mirror of
https://igit.ific.uv.es/alramos/latticegpu.jl.git
synced 2025-05-14 19:23:42 +02:00
Added basic support for Spinors and fields in fundamental rep.
This commit is contained in:
Alberto Ramos
parent
1ab51e0727
commit
cbdd0ec8fb
6 changed files with 366 additions and 8 deletions
78
src/Groups/FundamentalSU3.jl
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78
src/Groups/FundamentalSU3.jl
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@ -0,0 +1,78 @@
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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: FundamentalSU3.jl
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### created: Tue Nov 16 15:07:00 2021
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###
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SU3fund(a::T, b::T, c::T) where T <: AbstractFloat = SU3fund{T}(complex(a), complex(b), complex(c))
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"""
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norm(a::SU3fund{T})
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Returns the conjugate of a fundamental element.
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"""
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dag(a::SU3fund{T}) where T <: AbstractFloat = SU3fund{T}(conj(a.t1), conj(a.t2), conj(a.t3))
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"""
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norm2(a::SU3fund{T})
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Returns the norm squared of a fundamental element. Same result as dot(a,a).
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"""
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norm(a::SU3fund{T}) where T <: AbstractFloat = sqrt((abs2(a.t1) + abs2(a.t2) + abs2(a.t1)))
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"""
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norm(a::SU3fund{T})
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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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norm2(a::SU3fund{T}) where T <: AbstractFloat = (abs2(a.t1) + abs2(a.t2) + abs2(a.t1))
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"""
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dot(a::SU3fund{T},b::SU3fund{T})
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Returns the scalar product of two fundamental elements. The convention is for the product to the linear in the second argument, and anti-linear in the first argument.
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"""
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dot(g1::SU3fund{T},g2::SU3fund{T}) where T <: AbstractFloat = conj(g1.t1)*g2.t1+g1.t2*conj(g2.t2)+g1.t3*conj(g2.t3)
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"""
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*(g::SU3{T},b::SU3fund{T})
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Returns ga
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"""
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Base.:*(g::SU3{T},b::SU3fund{T}) where T <: AbstractFloat = SU3fund{T}(g.u11*b.t1 + g.u12*b.t2 + g.u13*b.t3,
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g.u21*b.t1 + g.u22*b.t2 + g.u23*b.t3,
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conj(g.u12*g.u23 - g.u13*g.u22)*b.t1 +
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conj(g.u13*g.u21 - g.u11*g.u23)*b.t2 +
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conj(g.u11*g.u22 - g.u12*g.u21)*b.t3)
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"""
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\(g::SU3{T},b::SU3fund{T})
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Returns g^dag b
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"""
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Base.:\(a::SU3{T},b::SU3fund{T}) where T <: AbstractFloat = SU3fund{T}(conj(g.u11)*b.t1 + conj(g.u21)*b.t2 + (a.u12*a.u23 - a.u13*a.u22)*b.t3,
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conj(g.u12)*b.t1 + conj(g.u22)*b.t2 + (a.u13*a.u21 - a.u11*a.u23)*b.t3,
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conj(g.u13)*b.t1 + conj(g.u23)*b.t2 + (a.u11*a.u22 - a.u12*a.u21)*b.t3)
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Base.:+(a::SU3fund{T},b::SU3fund{T}) where T <: AbstractFloat = SU3fund{T}(a.t1+b.t1,a.t2+b.t2,a.t3+b.t3)
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Base.:-(a::SU3fund{T},b::SU3fund{T}) where T <: AbstractFloat = SU3fund{T}(a.t1-b.t1,a.t2-b.t2,a.t3-b.t3)
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Base.:+(a::SU3fund{T}) where T <: AbstractFloat = SU3fund{T}(a.t1,a.t2,a.t3)
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Base.:-(a::SU3fund{T}) where T <: AbstractFloat = SU3fund{T}(-a.t1,-a.t2,-a.t3)
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imm(a::SU3fund{T}) where T <: AbstractFloat = SU3fund{T}(complex(-imag(a.t1),real(a.t1)),
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complex(-imag(a.t2),real(a.t2)),
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complex(-imag(a.t3),real(a.t3)))
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mimm(a::SU3fund{T}) where T <: AbstractFloat = SU3fund{T}(complex(imag(a.t1),-real(a.t1)),
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complex(imag(a.t2),-real(a.t2)),
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complex(imag(a.t3),-real(a.t3)))
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# Operations with numbers
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Base.:*(a::SU3fund{T},b::Number) where T <: AbstractFloat = SU3fund{T}(b*a.t1,b*a.t2,b*a.t3)
