lattice/latticegpu.jl
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Alberto Ramos 2022-01-05 19:55:51 +01:00
parent 6f6773d2ed
commit 65a619e554
7 changed files with 191 additions and 64 deletions
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82
src/Spinors/Spinors.jl
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@ -22,7 +22,7 @@ Base.zero(::Type{Spinor{NS,G}}) where {NS,G} = Spinor{NS,G}(ntuple(i->zero(G), N
"""
norm2(a::Spinor)
Returns the norm of a fundamental element. Same result as sqrt(dot(a,a)).
Returns the norm squared of a fundamental element. Same result as `dot(a,a)`.
"""
@generated function norm2(a::Spinor{NS,G}) where {NS,G}
@ -100,52 +100,52 @@ end
Returns ``(1+s\\gamma_N)a``.
"""
function pmul(::Type{Pgamma{4,1}}, a::Spinor{4,G}) where {NS,G}
@inline function pmul(::Type{Pgamma{4,1}}, a::Spinor{4,G}) where {NS,G}
r1 = a.s[1]+a.s[3]
r2 = a.s[2]+a.s[4]
return Spinor{4,G}((r1,r2,r1,r2))
end
function pmul(::Type{Pgamma{4,-1}}, a::Spinor{4,G}) where {NS,G}
@inline function pmul(::Type{Pgamma{4,-1}}, a::Spinor{4,G}) where {NS,G}
r1 = a.s[1]-a.s[3]
r2 = a.s[2]-a.s[4]
return Spinor{4,G}((r1,r2,-r1,-r2))
end
function pmul(::Type{Pgamma{1,1}}, a::Spinor{4,G}) where {NS,G}
@inline function pmul(::Type{Pgamma{1,1}}, a::Spinor{4,G}) where {NS,G}
r1 = a.s[1]+imm(a.s[4])
r2 = a.s[2]+imm(a.s[3])
return Spinor{4,G}((r1,r2,mimm(r2),mimm(r1)))
end
function pmul(::Type{Pgamma{1,-1}}, a::Spinor{4,G}) where {NS,G}
@inline function pmul(::Type{Pgamma{1,-1}}, a::Spinor{4,G}) where {NS,G}
r1 = a.s[1]-imm(a.s[4])
r2 = a.s[2]-imm(a.s[3])
return Spinor{4,G}((r1,r2,imm(r2),imm(r1)))
end
function pmul(::Type{Pgamma{2,1}}, a::Spinor{4,G}) where {NS,G}
@inline function pmul(::Type{Pgamma{2,1}}, a::Spinor{4,G}) where {NS,G}
r1 = a.s[1]+a.s[4]
r2 = a.s[2]-a.s[3]
return Spinor{4,G}((r1,r2,-r2,r1))
end
function pmul(::Type{Pgamma{2,-1}}, a::Spinor{4,G}) where {NS,G}
@inline function pmul(::Type{Pgamma{2,-1}}, a::Spinor{4,G}) where {NS,G}
r1 = a.s[1]-a.s[4]
r2 = a.s[2]+a.s[3]
return Spinor{4,G}((r1,r2,r2,-r1))
end
function pmul(::Type{Pgamma{3,1}}, a::Spinor{4,G}) where {NS,G}
@inline function pmul(::Type{Pgamma{3,1}}, a::Spinor{4,G}) where {NS,G}
r1 = a.s[1]+imm(a.s[3])
r2 = a.s[2]-imm(a.s[4])
return Spinor{4,G}((r1,r2,mimm(r1),imm(r2)))
end
function pmul(::Type{Pgamma{3,-1}}, a::Spinor{4,G}) where {NS,G}
@inline function pmul(::Type{Pgamma{3,-1}}, a::Spinor{4,G}) where {NS,G}
r1 = a.s[1]-imm(a.s[3])
r2 = a.s[2]+imm(a.s[4])
@ -158,52 +158,52 @@ end
Returns ``g(1+s\\gamma_N)a``
"""
function gpmul(::Type{Pgamma{4,1}}, g, a::Spinor{4,G}) where {NS,G}
@inline function gpmul(::Type{Pgamma{4,1}}, g, a::Spinor{4,G}) where {NS,G}
r1 = g*(a.s[1]+a.s[3])
r2 = g*(a.s[2]+a.s[4])
return Spinor{4,G}((r1,r2,r1,r2))
end
function gpmul(::Type{Pgamma{4,-1}}, g, a::Spinor{4,G}) where {NS,G}
@inline function gpmul(::Type{Pgamma{4,-1}}, g, a::Spinor{4,G}) where {NS,G}
r1 = g*(a.s[1]-a.s[3])
r2 = g*(a.s[2]-a.s[4])
return Spinor{4,G}((r1,r2,-r1,-r2))
end
function gpmul(::Type{Pgamma{1,1}}, g, a::Spinor{4,G}) where {NS,G}
@inline function gpmul(::Type{Pgamma{1,1}}, g, a::Spinor{4,G}) where {NS,G}
r1 = g*(a.s[1]+imm(a.s[4]))
r2 = g*(a.s[2]+imm(a.s[3]))
return Spinor{4,G}((r1,r2,mimm(r2),mimm(r1)))
end
function gpmul(::Type{Pgamma{1,-1}}, g, a::Spinor{4,G}) where {NS,G}
@inline function gpmul(::Type{Pgamma{1,-1}}, g, a::Spinor{4,G}) where {NS,G}
r1 = g*(a.s[1]-imm(a.s[4]))
r2 = g*(a.s[2]-imm(a.s[3]))
return Spinor{4,G}((r1,r2,imm(r2),imm(r1)))
end
function gpmul(::Type{Pgamma{2,1}}, g, a::Spinor{4,G}) where {NS,G}
@inline function gpmul(::Type{Pgamma{2,1}}, g, a::Spinor{4,G}) where {NS,G}
r1 = g*(a.s[1]+a.s[4])
r2 = g*(a.s[2]-a.s[3])
return Spinor{4,G}((r1,r2,-r2,r1))
end
function gpmul(::Type{Pgamma{2,-1}}, g, a::Spinor{4,G}) where {NS,G}
@inline function gpmul(::Type{Pgamma{2,-1}}, g, a::Spinor{4,G}) where {NS,G}
r1 = g*(a.s[1]-a.s[4])
r2 = g*(a.s[2]+a.s[3])
return Spinor{4,G}((r1,r2,r2,-r1))
end
function gpmul(::Type{Pgamma{3,1}}, g, a::Spinor{4,G}) where {NS,G}
@inline function gpmul(::Type{Pgamma{3,1}}, g, a::Spinor{4,G}) where {NS,G}
r1 = g*(a.s[1]+imm(a.s[3]))
