feynlag.dirac.dirac_conjugate

feynlag.dirac.dirac_conjugate(gamma)

Dirac-conjugate Γ̄ = γ⁰ Γ† γ⁰ of a Bilinear middle slot Γ.

Used to build the hermitian conjugate of a fermion sandwich: (ψ̄₁ Γ ψ₂)^† = ψ̄₂ Γ̄ ψ₁. Covers exactly the Γ structures this library builds (diracI/1, diracPL, diracPR, bare DiracGamma(mu), and DiracGamma(mu)*diracPL/diracPR):

• γ⁰ is hermitian and γ^{μ†} = γ⁰γ^μγ⁰ (standard Dirac representation with the (+,−,−,−) metric), so a bare γ^μ is self-conjugate: γ̄^μ = γ^μ.

• P_L/P_R are hermitian but anticommute with γ⁰ (since γ₅ anticommutes with every γ^μ), so γ⁰P_Lγ⁰ = P_R and vice versa: bare chiral projectors swap.

• Combined with a gamma matrix the two effects cancel — γ^μP_L = P_Rγ^μ — so a vector current γ^μP_L/γ^μP_R is self-conjugate (the standard “V−A ports to V−A” result: the h.c. of ν̄γ^μP_Lℓ is ℓ̄γ^μP_Lν, same Γ, bar/field swapped).

Raises:

NotImplementedError – for any other Γ structure (no silent guess).