lattice/latticegpu.jl
1
0
Fork 0
mirror of https://igit.ific.uv.es/alramos/latticegpu.jl.git synced 2025-05-14 19:23:42 +02:00
Code Issues Projects Releases Packages Wiki Activity Actions

Gamma matrices convention

Browse source
This commit is contained in:
Fernando P. Panadero 2023-11-20 14:23:39 +01:00
parent a32b7be66c
commit c05af76185
1 changed files with 67 additions and 67 deletions
Download patch file Download diff file Expand all files Collapse all files

134
src/Spinors/Spinors.jl
View file

@ -115,56 +115,56 @@ end
Returns ``(1+s\\gamma_N)a``. Returns ``(1+s\\gamma_N)a``.
""" """
@inline function pmul(::Type{Pgamma{4,1}}, a::Spinor{4,G}) where {NS,G} @inline function pmul(::Type{Pgamma{4,-1}}, a::Spinor{NS,G}) where {NS,G}
r1 = a.s[1]+a.s[3] r1 = a.s[1]+a.s[3]
r2 = a.s[2]+a.s[4] r2 = a.s[2]+a.s[4]
return Spinor{4,G}((r1,r2,r1,r2)) return Spinor{NS,G}((r1,r2,r1,r2))
end end
@inline function pmul(::Type{Pgamma{4,-1}}, a::Spinor{4,G}) where {NS,G} @inline function pmul(::Type{Pgamma{4,1}}, a::Spinor{NS,G}) where {NS,G}
r1 = a.s[1]-a.s[3] r1 = a.s[1]-a.s[3]
r2 = a.s[2]-a.s[4] r2 = a.s[2]-a.s[4]
return Spinor{4,G}((r1,r2,-r1,-r2)) return Spinor{NS,G}((r1,r2,-r1,-r2))
end end
@inline function pmul(::Type{Pgamma{1,1}}, a::Spinor{4,G}) where {NS,G} @inline function pmul(::Type{Pgamma{1,-1}}, a::Spinor{NS,G}) where {NS,G}
r1 = a.s[1]+imm(a.s[4]) r1 = a.s[1]+imm(a.s[4])
r2 = a.s[2]+imm(a.s[3]) r2 = a.s[2]+imm(a.s[3])
return Spinor{4,G}((r1,r2,mimm(r2),mimm(r1))) return Spinor{NS,G}((r1,r2,mimm(r2),mimm(r1)))
end end
@inline function pmul(::Type{Pgamma{1,-1}}, a::Spinor{4,G}) where {NS,G} @inline function pmul(::Type{Pgamma{1,1}}, a::Spinor{NS,G}) where {NS,G}
r1 = a.s[1]-imm(a.s[4]) r1 = a.s[1]-imm(a.s[4])
r2 = a.s[2]-imm(a.s[3]) r2 = a.s[2]-imm(a.s[3])
return Spinor{4,G}((r1,r2,imm(r2),imm(r1))) return Spinor{NS,G}((r1,r2,imm(r2),imm(r1)))
end end
@inline function pmul(::Type{Pgamma{2,1}}, a::Spinor{4,G}) where {NS,G} @inline function pmul(::Type{Pgamma{2,-1}}, a::Spinor{NS,G}) where {NS,G}
r1 = a.s[1]+a.s[4] r1 = a.s[1]+a.s[4]
r2 = a.s[2]-a.s[3] r2 = a.s[2]-a.s[3]
return Spinor{4,G}((r1,r2,-r2,r1)) return Spinor{NS,G}((r1,r2,-r2,r1))
end end
@inline function pmul(::Type{Pgamma{2,-1}}, a::Spinor{4,G}) where {NS,G} @inline function pmul(::Type{Pgamma{2,1}}, a::Spinor{NS,G}) where {NS,G}
r1 = a.s[1]-a.s[4] r1 = a.s[1]-a.s[4]
r2 = a.s[2]+a.s[3] r2 = a.s[2]+a.s[3]
return Spinor{4,G}((r1,r2,r2,-r1)) return Spinor{NS,G}((r1,r2,r2,-r1))
end end
@inline function pmul(::Type{Pgamma{3,1}}, a::Spinor{4,G}) where {NS,G} @inline function pmul(::Type{Pgamma{3,-1}}, a::Spinor{NS,G}) where {NS,G}
