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Added basic support for Spinors and fields in fundamental rep.
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Alberto Ramos
parent
1ab51e0727
commit
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6 changed files with 366 additions and 8 deletions
267
src/Spinors/Spinors.jl
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267
src/Spinors/Spinors.jl
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###
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### "THE BEER-WARE LICENSE":
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### Alberto Ramos wrote this file. As long as you retain this
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### notice you can do whatever you want with this stuff. If we meet some
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### day, and you think this stuff is worth it, you can buy me a beer in
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### return. <alberto.ramos@cern.ch>
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###
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### file: Spinor.jl
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### created: Wed Nov 17 13:00:31 2021
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###
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module Spinors
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using ..Groups
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struct Spinor{NS,G}
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s::NTuple{NS,G}
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end
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Base.zero(::Type{Spinor{NS,G}}) where {NS,G} = Spinor{NS,G}(ntuple(i->zero(G), NS))
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"""
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norm2(a::Spinor)
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Returns the norm of a fundamental element. Same result as sqrt(dot(a,a)).
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"""
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@generated function norm2(a::Spinor{NS,G}) where {NS,G}
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sum = :(norm2(a.s[1]))
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for i in 2:NS
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sum = :($sum + norm2(a.s[$i]))
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end
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return :($sum)
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end
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"""
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norm(a::Spinor)
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Returns the norm of a fundamental element. Same result as sqrt(dot(a,a)).
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"""
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norm(a::Spinor{NS,G}) where {NS,G} = sqrt(norm2(a))
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"""
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dot(a::Spinor,b::Spinor)
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Returns the scalar product of two spinors.
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"""
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@generated function dot(a::Spinor{NS,G},b::Spinor{NS,G}) where {NS,G}
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sum = :(dot(a.s[1],b.s[1]))
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for i in 2:NS
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sum = :($sum + norm2(a.s[$i]))
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end
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return :($sum)
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end
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"""
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*(g::SU3{T},b::Spinor)
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Returns ga
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"""
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Base.:*(g::S,b::Spinor{NS,G}) where {S <: Group,NS,G} = Spinor{NS,G}(ntuple(i->g*b.s[i], NS))
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"""
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\(g::SU3{T},b::Spinor{NS,G})
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Returns g^+ a
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"""
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Base.:\(g::S,b::Spinor{NS,G}) where {S <: Group,NS,G} = Spinor{NS,G}(ntuple(i->g\b.s[i], NS))
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Base.:+(a::Spinor{NS,G},b::Spinor{NS,G}) where {NS,G} = Spinor{NS,G}(ntuple(i->a.s[i]+b.s[i], NS))
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Base.:-(a::Spinor{NS,G},b::Spinor{NS,G}) where {NS,G} = Spinor{NS,G}(ntuple(i->a.s[i]-b.s[i], NS))
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Base.:+(a::Spinor{NS,G}) where {NS,G} = a
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Base.:-(a::Spinor{NS,G}) where {NS,G} = Spinor{NS,G}(ntuple(i->-b.s[i], NS))
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imm(a::Spinor{NS,G}) where {NS,G} = Spinor{NS,G}(ntuple(i->imm(b.s[i]), NS))
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mimm(a::Spinor{NS,G}) where {NS,G} = Spinor{NS,G}(ntuple(i->mimm(b.s[i]), NS))
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# Operations with numbers
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Base.:*(a::Spinor{NS,G},b::Number) where {NS,G} = Spinor{NS,G}(ntuple(i->b*a.s[i], NS))
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Base.:*(b::Number,a::Spinor{NS,G}) where {NS,G} = Spinor{NS,G}(ntuple(i->b*a.s[i], NS))
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Base.:/(a::Spinor{NS,G},b::Number) where {NS,G} = Spinor{NS,G}(ntuple(i->a.s[i]/b, NS))
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##
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# Operations specific for Spinors in 4D
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##
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# dummy structs for dispatch:
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# Projectors (1+s\gamma_N)
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struct Pgamma{N,S}
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end
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"""
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pmul(Pgamma{N,S}, a::Spinor)
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Returns (1+s\gamma_N)a.
