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Addition of SU2fund

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This commit is contained in:
Fernando P. Panadero 2023-11-21 11:44:02 +01:00
parent d7e63ebdf2
commit 1b57d86c79
6 changed files with 131 additions and 9 deletions
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23
src/Dirac/Dirac.jl
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@ -54,14 +54,27 @@ struct DiracWorkspace{T}
function DiracWorkspace(::Type{G}, ::Type{T}, lp::SpaceParm{4,6,B,D}) where {G,T <: AbstractFloat, B,D} function DiracWorkspace(::Type{G}, ::Type{T}, lp::SpaceParm{4,6,B,D}) where {G,T <: AbstractFloat, B,D}
sr = scalar_field(Spinor{4,G}, lp) @timeit "Allocating DiracWorkspace" begin
sp = scalar_field(Spinor{4,G}, lp) if G == SU3fund
sAp = scalar_field(Spinor{4,G}, lp) sr = scalar_field(Spinor{4,G}, lp)
st = scalar_field(Spinor{4,G}, lp) sp = scalar_field(Spinor{4,G}, lp)
sAp = scalar_field(Spinor{4,G}, lp)
st = scalar_field(Spinor{4,G}, lp)
csw = tensor_field(U3alg{T},lp)
end
csw = tensor_field(U3alg{T},lp) if G == SU2fund
sr = scalar_field(Spinor{4,G}, lp)
sp = scalar_field(Spinor{4,G}, lp)
sAp = scalar_field(Spinor{4,G}, lp)
st = scalar_field(Spinor{4,G}, lp)
csw = tensor_field(U2alg{T},lp)
end
end
return new{T}(sr,sp,sAp,st,csw,cs) return new{T}(sr,sp,sAp,st,csw,cs)
end
end end
end end

20
src/Groups/AlgebraU2.jl Normal file
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@ -0,0 +1,20 @@
struct U2alg{T} <: Algebra
u11::T
u22::T
u12::Complex{T}
end
function antsym(a::SU2{T}) where T <: AbstractFloat
return U2alg{T}(2.0*imag(a.t1),-2.0*imag(a.t1),2.0*a.t2)
end
Base.:*(a::U2alg{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(im*a.u11*b.t1 + a.u12*b.t2,
-conj(a.u12)*b.t1 + im*a.u22*b.t2)
Base.:+(a::U2alg{T},b::U2alg{T}) where T <: AbstractFloat = U2alg{T}(a.u11 + b.u11, a.u22 + b.u22, a.u12 + b.u12)
Base.:*(r::Number, a::U2alg{T}) where T <: AbstractFloat = U2alg{T}(r*a.u11, r*a.u22, r*a.u12)

76
src/Groups/FundamentalSU2.jl Normal file
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@ -0,0 +1,76 @@
Base.zero(::Type{SU2fund{T}}) where T <: AbstractFloat = SU2fund{T}(zero(T),zero(T))
Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU2fund{T}}) where T <: AbstractFloat = SU2fund{T}(complex(randn(rng,T),randn(rng,T)),
complex(randn(rng,T),randn(rng,T)))
SU2fund(a::T, b::T) where T <: AbstractFloat = SU2fund{T}(complex(a), complex(b))
"""
dag(a::SU2fund{T})
Returns the conjugate of a fundamental element.
"""
dag(a::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(conj(a.t1), conj(a.t2))
"""
norm(a::SU2fund{T})
Returns the norm of a fundamental element. Same result as dot(a,a).
"""
norm(a::SU2fund{T}) where T <: AbstractFloat = sqrt((abs2(a.t1) + abs2(a.t2)))
"""
norm(a::SU2fund{T})
Returns the norm of a fundamental element. Same result as sqrt(dot(a,a)).
"""
norm2(a::SU2fund{T}) where T <: AbstractFloat = (abs2(a.t1) + abs2(a.t2))
"""
dot(a::SU2fund{T},b::SU2fund{T})
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.
"""
dot(g1::SU2fund{T},g2::SU2fund{T}) where T <: AbstractFloat = conj(g1.t1)*g2.t1+conj(g1.t2)*g2.t2
"""
*(g::SU2{T},b::SU2fund{T})
Returns ga
"""
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)
"""
\\(g::SU2{T},b::SU2fund{T})
Returns g^dag b
"""
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)
"""
*(a::SU2alg{T},b::SU2fund{T})
Returns a*b
"""
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,
complex(-a.t2,a.t1)*b.t1/2 + complex(0.0, -a.t3)*b.t1/2)
Base.:+(a::SU2fund{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(a.t1+b.t1,a.t2+b.t2)
Base.:-(a::SU2fund{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(a.t1-b.t1,a.t2-b.t2)
Base.:+(a::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(a.t1,a.t2)
Base.:-(a::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(-a.t1,-a.t2)
imm(a::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(complex(-imag(a.t1),real(a.t1)),
complex(-imag(a.t2),real(a.t2)))
mimm(a::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(complex(imag(a.t1),-real(a.t1)),
complex(imag(a.t2),-real(a.t2)))
# Operations with numbers
Base.:*(a::SU2fund{T},b::Number) where T <: AbstractFloat = SU2fund{T}(b*a.t1,b*a.t2)
Base.:*(b::Number,a::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(b*a.t1,b*a.t2)
Base.:/(a::SU2fund{T},b::Number) where T <: AbstractFloat = SU2fund{T}(a.t1/b,a.t2/b)
Base.:*(a::M2x2{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(a.u11*b.t1 + a.u12*b.t2,
a.u21*b.t1 + a.u22*b.t2)

