- #1

- 31

- 0

, 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 homomorphism) then we have

##D(T_{μν})=(D(x_μ)D(x_ν))+(D(x_ν)D(x_μ))##

,or

Tμν

transform as

##(\cfrac{1}{2},\cfrac{1}{2})⊕(\cfrac{1}{2},\cfrac{1}{2})=(1⊕0)⊕(1⊕0)=1⊕1⊕0⊕0##

But we have trace of two components ##0##

. On wikipedia write that traceless symmetric tensors transform on representation ##(1,1)=2⊕0##

.

Where is error?