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Addition of SU2fund
This commit is contained in:
Fernando P. Panadero
parent
d7e63ebdf2
commit
1b57d86c79
6 changed files with 131 additions and 9 deletions
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@ -54,14 +54,27 @@ struct DiracWorkspace{T}
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function DiracWorkspace(::Type{G}, ::Type{T}, lp::SpaceParm{4,6,B,D}) where {G,T <: AbstractFloat, B,D}
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sr = scalar_field(Spinor{4,G}, lp)
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sp = scalar_field(Spinor{4,G}, lp)
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sAp = scalar_field(Spinor{4,G}, lp)
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st = scalar_field(Spinor{4,G}, lp)
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csw = tensor_field(U3alg{T},lp)
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@timeit "Allocating DiracWorkspace" begin
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if G == SU3fund
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sr = scalar_field(Spinor{4,G}, lp)
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sp = scalar_field(Spinor{4,G}, lp)
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sAp = scalar_field(Spinor{4,G}, lp)
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st = scalar_field(Spinor{4,G}, lp)
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csw = tensor_field(U3alg{T},lp)
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end
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if G == SU2fund
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sr = scalar_field(Spinor{4,G}, lp)
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sp = scalar_field(Spinor{4,G}, lp)
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sAp = scalar_field(Spinor{4,G}, lp)
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st = scalar_field(Spinor{4,G}, lp)
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csw = tensor_field(U2alg{T},lp)
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end
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end
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return new{T}(sr,sp,sAp,st,csw,cs)
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end
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end
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end
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20
src/Groups/AlgebraU2.jl
Normal file
20
src/Groups/AlgebraU2.jl
Normal file
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@ -0,0 +1,20 @@
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struct U2alg{T} <: Algebra
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u11::T
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u22::T
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u12::Complex{T}
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end
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function antsym(a::SU2{T}) where T <: AbstractFloat
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return U2alg{T}(2.0*imag(a.t1),-2.0*imag(a.t1),2.0*a.t2)
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end
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Base.:*(a::U2alg{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(im*a.u11*b.t1 + a.u12*b.t2,
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-conj(a.u12)*b.t1 + im*a.u22*b.t2)
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Base.:+(a::U2alg{T},b::U2alg{T}) where T <: AbstractFloat = U2alg{T}(a.u11 + b.u11, a.u22 + b.u22, a.u12 + b.u12)
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Base.:*(r::Number, a::U2alg{T}) where T <: AbstractFloat = U2alg{T}(r*a.u11, r*a.u22, r*a.u12)
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76
src/Groups/FundamentalSU2.jl
Normal file
76
src/Groups/FundamentalSU2.jl
Normal file
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@ -0,0 +1,76 @@
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Base.zero(::Type{SU2fund{T}}) where T <: AbstractFloat = SU2fund{T}(zero(T),zero(T))
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Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU2fund{T}}) where T <: AbstractFloat = SU2fund{T}(complex(randn(rng,T),randn(rng,T)),
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complex(randn(rng,T),randn(rng,T)))
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SU2fund(a::T, b::T) where T <: AbstractFloat = SU2fund{T}(complex(a), complex(b))
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"""
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dag(a::SU2fund{T})
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Returns the conjugate of a fundamental element.
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"""
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dag(a::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(conj(a.t1), conj(a.t2))
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"""
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norm(a::SU2fund{T})
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Returns the norm of a fundamental element. Same result as dot(a,a).