r1 = a.s[1]+imm(a.s[3]) r1 = a.s[1]+imm(a.s[3])
r2 = a.s[2]-imm(a.s[4]) r2 = a.s[2]-imm(a.s[4])
return Spinor{4,G}((r1,r2,mimm(r1),imm(r2))) return Spinor{NS,G}((r1,r2,mimm(r1),imm(r2)))
end end
@inline function pmul(::Type{Pgamma{3,-1}}, a::Spinor{4,G}) where {NS,G} @inline function pmul(::Type{Pgamma{3,1}}, a::Spinor{NS,G}) where {NS,G}
r1 = a.s[1]-imm(a.s[3]) r1 = a.s[1]-imm(a.s[3])
r2 = a.s[2]+imm(a.s[4]) r2 = a.s[2]+imm(a.s[4])
return Spinor{4,G}((r1,r2,imm(r1),mimm(r2))) return Spinor{NS,G}((r1,r2,imm(r1),mimm(r2)))
end end
@ -173,56 +173,56 @@ end
Returns ``g(1+s\\gamma_N)a`` Returns ``g(1+s\\gamma_N)a``
""" """
@inline function gpmul(::Type{Pgamma{4,1}}, g, a::Spinor{4,G}) where {NS,G} @inline function gpmul(::Type{Pgamma{4,-1}}, g, a::Spinor{NS,G}) where {NS,G}
r1 = g*(a.s[1]+a.s[3]) r1 = g*(a.s[1]+a.s[3])
r2 = g*(a.s[2]+a.s[4]) r2 = g*(a.s[2]+a.s[4])
return Spinor{4,G}((r1,r2,r1,r2)) return Spinor{NS,G}((r1,r2,r1,r2))
end end
@inline function gpmul(::Type{Pgamma{4,-1}}, g, a::Spinor{4,G}) where {NS,G} @inline function gpmul(::Type{Pgamma{4,1}}, g, a::Spinor{NS,G}) where {NS,G}
r1 = g*(a.s[1]-a.s[3]) r1 = g*(a.s[1]-a.s[3])
r2 = g*(a.s[2]-a.s[4]) r2 = g*(a.s[2]-a.s[4])
return Spinor{4,G}((r1,r2,-r1,-r2)) return Spinor{NS,G}((r1,r2,-r1,-r2))
end end
@inline function gpmul(::Type{Pgamma{1,1}}, g, a::Spinor{4,G}) where {NS,G} @inline function gpmul(::Type{Pgamma{1,-1}}, g, a::Spinor{NS,G}) where {NS,G}
r1 = g*(a.s[1]+imm(a.s[4])) r1 = g*(a.s[1]+imm(a.s[4]))
r2 = g*(a.s[2]+imm(a.s[3])) r2 = g*(a.s[2]+imm(a.s[3]))
return Spinor{4,G}((r1,r2,mimm(r2),mimm(r1))) return Spinor{NS,G}((r1,r2,mimm(r2),mimm(r1)))
end end
@inline function gpmul(::Type{Pgamma{1,-1}}, g, a::Spinor{4,G}) where {NS,G} @inline function gpmul(::Type{Pgamma{1,1}}, g, a::Spinor{NS,G}) where {NS,G}
r1 = g*(a.s[1]-imm(a.s[4])) r1 = g*(a.s[1]-imm(a.s[4]))
r2 = g*(a.s[2]-imm(a.s[3])) r2 = g*(a.s[2]-imm(a.s[3]))
return Spinor{4,G}((r1,r2,imm(r2),imm(r1))) return Spinor{NS,G}((r1,r2,imm(r2),imm(r1)))
end end
@inline function gpmul(::Type{Pgamma{2,1}}, g, a::Spinor{4,G}) where {NS,G} @inline function gpmul(::Type{Pgamma{2,-1}}, g, a::Spinor{NS,G}) where {NS,G}
r1 = g*(a.s[1]+a.s[4]) r1 = g*(a.s[1]+a.s[4])
r2 = g*(a.s[2]-a.s[3]) r2 = g*(a.s[2]-a.s[3])
return Spinor{4,G}((r1,r2,-r2,r1)) return Spinor{NS,G}((r1,r2,-r2,r1))
end end
@inline function gpmul(::Type{Pgamma{2,-1}}, g, a::Spinor{4,G}) where {NS,G} @inline function gpmul(::Type{Pgamma{2,1}}, g, a::Spinor{NS,G}) where {NS,G}
r1 = g*(a.s[1]-a.s[4]) r1 = g*(a.s[1]-a.s[4])
r2 = g*(a.s[2]+a.s[3]) r2 = g*(a.s[2]+a.s[3])
