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Cosmetic changes in Gamma basis multiplication

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This commit is contained in:
Alberto Ramos 2021-11-21 16:38:19 +01:00
parent c7543e48d9
commit 34ba7b6b81
1 changed files with 21 additions and 90 deletions
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111
src/Spinors/Spinors.jl
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@ -268,6 +268,11 @@ function gdagpmul(::Type{Pgamma{3,-1}}, g, a::Spinor{4,G}) where {NS,G}
end end
# dummy structs for dispatch:
# Basis of \\Gamma_n
struct Gamma{N}
end
""" """
dmul(n::Int64, a::Spinor) dmul(n::Int64, a::Spinor)
@ -293,96 +298,22 @@ indexing for Dirac basis ``\\Gamma_n``:
16 identity 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])
function dmul(n::Int64, a::Spinor{4,G}) where {NS,G} 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[2], -a.s[1])
if n == 1 then 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])
r1 = mimm(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]))
r2 = mimm(a.s[3]) 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])
r3 = imm(a.s[2]) 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]))
r4 = imm(a.s[1]) dmul(::Type{Gamma{9}}, a::Spinor{4,G}) where {G} = Spinor{4,G}( a.s[3], a.s[4], -a.s[2], -a.s[1])
elseif n == 2 then 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])
r1 = -a.s[4] 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]))
r2 = 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])
r3 = a.s[2] 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])
r4 = -a.s[1] 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])
elseif n == 3 then 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]))
r1 = mimm(a.s[3]) dmul(::Type{Gamma{16}}, a::Spinor{4,G}) where {G} = a
r2 = imm(a.s[4])
r3 = imm(a.s[1])
r4 = mimm(a.s[2])
elseif n == 4 then
r1 = -a.s[3]
r2 = -a.s[4]
r3 = -a.s[2]
r4 = -a.s[1]
elseif n == 5 then
r1 = a.s[1]
r2 = a.s[2]
r3 = -a.s[3]
r4 = -a.s[4]
elseif n == 6 then
r1 = imm(a.s[4])
r2 = imm(a.s[3])
r3 = imm(a.s[2])
r4 = imm(a.s[1])
elseif n == 7 then
r1 = a.s[4]
r2 = -a.s[3]
r3 = a.s[2]
r4 = -a.s[1]
elseif n == 8 then
r1 = imm(a.s[3])
r2 = mimm(a.s[4])
r3 = imm(a.s[1])
r4 = mimm(a.s[2])
elseif n == 9 then
r1 = a.s[3]
r2 = a.s[4]
r3 = -a.s[2]
r4 = -a.s[1]
elseif n == 10 then
r1 = a.s[2]
r2 = a.s[1]
r3 = -a.s[4]
r4 = -a.s[3]
elseif n == 11 then
r1 = mimm(a.s[2])
r2 = imm(a.s[1])
r3 = imm(a.s[4])
r4 = mimm(a.s[3])
elseif n == 12 then
r1 = a.s[1]
r2 = -a.s[2]
r3 = -a.s[3]
r4 = a.s[4]
elseif n == 13 then
r1 = -a.s[1]
r2 = a.s[2]
r3 = -a.s[3]
r4 = a.s[4]
elseif n == 14 then
r1 = -a.s[2]
r2 = -a.s[1]
r3 = -a.s[4]
r4 = -a.s[3]
elseif n == 15 then
r1 = imm(a.s[2])
r2 = mimm(a.s[1])
r3 = imm(a.s[4])
r4 = mimm(a.s[3])
elseif n == 16 then
r1 = a.s[1]
r2 = a.s[2]
r3 = a.s[3]
r4 = a.s[4]
end
return Spinor{4,G}((r1,r2,r3,r4))
end
export Spinor, Pgamma export Spinor, Pgamma
export norm, norm2, dot, imm, mimm export norm, norm2, dot, imm, mimm