7
src/Groups/Groups.jl
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@ -54,11 +54,12 @@ export Group, Algebra, GMatrix
# SU(2) and 2x2 matrix operations # SU(2) and 2x2 matrix operations
## ##
include("SU2Types.jl") include("SU2Types.jl")
export SU2, SU2alg, M2x2 export SU2, SU2alg, M2x2, SU2fund
include("GroupSU2.jl") include("GroupSU2.jl")
include("M2x2.jl") include("M2x2.jl")
include("AlgebraSU2.jl") include("AlgebraSU2.jl")
include("FundamentalSU2.jl")
## END SU(2) ## END SU(2)
## ##
@ -74,8 +75,10 @@ include("FundamentalSU3.jl")
export imm, mimm export imm, mimm
## END SU(3) ## END SU(3)
include("AlgebraU2.jl")
include("AlgebraU3.jl") include("AlgebraU3.jl")
export U3alg export U2alg, U3alg
include("GroupU1.jl") include("GroupU1.jl")
export U1, U1alg export U1, U1alg

10
src/Groups/SU2Types.jl
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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)
Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU2alg{T}}) where T <: AbstractFloat = SU2alg{T}(randn(rng,T),randn(rng,T),randn(rng,T)) Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU2alg{T}}) where T <: AbstractFloat = SU2alg{T}(randn(rng,T),randn(rng,T),randn(rng,T))
Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU2{T}}) where T <: AbstractFloat = exp(SU2alg{T}(randn(rng,T),randn(rng,T),randn(rng,T))) Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU2{T}}) where T <: AbstractFloat = exp(SU2alg{T}(randn(rng,T),randn(rng,T),randn(rng,T)))
struct SU2fund{T}
t1::Complex{T}
t2::Complex{T}
end
Base.zero(::Type{SU2fund{T}}) where T <: AbstractFloat = SU2fund{T}(zero(T),zero(T),zero(T))
Random.rand(rng::AbstractRNG, ::Random.SamplerType{SU2fund{T}}) where T <: AbstractFloat = SU2fund{T}(complex(randn(rng,T),randn(rng,T)),
complex(randn(rng,T),randn(rng,T)))

2
src/LatticeGPU.jl
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@ -16,7 +16,7 @@ include("Groups/Groups.jl")
using .Groups using .Groups
export Group, Algebra, GMatrix export Group, Algebra, GMatrix
export SU2, SU2alg, SU3, SU3alg, M3x3, M2x2, U1, U1alg, SU3fund, U3alg export SU2, SU2alg, SU3, SU3alg, M3x3, M2x2, U1, U1alg, SU3fund, U3alg, SU2fund, U2alg
export dot, expm, exp, dag, unitarize, inverse, tr, projalg, norm, norm2, isgroup, alg2mat, dev_one, antsym export dot, expm, exp, dag, unitarize, inverse, tr, projalg, norm, norm2, isgroup, alg2mat, dev_one, antsym
include("Space/Space.jl") include("Space/Space.jl")