return Spinor{4,G}((r1,r2,r2,-r1)) return Spinor{NS,G}((r1,r2,r2,-r1))
end end
@inline function gpmul(::Type{Pgamma{3,1}}, g, a::Spinor{4,G}) where {NS,G} @inline function gpmul(::Type{Pgamma{3,-1}}, g, a::Spinor{NS,G}) where {NS,G}
r1 = g*(a.s[1]+imm(a.s[3])) r1 = g*(a.s[1]+imm(a.s[3]))
r2 = g*(a.s[2]-imm(a.s[4])) r2 = g*(a.s[2]-imm(a.s[4]))
return Spinor{4,G}((r1,r2,mimm(r1),imm(r2))) return Spinor{NS,G}((r1,r2,mimm(r1),imm(r2)))
end end
@inline function gpmul(::Type{Pgamma{3,-1}}, g, a::Spinor{4,G}) where {NS,G} @inline function gpmul(::Type{Pgamma{3,1}}, g, a::Spinor{NS,G}) where {NS,G}
r1 = g*(a.s[1]-imm(a.s[3])) r1 = g*(a.s[1]-imm(a.s[3]))
r2 = g*(a.s[2]+imm(a.s[4])) r2 = g*(a.s[2]+imm(a.s[4]))
return Spinor{4,G}((r1,r2,imm(r1),mimm(r2))) return Spinor{NS,G}((r1,r2,imm(r1),mimm(r2)))
end end
""" """
@ -230,56 +230,56 @@ end
Returns ``g^+ (1+s\\gamma_N)a`` Returns ``g^+ (1+s\\gamma_N)a``
""" """
@inline function gdagpmul(::Type{Pgamma{4,1}}, g, a::Spinor{4,G}) where {NS,G} @inline function gdagpmul(::Type{Pgamma{4,-1}}, g, a::Spinor{NS,G}) where {NS,G}
r1 = g\(a.s[1]+a.s[3]) r1 = g\(a.s[1]+a.s[3])
r2 = g\(a.s[2]+a.s[4]) r2 = g\(a.s[2]+a.s[4])
return Spinor{4,G}((r1,r2,r1,r2)) return Spinor{NS,G}((r1,r2,r1,r2))
end end
@inline function gdagpmul(::Type{Pgamma{4,-1}}, g, a::Spinor{4,G}) where {NS,G} @inline function gdagpmul(::Type{Pgamma{4,1}}, g, a::Spinor{NS,G}) where {NS,G}
r1 = g\(a.s[1]-a.s[3]) r1 = g\(a.s[1]-a.s[3])
r2 = g\(a.s[2]-a.s[4]) r2 = g\(a.s[2]-a.s[4])
return Spinor{4,G}((r1,r2,-r1,-r2)) return Spinor{NS,G}((r1,r2,-r1,-r2))
end end
@inline function gdagpmul(::Type{Pgamma{1,1}}, g, a::Spinor{4,G}) where {NS,G} @inline function gdagpmul(::Type{Pgamma{1,-1}}, g, a::Spinor{NS,G}) where {NS,G}
r1 = g\(a.s[1]+imm(a.s[4])) r1 = g\(a.s[1]+imm(a.s[4]))
r2 = g\(a.s[2]+imm(a.s[3])) r2 = g\(a.s[2]+imm(a.s[3]))
return Spinor{4,G}((r1,r2,mimm(r2),mimm(r1))) return Spinor{NS,G}((r1,r2,mimm(r2),mimm(r1)))
end end
@inline function gdagpmul(::Type{Pgamma{1,-1}}, g, a::Spinor{4,G}) where {NS,G} @inline function gdagpmul(::Type{Pgamma{1,1}}, g, a::Spinor{NS,G}) where {NS,G}
r1 = g\(a.s[1]-imm(a.s[4])) r1 = g\(a.s[1]-imm(a.s[4]))
r2 = g\(a.s[2]-imm(a.s[3])) r2 = g\(a.s[2]-imm(a.s[3]))
return Spinor{4,G}((r1,r2,imm(r2),imm(r1))) return Spinor{NS,G}((r1,r2,imm(r2),imm(r1)))
end end
@inline function gdagpmul(::Type{Pgamma{2,1}}, g, a::Spinor{4,G}) where {NS,G} @inline function gdagpmul(::Type{Pgamma{2,-1}}, g, a::Spinor{NS,G}) where {NS,G}
r1 = g\(a.s[1]+a.s[4]) r1 = g\(a.s[1]+a.s[4])
r2 = g\(a.s[2]-a.s[3]) r2 = g\(a.s[2]-a.s[3])