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"""
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function pmul(::Type{Pgamma{4,1}}, a::Spinor{4,G}) where {NS,G}
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r1 = a.s[1]+a.s[3]
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r2 = a.s[2]+a.s[4]
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return Spinor{4,G}((r1,r2,r1,r2))
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end
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function pmul(::Type{Pgamma{4,-1}}, a::Spinor{4,G}) where {NS,G}
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r1 = a.s[1]-a.s[3]
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r2 = a.s[2]-a.s[4]
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return Spinor{4,G}((r1,r2,-r1,-r2))
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end
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function pmul(::Type{Pgamma{1,1}}, a::Spinor{4,G}) where {NS,G}
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r1 = a.s[1]+imm(a.s[4])
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r2 = a.s[2]+imm(a.s[3])
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return Spinor{4,G}((r1,r2,mimm(r2),mimm(r1)))
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end
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function pmul(::Type{Pgamma{1,-1}}, a::Spinor{4,G}) where {NS,G}
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r1 = a.s[1]-imm(a.s[4])
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r2 = a.s[2]-imm(a.s[3])
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return Spinor{4,G}((imm(r2),imm(r1)))
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end
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function pmul(::Type{Pgamma{2,1}}, a::Spinor{4,G}) where {NS,G}
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r1 = a.s[1]+a.s[4]
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r2 = a.s[2]-a.s[3]
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return Spinor{4,G}((r1,r2,-r2,r1))
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end
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function pmul(::Type{Pgamma{2,-1}}, a::Spinor{4,G}) where {NS,G}
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r1 = a.s[1]-a.s[4]
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r2 = a.s[2]+a.s[3]
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return Spinor{4,G}((r1,r2,r2,-r1))
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end
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function pmul(::Type{Pgamma{3,1}}, a::Spinor{4,G}) where {NS,G}
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r1 = a.s[1]+imm(a.s[3])
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r2 = a.s[2]-imm(a.s[4])
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return Spinor{4,G}((r1,r2,mimm(r1),imm(r2)))
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end
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function pmul(::Type{Pgamma{3,-1}}, a::Spinor{4,G}) where {NS,G}
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r1 = a.s[1]-imm(a.s[3])
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r2 = a.s[2]+imm(a.s[4])
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return Spinor{4,G}((r1,r2,imm(r1),mimm(r2)))
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end
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"""
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gpmul(pgamma{N,S}, g::G, a::Spinor) G <: Group
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Returns g(1+s\gamma_N)a
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"""
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function gpmul(::Type{Pgamma{4,1}}, g, a::Spinor{4,G}) where {NS,G}
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r1 = g*(a.s[1]+a.s[3])
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r2 = g*(a.s[2]+a.s[4])
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return Spinor{4,G}((r1,r2,r1,r2))
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end
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function gpmul(::Type{Pgamma{4,-1}}, g, a::Spinor{4,G}) where {NS,G}
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r1 = g*(a.s[1]-a.s[3])
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r2 = g*(a.s[2]-a.s[4])
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return Spinor{4,G}((r1,r2,-r1,-r2))
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end
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function gpmul(::Type{Pgamma{1,1}}, g, a::Spinor{4,G}) where {NS,G}
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r1 = g*(a.s[1]+imm(a.s[4]))
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r2 = g*(a.s[2]+imm(a.s[3]))
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return Spinor{4,G}((r1,r2,mimm(r2),mimm(r1)))
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end
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function gpmul(::Type{Pgamma{1,-1}}, g, a::Spinor{4,G}) where {NS,G}
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r1 = g*(a.s[1]-imm(a.s[4]))
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r2 = g*(a.s[2]-imm(a.s[3]))
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return Spinor{4,G}((imm(r2),imm(r1)))
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end
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function gpmul(::Type{Pgamma{2,1}}, g, a::Spinor{4,G}) where {NS,G}
