b)## ?
Let ##J\in {{J_1,J_2,J_3}}##
Then we have :
##[(m,n)⊗(a,b)](J)=(m,n)(J)I_{(a,b)}+I_{(m,n)}⊗(a,b)(J)=##
##=I_m⊗J_n⊗I_a⊗I_b+J_m⊗I_n⊗I_a⊗I_b+I_m⊗I_n⊗J_a⊗I_b+I_m⊗I_n⊗I_a⊗J_b##
and...
Ok, this is partialy cleared.
##(1/2,1/2)⊗(1/2,1/2)=1/2⊗1/2⊗1/2⊗1/2=(1\oplus 0)⊗(1\oplus 0)=##
##=(1⊗1)\oplus(0\otimes 0)=2\oplus 0\oplus0##, and on Wikipedia write that
traceless symmetric second rank tensor transformed as ##(1,1)=2\oplus 0\neq 2\oplus 0\oplus0##. We have traces in both (in...
We have 4-tensor of second rank. For example energy-momentum tensor ##T_μν##
, which is symmetric and traceless. Then
##T_{μν}=x_μx_ν+x_νx_μ##
where ##x_μ##
is 4-vector. Every 4- vector transform under Lorentz transform as (12,12). If we act on ## T_{μν}##
, by representation( with...
I was reading Thermodynamics by Enrico Fermi first they give this function ##\frac{Q_2}{Q_1}=f(t_2,t_1)=\frac{g(t_2)}{g(t_1)}##, where ##g## is monotone increasing function. Idea is if we have scales of temperature ##r,s## (monotone increasing), but and their inverses is also scales of...
If we have that quotient of heats ##Q_2/Q_1=f(t_2,t_1)##, where ##t_1,t_2## are emirical temperatures. Is this function satisfies :
##f(t_2,t_1)=f(t_2-t_1,0)##
I try prove it with Taylor series of two variables, but i can't prove anything.
I read Aczel book "Lectures of functional equations an their applications".
On page 223. (Sincov's equation) is equation :
##F(x,y)+F(y,z)=F(x,z)##
and general solution of this
##F(x,y)=g(x)−g(y)##
, but how I prove that this function satisfies conditions
##F(x,y)=F(0,y−x)##
??
I was read this article(https://engineering.purdue.edu/wcchew/ece604f19/Lecture%20Notes/Lect31.pdf).
I was read this paper about Huygens' principle(https://engineering.purdue.edu/wcchew/ece604f19/Lecture%20Notes/Lect31.pdf)
Main idea of Huygens' principle is how wave function ##ψ(r)##...
Problem is biger. How we find representation ##D## ?
I assumed that ##D##is ##2##x##2## matrices. ##D(C_3)A=E(C_3)AE(C_3^{-1})=\begin{bmatrix}
D_{11} & D_{12}\\...
Group action on ##2##x##2## complex matrices of group ##C_{3v}## for all matrices from ##C^{22}##, for all ##g## from ##C_{3v}## is given by:
##D(g)A=E(g)AE(g^{-1}), A=\begin{bmatrix}...
filip97
Can we raising and lowering indices of mwtric spinor with 2-contravariant or 2-covariant with metric tensor ? I think that we can do this with sigma(mu,nu) this write in Sexl Urbantke book of group representation. I was post this question because don't clear ho we contract Dirac equation...
Can we raising and lowering indices of mwtric spinor with 2-contravariant or 2-covariant with metric tensor ? I think that we can do this with sigma(mu,nu) this write in Sexl Urbantke book of group representation. I was post this question because don't clear ho we contract Dirac equation with...