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Added file with operations in the fundamental of SU(2)

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Alberto Ramos 2021-10-06 09:54:54 +02:00
parent 3f8ba58848
commit 97e46a538c
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src/Groups/FundamentalSU2.jl Normal file
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###
### "THE BEER-WARE LICENSE":
### Alberto Ramos wrote this file. As long as you retain this
### notice you can do whatever you want with this stuff. If we meet some
### day, and you think this stuff is worth it, you can buy me a beer in
### return. <alberto.ramos@cern.ch>
###
### file: FundamentalSU2.jl
### created: Tue Oct 5 10:31:09 2021
###
SU2fund(a::T, b::T) where T <: AbstractFloat = SU2fund{T}(complex(a), complex(b))
dag(a::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(conj(b.t1), -b.t2)
norm(a::SU2fund{T}) where T <: AbstractFloat = sqrt((abs2(a.t1) + abs2(a.t2))/2)
norm2(a::SU2fund{T}) where T <: AbstractFloat = (abs2(a.t1) + abs2(a.t2))/2
tr(g::SU2fund{T}) where T <: AbstractFloat = complex(real(g.t1), 0.0)
dot(g1::SU2fund{T},g2::SU2fund{T}) where T <: AbstractFloat = real(conj(g1.t1)*g2.t1+g1.t2*conj(g2.t2))
Base.:*(a::SU2{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(a.t1*b.t1-a.t2*conj(b.t2),a.t1*b.t2+a.t2*conj(b.t1))
Base.:/(a::SU2fund{T},b::SU2{T}) where T <: AbstractFloat = SU2fund{T}(a.t1*conj(b.t1)+a.t2*conj(b.t2),-a.t1*b.t2+a.t2*b.t1)
Base.:\(a::SU2{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(conj(a.t1)*b.t1+a.t2*conj(b.t2),conj(a.t1)*b.t2-a.t2*conj(b.t1))
"""
\(phi::SU2fund{T},u::SU2{T})
This operation has to be understood as (phi^+ u)
"""
Base.:\(a::SU2fund{T},b::SU2{T}) where T <: AbstractFloat = SU2fund{T}(conj(a.t1)*b.t1+a.t2*conj(b.t2),conj(a.t1)*b.t2-a.t2*conj(b.t1))