return Spinor{4,G}((r1,r2,-r2,r1)) return Spinor{NS,G}((r1,r2,-r2,r1))
end end
@inline function gdagpmul(::Type{Pgamma{2,-1}}, g, a::Spinor{4,G}) where {NS,G} @inline function gdagpmul(::Type{Pgamma{2,1}}, g, a::Spinor{NS,G}) where {NS,G}
r1 = g\(a.s[1]-a.s[4]) r1 = g\(a.s[1]-a.s[4])
r2 = g\(a.s[2]+a.s[3]) r2 = g\(a.s[2]+a.s[3])
return Spinor{4,G}((r1,r2,r2,-r1)) return Spinor{NS,G}((r1,r2,r2,-r1))
end end
@inline function gdagpmul(::Type{Pgamma{3,1}}, g, a::Spinor{4,G}) where {NS,G} @inline function gdagpmul(::Type{Pgamma{3,-1}}, g, a::Spinor{NS,G}) where {NS,G}
r1 = g\(a.s[1]+imm(a.s[3])) r1 = g\(a.s[1]+imm(a.s[3]))
r2 = g\(a.s[2]-imm(a.s[4])) r2 = g\(a.s[2]-imm(a.s[4]))
return Spinor{4,G}((r1,r2,mimm(r1),imm(r2))) return Spinor{NS,G}((r1,r2,mimm(r1),imm(r2)))
end end
@inline function gdagpmul(::Type{Pgamma{3,-1}}, g, a::Spinor{4,G}) where {NS,G} @inline function gdagpmul(::Type{Pgamma{3,1}}, g, a::Spinor{NS,G}) where {NS,G}
r1 = g\(a.s[1]-imm(a.s[3])) r1 = g\(a.s[1]-imm(a.s[3]))
r2 = g\(a.s[2]+imm(a.s[4])) r2 = g\(a.s[2]+imm(a.s[4]))
return Spinor{4,G}((r1,r2,imm(r1),mimm(r2))) return Spinor{NS,G}((r1,r2,imm(r1),mimm(r2)))
end end
@ -307,30 +307,30 @@ indexing for Dirac basis ``\\Gamma_n``:
10 sigma01 10 sigma01
11 sigma02 11 sigma02
12 sigma03 12 sigma03
13 sigma12 13 sigma21
14 sigma23 14 sigma32
15 sigma31 15 sigma31
16 identity 16 identity
""" """
@inline dmul(::Type{Gamma{1}}, a::Spinor{4,G}) where {G} = Spinor{4,G}(mimm(a.s[4]), mimm(a.s[3]), imm(a.s[2]), imm(a.s[1])) @inline dmul(::Type{Gamma{1}}, a::Spinor{NS,G}) where {NS,G} = Spinor{NS,G}((mimm(a.s[4]), mimm(a.s[3]), imm(a.s[2]), imm(a.s[1])))
@inline dmul(::Type{Gamma{2}}, a::Spinor{4,G}) where {G} = Spinor{4,G}(-a.s[4], a.s[3], a.s[2], -a.s[1]) @inline dmul(::Type{Gamma{2}}, a::Spinor{NS,G}) where {NS,G} = Spinor{NS,G}((-a.s[4], a.s[3], a.s[2], -a.s[1]))
@inline dmul(::Type{Gamma{3}}, a::Spinor{4,G}) where {G} = Spinor{4,G}(mimm(a.s[3]), imm(a.s[4]), imm(a.s[1]), mimm(a.s[2])) @inline dmul(::Type{Gamma{3}}, a::Spinor{NS,G}) where {NS,G} = Spinor{NS,G}((mimm(a.s[3]), imm(a.s[4]), imm(a.s[1]), mimm(a.s[2])))
@inline dmul(::Type{Gamma{4}}, a::Spinor{4,G}) where {G} = Spinor{4,G}(-a.s[3], -a.s[4], -a.s[1], -a.s[2]) @inline dmul(::Type{Gamma{4}}, a::Spinor{NS,G}) where {NS,G} = Spinor{NS,G}((-a.s[3], -a.s[4], -a.s[1], -a.s[2]))
@inline dmul(::Type{Gamma{5}}, a::Spinor{4,G}) where {G} = Spinor{4,G}( a.s[1], a.s[2], -a.s[3], -a.s[4]) @inline dmul(::Type{Gamma{5}}, a::Spinor{NS,G}) where {NS,G} = Spinor{NS,G}((a.s[1], a.s[2], -a.s[3], -a.s[4]))