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"""
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norm(a::SU2fund{T}) where T <: AbstractFloat = sqrt((abs2(a.t1) + abs2(a.t2)))
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"""
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norm(a::SU2fund{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::SU2fund{T}) where T <: AbstractFloat = (abs2(a.t1) + abs2(a.t2))
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"""
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dot(a::SU2fund{T},b::SU2fund{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::SU2fund{T},g2::SU2fund{T}) where T <: AbstractFloat = conj(g1.t1)*g2.t1+conj(g1.t2)*g2.t2
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"""
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*(g::SU2{T},b::SU2fund{T})
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Returns ga
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"""
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Base.:*(g::SU2{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(g.t1*b.t1 + g.t2*b.t2,-conj(g.t2)*b.t1 + conj(g.t1)*b.t2)
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"""
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\\(g::SU2{T},b::SU2fund{T})
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Returns g^dag b
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"""
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Base.:\(g::SU2{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(conj(g.t1)*b.t1 - g.t2 * b.t2,conj(g.t2)*b.t1 + g.t1 * b.t2)
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"""
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*(a::SU2alg{T},b::SU2fund{T})
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Returns a*b
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"""
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Base.:*(a::SU2alg{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(complex(0.0, a.t3)*b.t1/2 + complex(a.t2,a.t1)*b.t2/2,
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complex(-a.t2,a.t1)*b.t1/2 + complex(0.0, -a.t3)*b.t1/2)
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Base.:+(a::SU2fund{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(a.t1+b.t1,a.t2+b.t2)
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Base.:-(a::SU2fund{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(a.t1-b.t1,a.t2-b.t2)
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Base.:+(a::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(a.t1,a.t2)
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Base.:-(a::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(-a.t1,-a.t2)
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imm(a::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(complex(-imag(a.t1),real(a.t1)),
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complex(-imag(a.t2),real(a.t2)))
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mimm(a::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(complex(imag(a.t1),-real(a.t1)),
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complex(imag(a.t2),-real(a.t2)))
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# Operations with numbers
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Base.:*(a::SU2fund{T},b::Number) where T <: AbstractFloat = SU2fund{T}(b*a.t1,b*a.t2)
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Base.:*(b::Number,a::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(b*a.t1,b*a.t2)
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Base.:/(a::SU2fund{T},b::Number) where T <: AbstractFloat = SU2fund{T}(a.t1/b,a.t2/b)
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Base.:*(a::M2x2{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(a.u11*b.t1 + a.u12*b.t2,
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a.u21*b.t1 + a.u22*b.t2)
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@ -54,11 +54,12 @@ export Group, Algebra, GMatrix
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# SU(2) and 2x2 matrix operations
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##
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include("SU2Types.jl")
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export SU2, SU2alg, M2x2
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export SU2, SU2alg, M2x2, SU2fund
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include("GroupSU2.jl")
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include("M2x2.jl")
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include("AlgebraSU2.jl")
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include("FundamentalSU2.jl")
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## END SU(2)
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##
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@ -74,8 +75,10 @@ include("FundamentalSU3.jl")
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export imm, mimm
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## END SU(3)
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include("AlgebraU2.jl")
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include("AlgebraU3.jl")
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export U3alg
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export U2alg, U3alg
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include("GroupU1.jl")
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export U1, U1alg
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@ -53,3 +53,13 @@ Base.convert(::Type{M2x2{T}}, a::SU2{T}) where T = M2x2{T}(a.t1,a.t2,-conj(a.t2)
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Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU2alg{T}}) where T <: AbstractFloat = SU2alg{T}(randn(rng,T),randn(rng,T),randn(rng,T))
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Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU2{T}}) where T <: AbstractFloat = exp(SU2alg{T}(randn(rng,T),randn(rng,T),randn(rng,T)))
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struct SU2fund{T}
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t1::Complex{T}
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t2::Complex{T}
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end
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Base.zero(::Type{SU2fund{T}}) where T <: AbstractFloat = SU2fund{T}(zero(T),zero(T),zero(T))
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Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU2fund{T}}) where T <: AbstractFloat = SU2fund{T}(complex(randn(rng,T),randn(rng,T)),
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complex(randn(rng,T),randn(rng,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, GMatrix
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export SU2, SU2alg, SU3, SU3alg, M3x3, M2x2, U1, U1alg, SU3fund, U3alg
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export SU2, SU2alg, SU3, SU3alg, M3x3, M2x2, U1, U1alg, SU3fund, U3alg, SU2fund, U2alg
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export dot, expm, exp, dag, unitarize, inverse, tr, projalg, norm, norm2, isgroup, alg2mat, dev_one, antsym
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include("Space/Space.jl")
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