r2 = g*(a.s[2]-imm(a.s[4]))
return Spinor{4,G}((r1,r2,mimm(r1),imm(r2)))
end
function gpmul(::Type{Pgamma{3,-1}}, g, a::Spinor{4,G}) where {NS,G}
@inline function gpmul(::Type{Pgamma{3,-1}}, g, a::Spinor{4,G}) where {NS,G}
r1 = g*(a.s[1]-imm(a.s[3]))
r2 = g*(a.s[2]+imm(a.s[4]))
@ -215,52 +215,52 @@ end
Returns ``g^+ (1+s\\gamma_N)a``
"""
function gdagpmul(::Type{Pgamma{4,1}}, g, a::Spinor{4,G}) where {NS,G}
@inline function gdagpmul(::Type{Pgamma{4,1}}, g, a::Spinor{4,G}) where {NS,G}
r1 = g\(a.s[1]+a.s[3])
r2 = g\(a.s[2]+a.s[4])
return Spinor{4,G}((r1,r2,r1,r2))
end
function gdagpmul(::Type{Pgamma{4,-1}}, g, a::Spinor{4,G}) where {NS,G}
@inline function gdagpmul(::Type{Pgamma{4,-1}}, g, a::Spinor{4,G}) where {NS,G}
r1 = g\(a.s[1]-a.s[3])
r2 = g\(a.s[2]-a.s[4])
return Spinor{4,G}((r1,r2,-r1,-r2))
end
function gdagpmul(::Type{Pgamma{1,1}}, g, a::Spinor{4,G}) where {NS,G}
@inline function gdagpmul(::Type{Pgamma{1,1}}, g, a::Spinor{4,G}) where {NS,G}
r1 = g\(a.s[1]+imm(a.s[4]))
r2 = g\(a.s[2]+imm(a.s[3]))
return Spinor{4,G}((r1,r2,mimm(r2),mimm(r1)))
end
function gdagpmul(::Type{Pgamma{1,-1}}, g, a::Spinor{4,G}) where {NS,G}
@inline function gdagpmul(::Type{Pgamma{1,-1}}, g, a::Spinor{4,G}) where {NS,G}
r1 = g\(a.s[1]-imm(a.s[4]))
r2 = g\(a.s[2]-imm(a.s[3]))
return Spinor{4,G}((r1,r2,imm(r2),imm(r1)))
end
function gdagpmul(::Type{Pgamma{2,1}}, g, a::Spinor{4,G}) where {NS,G}
@inline function gdagpmul(::Type{Pgamma{2,1}}, g, a::Spinor{4,G}) where {NS,G}
r1 = g\(a.s[1]+a.s[4])
r2 = g\(a.s[2]-a.s[3])
return Spinor{4,G}((r1,r2,-r2,r1))
end
function gdagpmul(::Type{Pgamma{2,-1}}, g, a::Spinor{4,G}) where {NS,G}
@inline function gdagpmul(::Type{Pgamma{2,-1}}, g, a::Spinor{4,G}) where {NS,G}
r1 = g\(a.s[1]-a.s[4])
r2 = g\(a.s[2]+a.s[3])
return Spinor{4,G}((r1,r2,r2,-r1))
end
function gdagpmul(::Type{Pgamma{3,1}}, g, a::Spinor{4,G}) where {NS,G}
@inline function gdagpmul(::Type{Pgamma{3,1}}, g, a::Spinor{4,G}) where {NS,G}
r1 = g\(a.s[1]+imm(a.s[3]))
r2 = g\(a.s[2]-imm(a.s[4]))
return Spinor{4,G}((r1,r2,mimm(r1),imm(r2)))
end
function gdagpmul(::Type{Pgamma{3,-1}}, g, a::Spinor{4,G}) where {NS,G}
@inline function gdagpmul(::Type{Pgamma{3,-1}}, g, a::Spinor{4,G}) where {NS,G}
r1 = g\(a.s[1]-imm(a.s[3]))
r2 = g\(a.s[2]+imm(a.s[4]))
@ -298,22 +298,22 @@ indexing for Dirac basis ``\\Gamma_n``:
16 identity
"""
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]))
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])
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]))
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])
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])
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]))
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])
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]))
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])
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])
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]))
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])
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])
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])
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]))
dmul(::Type{Gamma{16}}, a::Spinor{4,G}) where {G} = a
@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{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{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{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{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{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{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{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{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{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{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{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{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{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{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{16}}, a::Spinor{4,G}) where {G} = a
export Spinor, Pgamma
export norm, norm2, dot, imm, mimm