Here it is a simple problem which is giving me an headache, Recall from class that in order to build an invariant out of spinors we had to introduce a somewhat unexpected form for the dual spinor, i.e. ߰ψ = ψ†⋅γ0 Then showing that ߰ is invariant depends on the result that (ei/4⋅σμν⋅ωμν)† ⋅γ0 = γ0⋅e-i/4⋅σμν⋅ωμν Prove this by expanding out the exponential for the first three terms and using the (anti)commutation relations of the gamma matrices. 2. Relevant equations The Metric signature is (-+++) You can read the problem (number 2) by clicking the link below. https://inside.mines.edu/~aflourno/Particle/HW4.pdf 3. The attempt at a solution My issue is that I can't see why there is a - sign in the exponential after transpose/conjugating and moving the gamma matrix. Moving the gamma matrix γ0 to the left cancels the negative sign from conjugating the σ0j in the exponential hence the + sign should not change. Which step am I missing? You can read the solution by clicking the link below. https://inside.mines.edu/~aflourno/Particle/HW4solutions.pdf Thank you for reading and any replies.