Recent content by filip97

  1. filip97

    A Decoupled spin vectors A and B

    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...
  2. filip97

    A Product of Representations of Lorentz Group

    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...
  3. filip97

    A Transformation law of the energy momentum tensor

    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...
  4. filip97

    A Transformation law of the energy momentum tensor

    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...
  5. filip97

    Carnot function -- How can I prove f(t2,t1)=f(t2−t1,0)

    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...
  6. filip97

    Carnot function -- How can I prove f(t2,t1)=f(t2−t1,0)

    No, this is my intuitive thinking about empirical temperature scales because temperature is variable of interval type(levels of measurement).
  7. filip97

    Carnot function -- How can I prove f(t2,t1)=f(t2−t1,0)

    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.
  8. filip97

    Sincov's functional equation

    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)## ??
  9. filip97

    A Huygens Principle - how to explain this with classical language?

    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)##...
  10. filip97

    Group Action of C3v on 2x2 Complex Matrices

    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}\\...
  11. filip97

    Group Action of C3v on 2x2 Complex Matrices

    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}...
  12. filip97

    A Why Spinors Are Irreducible if Gamma-Traceless: Explained

    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...
  13. filip97

    A How to construct a spin-3/2 theory from the ground up

    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...
  14. filip97

    A Why Spinors Are Irreducible if Gamma-Traceless: Explained

    Ok, it is clearer. But why 1/2 component carried with divergence of Dirac spinor ? (This removing ghosts ?)
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