- #1

Basu23

**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

Then showing that ߰ is invariant depends on the result that (e

Prove this by expanding out the exponential for the first three terms and using the (anti)commutation relations of the gamma matrices.

2. Homework Equations

The Metric signature is (-+++)

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

^{†}⋅γ^{0}Then showing that ߰ is invariant depends on the result that (e

^{i/4⋅σμν⋅ωμν})^{†}⋅γ^{0}= γ^{0}⋅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. Homework 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

## 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 γ

^{0}to the left cancels the negative sign from conjugating the σ

^{0j}in the exponential hence the + sign should not change.

Which step am I missing?

You can read the solution by clicking the link below.

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.[/B]