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r1 = g*(a.s[1]+a.s[4])
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r2 = g*(a.s[2]-a.s[3])
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return Spinor{4,G}((r1,r2,-r2,r1))
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end
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function gpmul(::Type{Pgamma{2,-1}}, g, a::Spinor{4,G}) where {NS,G}
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r1 = g*(a.s[1]-a.s[4])
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r2 = g*(a.s[2]+a.s[3])
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return Spinor{4,G}((r1,r2,r2,-r1))
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end
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function gpmul(::Type{Pgamma{3,1}}, g, a::Spinor{4,G}) where {NS,G}
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r1 = g*(a.s[1]+imm(a.s[3]))
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r2 = g*(a.s[2]-imm(a.s[4]))
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return Spinor{4,G}((r1,r2,mimm(r1),imm(r2)))
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end
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function gpmul(::Type{Pgamma{3,-1}}, g, a::Spinor{4,G}) where {NS,G}
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r1 = g*(a.s[1]-imm(a.s[3]))
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r2 = g*(a.s[2]+imm(a.s[4]))
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return Spinor{4,G}((r1,r2,imm(r1),mimm(r2)))
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end
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"""
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gdagpmul(pgamma{N,S}, g::G, a::Spinor) G <: Group
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Returns g^+ (1+s\gamma_N)a
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"""
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function gdagpmul(::Type{Pgamma{4,1}}, g, a::Spinor{4,G}) where {NS,G}
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r1 = g\(a.s[1]+a.s[3])
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r2 = g\(a.s[2]+a.s[4])
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return Spinor{4,G}((r1,r2,r1,r2))
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end
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function gdagpmul(::Type{Pgamma{4,-1}}, g, a::Spinor{4,G}) where {NS,G}
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r1 = g\(a.s[1]-a.s[3])
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r2 = g\(a.s[2]-a.s[4])
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return Spinor{4,G}((r1,r2,-r1,-r2))
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end
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function gdagpmul(::Type{Pgamma{1,1}}, g, a::Spinor{4,G}) where {NS,G}
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r1 = g\(a.s[1]+imm(a.s[4]))
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r2 = g\(a.s[2]+imm(a.s[3]))
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return Spinor{4,G}((r1,r2,mimm(r2),mimm(r1)))
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end
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function gdagpmul(::Type{Pgamma{1,-1}}, g, a::Spinor{4,G}) where {NS,G}
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r1 = g\(a.s[1]-imm(a.s[4]))
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r2 = g\(a.s[2]-imm(a.s[3]))
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return Spinor{4,G}((imm(r2),imm(r1)))
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end
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function gdagpmul(::Type{Pgamma{2,1}}, g, a::Spinor{4,G}) where {NS,G}
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r1 = g\(a.s[1]+a.s[4])
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r2 = g\(a.s[2]-a.s[3])
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return Spinor{4,G}((r1,r2,-r2,r1))
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end
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function gdagpmul(::Type{Pgamma{2,-1}}, g, a::Spinor{4,G}) where {NS,G}
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r1 = g\(a.s[1]-a.s[4])
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r2 = g\(a.s[2]+a.s[3])
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return Spinor{4,G}((r1,r2,r2,-r1))
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end
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function gdagpmul(::Type{Pgamma{3,1}}, g, a::Spinor{4,G}) where {NS,G}
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r1 = g\(a.s[1]+imm(a.s[3]))
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r2 = g\(a.s[2]-imm(a.s[4]))
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return Spinor{4,G}((r1,r2,mimm(r1),imm(r2)))
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end
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function gdagpmul(::Type{Pgamma{3,-1}}, g, a::Spinor{4,G}) where {NS,G}
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r1 = g\(a.s[1]-imm(a.s[3]))
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r2 = g\(a.s[2]+imm(a.s[4]))
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return Spinor{4,G}((r1,r2,imm(r1),mimm(r2)))
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end
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