- #1
Nusc
- 760
- 2
Landau and Lifshitz, second volume - Classical Theory of Fields, page 7
$$e_mu,nu,alpha,beta e^alpha, beta, gamma, sigma = -2 ( delta^gamma_mu * delta^sigma_nu delta delta^sigma_mu * delta^gamma_nu )
$$
If for example I calculate the following:
$$
e^0,1_alpha,beta e^alpha,beta_0,1 = e_0123 e^2301 + e_0132 e^3201
= 1(+1) +(-1)(-1) = +2$$
If we use LL:
$$-2(delta^0_0 delta^1_1 - delta^0_1 delta^1_0) = -2$$
and one can do that for
##e^1,0_alpha,beta e^alpha,beta_0,1## and you get the opposite result
Same with
##e^0,1_alpha,beta e^alpha,beta_1,0## and you get the opposite result
I don't think LL is correct.
I have been told that this relation can be proved using group theory, in particular, methods for SO(4)
I don't think it's true but I wanted to know if anyone here could do it since I don't know group theory.
$$e_mu,nu,alpha,beta e^alpha, beta, gamma, sigma = -2 ( delta^gamma_mu * delta^sigma_nu delta delta^sigma_mu * delta^gamma_nu )
$$
If for example I calculate the following:
$$
e^0,1_alpha,beta e^alpha,beta_0,1 = e_0123 e^2301 + e_0132 e^3201
= 1(+1) +(-1)(-1) = +2$$
If we use LL:
$$-2(delta^0_0 delta^1_1 - delta^0_1 delta^1_0) = -2$$
and one can do that for
##e^1,0_alpha,beta e^alpha,beta_0,1## and you get the opposite result
Same with
##e^0,1_alpha,beta e^alpha,beta_1,0## and you get the opposite result
I don't think LL is correct.
I have been told that this relation can be proved using group theory, in particular, methods for SO(4)
I don't think it's true but I wanted to know if anyone here could do it since I don't know group theory.
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