@inline dmul(::Type{Gamma{6}}, a::Spinor{4,G}) where {G} = Spinor{4,G}( imm(a.s[4]), imm(a.s[3]), imm(a.s[2]), imm(a.s[1])) @inline dmul(::Type{Gamma{6}}, a::Spinor{NS,G}) where {NS,G} = Spinor{NS,G}(( imm(a.s[4]), imm(a.s[3]), imm(a.s[2]), imm(a.s[1])))
@inline dmul(::Type{Gamma{7}}, a::Spinor{4,G}) where {G} = Spinor{4,G}( a.s[4], -a.s[3], a.s[2], -a.s[1]) @inline dmul(::Type{Gamma{7}}, a::Spinor{NS,G}) where {NS,G} = Spinor{NS,G}(( a.s[4], -a.s[3], a.s[2], -a.s[1]))
@inline dmul(::Type{Gamma{8}}, a::Spinor{4,G}) where {G} = Spinor{4,G}( imm(a.s[3]), mimm(a.s[4]), imm(a.s[1]), mimm(a.s[2])) @inline dmul(::Type{Gamma{8}}, a::Spinor{NS,G}) where {NS,G} = Spinor{NS,G}(( imm(a.s[3]), mimm(a.s[4]), imm(a.s[1]), mimm(a.s[2])))
@inline dmul(::Type{Gamma{9}}, a::Spinor{4,G}) where {G} = Spinor{4,G}( a.s[3], a.s[4], -a.s[1], -a.s[2]) @inline dmul(::Type{Gamma{9}}, a::Spinor{NS,G}) where {NS,G} = Spinor{NS,G}(( a.s[3], a.s[4], -a.s[1], -a.s[2]))
@inline dmul(::Type{Gamma{10}}, a::Spinor{4,G}) where {G} = Spinor{4,G}( a.s[2], a.s[1], -a.s[4], -a.s[3]) @inline dmul(::Type{Gamma{10}}, a::Spinor{NS,G}) where {NS,G} = Spinor{NS,G}(( a.s[2], a.s[1], -a.s[4], -a.s[3]))
@inline dmul(::Type{Gamma{11}}, a::Spinor{4,G}) where {G} = Spinor{4,G}(mimm(a.s[2]), imm(a.s[1]), imm(a.s[4]), mimm(a.s[3])) @inline dmul(::Type{Gamma{11}}, a::Spinor{NS,G}) where {NS,G} = Spinor{NS,G}((mimm(a.s[2]), imm(a.s[1]), imm(a.s[4]), mimm(a.s[3])))
@inline dmul(::Type{Gamma{12}}, a::Spinor{4,G}) where {G} = Spinor{4,G}( a.s[1], -a.s[2], -a.s[3], a.s[4]) @inline dmul(::Type{Gamma{12}}, a::Spinor{NS,G}) where {NS,G} = Spinor{NS,G}(( a.s[1], -a.s[2], -a.s[3], a.s[4]))
@inline dmul(::Type{Gamma{13}}, a::Spinor{4,G}) where {G} = Spinor{4,G}(-a.s[1], a.s[2], -a.s[3], a.s[4]) @inline dmul(::Type{Gamma{13}}, a::Spinor{NS,G}) where {NS,G} = Spinor{NS,G}((a.s[1], -a.s[2], a.s[3], -a.s[4]))
@inline dmul(::Type{Gamma{14}}, a::Spinor{4,G}) where {G} = Spinor{4,G}(-a.s[2], -a.s[1], -a.s[4], -a.s[3]) @inline dmul(::Type{Gamma{14}}, a::Spinor{NS,G}) where {NS,G} = Spinor{NS,G}((a.s[2], a.s[1], a.s[4], a.s[3]))
@inline dmul(::Type{Gamma{15}}, a::Spinor{4,G}) where {G} = Spinor{4,G}( imm(a.s[2]), mimm(a.s[1]), imm(a.s[4]), mimm(a.s[3])) @inline dmul(::Type{Gamma{15}}, a::Spinor{NS,G}) where {NS,G} = Spinor{NS,G}((imm(a.s[2]), mimm(a.s[1]), imm(a.s[4]), mimm(a.s[3])))
@inline dmul(::Type{Gamma{16}}, a::Spinor{4,G}) where {G} = a @inline dmul(::Type{Gamma{16}}, a::Spinor{NS,G}) where {NS,G} = a
export Spinor, Pgamma export Spinor, Pgamma, Gamma
export norm, norm2, dot, imm, mimm export norm, norm2, dot, imm, mimm
export pmul, gpmul, gdagpmul, dmul export pmul, gpmul, gdagpmul, dmul