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Added basic support for Spinors and fields in fundamental rep.

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This commit is contained in:
Alberto Ramos 2021-11-18 13:37:32 +01:00
parent 1ab51e0727
commit cbdd0ec8fb
6 changed files with 366 additions and 8 deletions
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78
src/Groups/FundamentalSU3.jl Normal file
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@ -0,0 +1,78 @@
###
### "THE BEER-WARE LICENSE":
### Alberto Ramos wrote this file. As long as you retain this
### notice you can do whatever you want with this stuff. If we meet some
### day, and you think this stuff is worth it, you can buy me a beer in
### return. <alberto.ramos@cern.ch>
###
### file: FundamentalSU3.jl
### created: Tue Nov 16 15:07:00 2021
###
SU3fund(a::T, b::T, c::T) where T <: AbstractFloat = SU3fund{T}(complex(a), complex(b), complex(c))
"""
norm(a::SU3fund{T})
Returns the conjugate of a fundamental element.
"""
dag(a::SU3fund{T}) where T <: AbstractFloat = SU3fund{T}(conj(a.t1), conj(a.t2), conj(a.t3))
"""
norm2(a::SU3fund{T})
Returns the norm squared of a fundamental element. Same result as dot(a,a).
"""
norm(a::SU3fund{T}) where T <: AbstractFloat = sqrt((abs2(a.t1) + abs2(a.t2) + abs2(a.t1)))
"""
norm(a::SU3fund{T})
Returns the norm of a fundamental element. Same result as sqrt(dot(a,a)).
"""
norm2(a::SU3fund{T}) where T <: AbstractFloat = (abs2(a.t1) + abs2(a.t2) + abs2(a.t1))
"""
dot(a::SU3fund{T},b::SU3fund{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::SU3fund{T},g2::SU3fund{T}) where T <: AbstractFloat = conj(g1.t1)*g2.t1+g1.t2*conj(g2.t2)+g1.t3*conj(g2.t3)
"""
*(g::SU3{T},b::SU3fund{T})
Returns ga
"""
Base.:*(g::SU3{T},b::SU3fund{T}) where T <: AbstractFloat = SU3fund{T}(g.u11*b.t1 + g.u12*b.t2 + g.u13*b.t3,
g.u21*b.t1 + g.u22*b.t2 + g.u23*b.t3,
conj(g.u12*g.u23 - g.u13*g.u22)*b.t1 +
conj(g.u13*g.u21 - g.u11*g.u23)*b.t2 +
conj(g.u11*g.u22 - g.u12*g.u21)*b.t3)
"""
\(g::SU3{T},b::SU3fund{T})
Returns g^dag b
"""
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,
conj(g.u12)*b.t1 + conj(g.u22)*b.t2 + (a.u13*a.u21 - a.u11*a.u23)*b.t3,
conj(g.u13)*b.t1 + conj(g.u23)*b.t2 + (a.u11*a.u22 - a.u12*a.u21)*b.t3)
Base.:+(a::SU3fund{T},b::SU3fund{T}) where T <: AbstractFloat = SU3fund{T}(a.t1+b.t1,a.t2+b.t2,a.t3+b.t3)
Base.:-(a::SU3fund{T},b::SU3fund{T}) where T <: AbstractFloat = SU3fund{T}(a.t1-b.t1,a.t2-b.t2,a.t3-b.t3)
Base.:+(a::SU3fund{T}) where T <: AbstractFloat = SU3fund{T}(a.t1,a.t2,a.t3)
Base.:-(a::SU3fund{T}) where T <: AbstractFloat = SU3fund{T}(-a.t1,-a.t2,-a.t3)
imm(a::SU3fund{T}) where T <: AbstractFloat = SU3fund{T}(complex(-imag(a.t1),real(a.t1)),
complex(-imag(a.t2),real(a.t2)),
complex(-imag(a.t3),real(a.t3)))
mimm(a::SU3fund{T}) where T <: AbstractFloat = SU3fund{T}(complex(imag(a.t1),-real(a.t1)),
complex(imag(a.t2),-real(a.t2)),
complex(imag(a.t3),-real(a.t3)))
# Operations with numbers
Base.:*(a::SU3fund{T},b::Number) where T <: AbstractFloat = SU3fund{T}(b*a.t1,b*a.t2,b*a.t3)
Base.:*(b::Number,a::SU3fund{T}) where T <: AbstractFloat = SU3fund{T}(b*a.t1,b*a.t2,b*a.t3)
Base.:/(a::SU3fund{T},b::Number) where T <: AbstractFloat = SU3fund{T}(a.t1/b,a.t2/b,a.t3/b)

1
src/Groups/Groups.jl
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@ -41,6 +41,7 @@ export SU3, SU3alg, M3x3
include("GroupSU3.jl")
include("M3x3.jl")
include("AlgebraSU3.jl")
include("FundamentalSU3.jl")
## END SU(3)
include("GroupU1.jl")

6
src/Groups/SU3Types.jl
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@ -57,4 +57,10 @@ end
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)))
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))
struct SU3fund{T}
t1::Complex{T}
t2::Complex{T}
t3::Complex{T}
end
Base.zero(::Type{SU3fund{T}}) where T <: AbstractFloat = SU3fund{T}(zero(T),zero(T),zero(T))