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Base.:*(b::Number,a::SU3fund{T}) where T <: AbstractFloat = SU3fund{T}(b*a.t1,b*a.t2,b*a.t3)
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Base.:/(a::SU3fund{T},b::Number) where T <: AbstractFloat = SU3fund{T}(a.t1/b,a.t2/b,a.t3/b)
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@ -41,6 +41,7 @@ export SU3, SU3alg, M3x3
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include("GroupSU3.jl")
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include("M3x3.jl")
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include("AlgebraSU3.jl")
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include("FundamentalSU3.jl")
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## END SU(3)
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include("GroupU1.jl")
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@ -57,4 +57,10 @@ end
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Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU3{T}}) where T <: AbstractFloat = exp(SU3alg{T}(randn(rng,T),randn(rng,T),randn(rng,T),randn(rng,T),randn(rng,T),randn(rng,T),randn(rng,T),randn(rng,T)))
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Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU3alg{T}}) where T <: AbstractFloat = SU3alg{T}(randn(rng,T),randn(rng,T),randn(rng,T),randn(rng,T),randn(rng,T),randn(rng,T),randn(rng,T),randn(rng,T))
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struct SU3fund{T}
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t1::Complex{T}
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t2::Complex{T}
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t3::Complex{T}
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end
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Base.zero(::Type{SU3fund{T}}) where T <: AbstractFloat = SU3fund{T}(zero(T),zero(T),zero(T))
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@ -16,7 +16,7 @@ include("Groups/Groups.jl")
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using .Groups
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export Group, Algebra
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export SU2, SU2alg, SU3, SU3alg, M3x3, M2x2, U1, U1alg
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export SU2, SU2alg, SU3, SU3alg, M3x3, M2x2, U1, U1alg, SU3fund
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export dot, expm, exp, dag, unitarize, inverse, tr, projalg, norm, norm2, isgroup, alg2mat, dev_one
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include("Space/Space.jl")
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@ -47,4 +47,11 @@ export flw, flw_adapt
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export sfcoupling, bndfield, setbndfield
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export import_lex64, import_cern64
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include("Spinors/Spinor.jl")
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using .Spinors
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export Pgamma
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export norm, norm2, dot, imm, mimm
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export pmul, gpmul, gdagpmul
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end # module
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267
src/Spinors/Spinors.jl
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267
src/Spinors/Spinors.jl
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@ -0,0 +1,267 @@
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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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||||
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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]))
|
||||
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}
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|
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r1 = g\(a.s[1]-imm(a.s[3]))
|
||||
r2 = g\(a.s[2]+imm(a.s[4]))
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return Spinor{4,G}((r1,r2,imm(r1),mimm(r2)))
|
||||
end
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|
|
@ -33,11 +33,10 @@ function sfcoupling(U, lp::SpaceParm{N,M,B,D}, gp::GaugeParm, ymws::YMworkspace)
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end
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|
||||
tp = ntuple(i->i, N-1)
|
||||
V3 = prod(lp.iL[1:end-1])
|
||||
tmp .= reshape(Array(CUDA.reduce(+, ymws.rm;dims=tp)),lp.iL[end])
|
||||
|
||||
dsdeta = (gp.cG[1]*gp.beta/(2*gp.ng*V3))*(tmp[1] + tmp[end])
|
||||
ddnu = (gp.cG[1]*gp.beta/(2*gp.ng*V3))*(tmp[2] + tmp[end-1])
|
||||
dsdeta = (gp.cG[1]*gp.beta/(2*gp.ng))*(tmp[1] + tmp[end])
|
||||
ddnu = (gp.cG[1]*gp.beta/(2*gp.ng))*(tmp[2] + tmp[end-1])
|
||||
end
|
||||
|
||||
return dsdeta, ddnu
|
||||
|
|
@ -59,8 +58,8 @@ function krnl_sfcoupling!(rm, U::AbstractArray{T}, Ubnd, lp::SpaceParm{N,M,B,D})
|
|||
bu, ru = up((b,r), id, lp)
|
||||
|
||||
X = projalg(U[b,id,r]*U[bu,N,ru]/(U[b,N,r]*U[but,id,rut]))
|
||||
rm[I] += 3*X.t7 + SR3 * X.t8
|
||||
rm[IU] += 2*X.t7 - SR3x2 * X.t8
|
||||
rm[I] += (3*X.t7 + SR3 * X.t8)/lp.iL[id]
|
||||
rm[IU] += (2*X.t7 - SR3x2 * X.t8)/lp.iL[id]
|
||||
end
|
||||
elseif (it == lp.iL[end])
|
||||
bdt, rdt = up((b,r), N, lp)
|
||||
|
|
@ -69,8 +68,8 @@ function krnl_sfcoupling!(rm, U::AbstractArray{T}, Ubnd, lp::SpaceParm{N,M,B,D})
|
|||
bu, ru = up((b,r), id, lp)
|
||||
|
||||
X = projalg(Ubnd[id]/(U[b,id,r]*U[bu,N,ru])*U[b,N,r])
|
||||
rm[I] -= 3*X.t7 + SR3 * X.t8
|
||||
rm[ID] += 2*X.t7 - SR3x2 * X.t8
|
||||
rm[I] -= (3*X.t7 + SR3 * X.t8)/lp.iL[id]
|
||||
rm[ID] += (2*X.t7 - SR3x2 * X.t8)/lp.iL[id]
|
||||
end
|
||||
end
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue