def F(w0, qbp, qb, wt, rt, tb, t, w0p, qp, q):
"""
Calculates the F coefficient for full calculation
rbp, rb come from initila unit tensor
"""
f1 = 0
f2 = 0
if (qp, q) == (qbp + tb, qb - t):
f1 = (
math.sqrt(
utils.choose(qp, tb) * utils.choose(qb, t)
#(1.
#*math.factorial(qp)
#*math.factorial(qb)
#/math.factorial(qbp)
#/math.factorial(tb)
#/math.factorial(q)
#/math.factorial(t)
) * u3.coupling_9lm(SU3State(0, tb), SU3State(0, t), wt.conj(), 1,
SU3State(qp, 0), SU3State(0, q), w0p, 1,
SU3State(qbp, 0), SU3State(0, qb), w0, 1, 1, 1,
rt))
if ((qp, q) == (qbp + tb + t, qb)) and (wt.su3 == SU3State(t + tb, 0)):
f2 = (math.sqrt(1. * math.factorial(qp) / math.factorial(t) /
math.factorial(tb) / math.factorial(qbp)) *
u3.U(SU3State(0, t + tb), SU3State(qp, 0), w0, SU3State(0, qb),
SU3State(qbp, 0), 1, 1, w0p, 1, 1))
fcoef = f1 - f2
return fcoef
def C_n(psipred, psired, r0=1):
"""
Matrix element of C acting on the raising polynomial space
"""
matrix = 0.0
n = psired.n
np = psipred.n
if np == n:
s = psired.s
r = psired.r
w = psired.w
rp = psipred.r
wp = psipred.w
matrix = u3.U(s, n, wp, SU3State(1, 1), w, r, r0, n, 1,
rp) * u3.C_su3(n)
return matrix
def C_n_conj(psipred, psired, r0=1):
"""
Conjugate matrix element of Cn_weylboson
"""
matrix = 0.0
n = psired.n
np = psipred.n
if np == n:
s = psired.s
r = psired.r
w = psired.w
rp = psipred.r
wp = psipred.w
matrix = utils.parity(w.pt() - wp.pt()) * numpy.sqrt(
w.dim() / wp.dim()) * u3.U(s, n, w, SU3State(1, 1), wp, rp, 1, n,
1, r) * u3.C_su3(n)
return matrix
def P(n0, psipred, psired, r0):
"""
Calculates the matrix element of the polynomial of A's with u3 character n0
args:
n0 is U(3) symmetry of polynomial (U3State class)
psipred,psired are reduced basis states (SpStateReduced class)
r0 is outer multiplicity of psired.wxA->psipred.w
returns:
prme which is the reduced matrix element of P (float)
"""
# if (n0,psipred,psired,r0) in Pdic:
# prme=Pdic[n0,psipred,psired,r0]
# else:
prme = 0
## Calculate the K matrix element and generating index list
K, nitr = kmatrix(psired.s, psired.w)
## inverting the K matrix
Kinv = K**(-1)
## calculating the Kp matrix and generating index list
Kp, npitr = kmatrix(psipred.s, psipred.w)
## obtaining index of psired.n,psired.r in K matrix
i = nitr[psired.n, psired.r]
## obtaining index of psipred.n,psipred.r in Kp matrix
ip = npitr[psipred.n, psipred.r]
# suming over index values of n1,r1 in K matrix
for n1, r1, in nitr:
## obtaining index of n1,r1 in K matrix
j = nitr[n1, r1]
# suming over index values of n1p,r1p in Kp matrix
for n1p, r0p in npitr:
## obtaining index of n1p,r1p in Kp matrix
jp = npitr[n1p, r0p]
## Calculating the max multiplicity of sxn1p->wp
r1pmax = u3.mult(n0, n1, n1p)
## summing over multiplicity
for r1p in range(1, r1pmax + 1):
##calculating RME of P
prme = prme + (Kinv[i, j] * u3.U(
n0, n1, psipred.w, psired.s, n1p, r1p, r0p, psired.w, r1,
r0) * coef.bcoef(n0, n1, n1p, r1p) * Kp[ip, jp])
#Pdic[n0,psipred,psired,r0]=prme
return prme
def C_s1(psi2red, psi1red, r0=1):
matrix = 0.0
if psi2red.check() and psi1red.check():
n1 = psi1red.n
n2 = psi2red.n
if n2 == n1:
s = psi1red.s
w1 = psi1red.w
r1 = psi1red.r
w2 = psi2red.w
r2 = psi2red.r
mult1max = u3.mult(s, n1, w1)
mult2max = u3.mult(s, n2, w2)
for r1p in range(1, mult1max + 1):
for r2p in range(1, mult2max + 1):
matrix = matrix + (u3.phi(s, n1, w1, r1, r1p) * u3.phi(
n1, s, w2, r2, r2p) * u3.U(n1, s, w2, SU3State(
1, 1), w1, r1p, r0, s, 1, r2p) * u3.C_su3(s))
return matrix
def CoupledOperators_Sp3R(operator1, operator2, w0, r0, psi2, psi1, r0p):
s = psi1.s
w1 = psi1.w
n1 = psi1.n
r1 = psi1.r
w2 = psi2.w
n2 = psi2.n
r2 = psi2.r
matrix = 0.0
m1 = 0
m2 = 0
m3 = 0
if (w1.N + operator1.u3.N + operator2.u3.N) != w2.N:
return matrix
#coupling w to first tensor
#Checking if operators are C operators and restricting w12 accordingly
w12set = u3.couple(w1, operator2.u3)
r1max = u3.mult(s, n1, w1)
r2max = u3.mult(s, n2, w2)
for lambdamu12 in w12set:
mult1 = u3.mult(lambdamu12, operator1.u3, w2)
#mult1=min(mult1max,r2max)
if mult1 == 0:
continue
mult2 = w12set[lambdamu12]
#mult2=min(mult2max, r1max)
w12 = U3State(w1.N + operator2.u3.N, lambdamu12)
n12set = u3boson.nlist(s, w12)
if n12set == {}:
continue
for n12 in n12set:
r12max = n12set[n12]
#mult2=min(mult2max,r12max)
for r12 in range(1, r12max + 1):
psi12 = SpStateReduced(s, n12, r12, w12)
for r1p in range(1, mult1 + 1):
for r2p in range(1, mult2 + 1):
matrix = matrix + (u3.U(
w1, operator2.u3, w2, operator1.u3, w12, r2p, r1p,
w0, r0, r0p) * operator1.SU3RME(psi2, psi12, r1p) *
operator2.SU3RME(psi12, psi1, r2p))
return matrix
def A(psipred, psired, r0=1):
"""
Calculates (s np rp wp||a^\dagger|s n r w)
Args:
s: symplectic bandhead. u3 class variable.
np: U(3) label for raising polynomial of final state. u3 class var.
rp: SU(3) outer multiplicity of s x np -> wp. Integer var.
wp: U(3) label for symplectic weight of final state. u3 class var
n: U(3) label for raising polynomail of initial state. U2 class var.
r: SU(3) outer mult. of s x n ->w. Integer var.
w: U(3) label for symplectic weight of initial state. u3 class var.
Returns:
Matrix element (s np rp wp||a^\dagger|s n r w). For example
wp=u3([22,15,10])
np=u3([4,0,0])
rp=1
w=u3([21,14,10])
n=u3([2,0,0])
r=1
s=u3([20,13,10])
A_weylboson(s,np,rp,wp,n,r,w)
returns
1.12687233964
"""
matrix = 0.0
if r0 == 1:
s = psired.s
n = psired.n
r = psired.r
w = psired.w
np = psipred.n
rp = psipred.r
wp = psipred.w
matrix = u3.U(s, n, wp, SU3State(2, 0), w, r, 1, np, 1, rp) * A_n(
np, n)
return matrix
def ccoef(n, q, np):
"""
Calculates the C coefficients in the expansion of the raising polynomial into a single jacobi particle and remaining jacobi particles
nbx(q,0)->n
Args:
q: even int
n, nb: U3State or SU3State class variables
Returns:
Coef, for example
CCoef(10,6,2,2,4,2)
returns
1.96396101212
"""
if (n, q, np) in Cdict:
Coef = Cdict[n, q, np]
else:
####################################################################
N = n.N
lbdaN = n.su3.lbda
muN = n.su3.mu
Coef = 0.0
## base case
if q == 0:
if n == np:
Coef = 1
##recursion relation
else:
## special case
if n.su3 == SU3State(N, 0):
if SU3State(N - q, 0) == np.su3:
Coef = math.sqrt(
math.factorial(N / 2) * math.factorial(q) /
(math.factorial(N / 2 - q / 2) * 2**
(q / 2))) / math.factorial(q / 2)
## recurance
else:
[m1, m2, m3] = n.cartesian()
n2list = []
if (m1 - 2) >= m2:
nb = U3State([m1 - 2, m2, m3])
elif (m2 - 2) >= m3:
nb = U3State([m1, m2 - 2, m3])
elif (m3 - 2) >= 0:
nb = U3State([m1, m2, m3 - 2])
else:
return 0.0
coef1 = ccoef(nb, q - 2, np) * u3.U(SU3State(
2, 0), SU3State(q - 2, 0), n, np, SU3State(
q, 0), 1, 1, nb, 1, 1) * math.sqrt(q * (q - 1) / 2.)
## coef2
coef2 = 0
[m1, m2, m3] = np.cartesian()
## obtain list of possible n2's
if (m1 - 2) >= m2:
n2list.append(U3State([m1 - 2, m2, m3]))
if (m2 - 2) >= m3:
n2list.append(U3State([m1, m2 - 2, m3]))
if (m3 - 2) >= 0:
n2list.append(U3State([m1, m2, m3 - 2]))
## sum over possible n2's
for n2 in n2list:
coef2 = coef2 + u3boson.A_n(np, n2) * ccoef(
nb, q, n2) * u3.Z(SU3State(q, 0), n2, n, SU3State(
2, 0), nb, 1, 1, np, 1, 1)
#print n,nb
Coef = (coef1 + coef2) / u3boson.A_n(n, nb)
#################################################################
Cdict[n, q, np] = Coef
return Coef
def bcoef(n1, n2, n3, r):
"""
Calculates the B coefficient needed for the coupling of two symplectic raising polynomials
Args:
n1, n2, n3: U3State class variable
r: integers, coupling multiplicity of n1xn2->n3
Returns:
b coefficient. For example,
n1=U3State([2,2,0])
n2=U3State([2,2,0])
n3=U3State([4,2,2])
bcoef(n1,n2,n3,1)
returns
1.63299316186
"""
#Should probably check that the elements in the su3lib table are correct if we get multiplicity
if (n1, n2, n3, r) in bdict:
coef = bdict[n1, n2, n3, r]
else:
nset = []
coef = 0.0
n0 = U3State([0, 0, 0])
#I'm not sure why I had if n3p==[0,0,0], so I'm eliminating it for now.
#if n1 or n2 is 0(0,0) then coefficient is trivial
if n1 == n0 or n2 == n0:
coef = 1
else:
rmax = u3.mult(n1, n2, n3)
m1 = n3.one()
m2 = n3.two()
m3 = n3.three()
if (m1 - 2) >= m2:
nset.append(U3State([m1 - 2, m2, m3]))
if (m2 - 2) >= m3:
nset.append(U3State([m1, m2 - 2, m3]))
if (m3 - 2) >= 0:
nset.append(U3State([m1, m2, m3 - 2]))
t1 = n1.one()
t2 = n1.two()
t3 = n1.three()
if (t1 - 2) >= t2:
n1p = U3State([t1 - 2, t2, t3])
else:
if (t2 - 2) >= t3:
n1p = U3State([t1, t2 - 2, t3])
else:
if (t3 - 2) >= 0:
n1p = U3State([t1, t2, t3 - 2])
else:
print("n1 not valid")
n1p = 0
for np in nset:
rpmax = u3.mult(n1p, n2, np)
for rp in range(1, rpmax + 1):
#print SU3State(2,0),n1p,n3,n2,n1,1,r,np,rp,1
coef = coef + u3boson.A_n(
n3, np) * bcoef(n1p, n2, np, rp) * u3.U(
SU3State(2, 0), n1p, n3, n2, n1, 1, r, np, rp, 1)
coef = coef / u3boson.A_n(n1, n1p)
bdict[n1, n2, n3, r] = coef
return coef
