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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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src/Groups/FundamentalSU2.jl Normal file
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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)