def W(w1, k1, L1, w2, k2, L2, w3, k3, L3, r, c1=0, c2=0, c3=0):
"""
Calculates the SO(3) reduced SU(3) wigner coupling coefficients
Note
"""
W = 0.0
if (c1 + c2 + c3) == 0:
wdic = Wreduced_su3_dic(w1, L1, w2, L2, w3, L3)
######add conjugate
#print wdic
if (r, k1, k2, k3) in wdic:
W = wdic[r, k1, k2, k3]
if (c1, c2, c3) == (1, 0, 0):
rpmax = mult(w1, w2, w3)
wdic = Wreduced_su3_dic(w3, L3, w1.conj(), L1, w2, L2)
for rp in range(1, rpmax + 1):
W = W + (utils.parity(w2.pt() - w3.pt()) * phi(w1, w2, w3, r, rp) *
numpy.sqrt(w3.dim() / w2.dim()) * wdic[rp, k3, k1, k2])
if (c1, c2, c3) == (0, 1, 0):
wdic = Wreduced_su3_dic(w3, L3, w2.conj(), L2, w1, L1)
if (r, k3, k2, k1) in wdic:
W = (utils.parity(w1.pt() - w3.pt() + L1 + L2 - L3) *
numpy.sqrt(w3.dim() / w1.dim()) * wdic[r, k3, k2, k1])
if (c1, c2, c3) == (0, 0, 1):
print "unfinished code"
if (c1 + c2 + c3) >= 2:
print "unfinished code"
if abs(W) < 10**(-10):
W = 0.0
return W
def B_asymptotic(psi2red, psi1red, r0=1):
"""
Calculates the asymptotic approximation of the RME of B in the symplectic basis
args:
psi2red,psi1red are reduced symplectic basis states (SpStateReduced class)
r0 is outer multiplicity of psi1redxB->psi2red
Example:
s=U3State([20,13,10])
wp=U3State([22,15,10])
np=U3State([4,0,0])
rp=1
w=U3State([21,14,10])
n=U3State([2,0,0])
r=1
psipred=SpStateReduced(s,np,rp,wp)
psired=SpStateReduced(s,n,r,w)
B(psired, psipred) returns
-7.13059078469
"""
matrix = 0.0
#check that outer multiplicity is 1, else RME=0
if r0 == 1:
w1 = psi1red.w
w2 = psi2red.w
#calculate the RME
matrix = utils.parity(w1.pt() + w2.pt()) * numpy.sqrt(
w1.dim() / w2.dim()) * A_asymptotic(psi1red, psi2red)
return matrix
def B2(psi2red, psi1red, r0=1):
"""
Alternative method for calculating exact RME of B in the symplectic basis using exact RME of A in symplectic basis
args:
psi2red, psi1red are reduced symplectic basis states (SpStateReduced class)
r0 is outer multiplicity of psi1redxB->psi2red (int=1)
Example:
s=U3([20,13,10])
wp=U3([22,15,10])
np=U3([4,0,0])
rp=1
w=U3([21,14,10])
n=U3([2,0,0])
r=1
psipred=SpStateReduced(s,np,rp,wp)
psired=SpStateReduced(s,n,r,w)
B(psipred,psired) returns
-5.51771905958
"""
matrix = 0.0
#check that outer mutliplicity is 1, else RME=0
if r0 == 1:
w1 = psi1red.w
w2 = psi2red.w
#calculate RME
matrix = utils.parity(w1.pt() + w2.pt()) * numpy.sqrt(
w1.dim() / w2.dim()) * A(psi1red, psi2red, r0)
return matrix
def B(psipred, psired, r0=1):
"""
Calculates (s np rp wp||a||s n r w).
Args:
Returns:
Matrix element (s np rp wp||a||s n r w). For example
w=U3State([22,15,10])
n=U3State([4,0,0])
r=1
wp=U3State([21,14,10])
np=U3State([2,0,0])
rp=1
s=U3State3([20,13,10])
B_weylboson(s,np,rp,wp,n,r,w)
returns
-1.28102523044
"""
matrix = 0.0
if r0 == 1:
w = psired.w
wp = psipred.w
matrix = utils.parity(wp.pt() - w.pt()) * numpy.sqrt(
w.dim() / wp.dim()) * A(psired, psipred)
return matrix
def phi(w1, w2, w3, r, rp):
"""
Phi phase factor that arrises in changing the coupling order of SU(3) irreps
"""
phi = 0
mlt = mult(w1, w2, w3)
if (mlt < r) or (mult < rp):
print "invalid multiplicity"
return phi
if mlt == 1:
phi = utils.parity(w1.pt() + w2.pt() - w3.pt())
else:
phi = Z_SU3(w1, SU3State(0, 0), w3, w2, w1, 1, r, w2, 1, rp)
return phi
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
# generating list of w's
wset = u3.couple(w1, w2)
## summing over w in wset
for w in wset:
## check that w is also in {wrxwc}
if u3.mult(wr, wc, w) == 0:
continue
## calculate max branching multiplicity of L in w
kmax = so3.multk(w, L)
## summing over branching multplicity from 1 to kmax
for k in range(1, kmax + 1):
## calculating moshinksy coefficient
mosh = mosh + (u3.W(wr, 1, Lr, wc, 1, Lc, w, k, L, 1) *
u3.W(w1, 1, L1, w2, 1, L2, w, k, L, 1) *
mosh_SU3(w1, w2, wr, wc, w) *
utils.parity(n1 + n2 + nr + nc))
return mosh
#######################################################################################################
def moshinsky(state1, state2, stater, statec, state, type):
"""
calculates the moshinsky coefficients used to transform between the two-particle and relative-center of mass frames.
w1 x w2->w
wr x wc->w
type can be either "SU3" or "SO3"
if type=="SU3":
state1,state2,stater,statec,state are simply SU3State class
if type=="SO3" then state1 etc are (n1,L1) where N1=2*n1+L1 and w1=SU3State(N1,0)
args:
J1, J2, J3, J4, J5, J6 are angular momenta (int or half int)
"""
cj9=pygsl.sf.coupling_9j(
int(2*J1),int(2*J2), int(2*J3),
int(2*J4),int(2*J5), int(2*J6),
int(2*J7),int(2*J8), int(2*J9)
)[0]
cj9=cj9*hat(J3)*hat(J6)*hat(J7)*hat(J8)
if abs(cj9)<10**(-13):
cj9=0.0
return cj9
if __name__ == '__main__':
print "coupling_9j",coupling_9j((1,1,1),(2,3,4),(3,4,5))
print "coupling_9j",coupling_9j((0,.5,.5),(1,.5,.5),(1,1,0))#, coupling_6j((1,1,1),(3,2,3))
print "coupling_9j",coupling_9j((1,1,1),(1,1,1),(2,2,0)), coupling_6j((1,1,1),(1,1,2))*utils.parity(1+1+1)
print "coupling_9j",coupling_9j((1,1,0),(1,1,0),(2,2,0)), coupling_6j((1,1,0),(1,1,2))*utils.parity(1+1+0),1.*hat(2)/hat(1)/hat(1)
print "basis testing"
print "coupling_9j",coupling_9j((1,.5,.5),(1,.5,.5),(0,0,0))**2
print "coupling_9j",coupling_9j((1,.5,.5),(1,.5,.5),(1,1,0))**2
print "coupling_9j",coupling_9j((1,1,0),(0,0,0),(1,1,0))**2
print "coupling_9j",coupling_9j((1,1,0),(1,1,0),(1,1,0))**2
print "coupling_9j",coupling_9j((1,1,0),(2,2,0),(1,1,0))**2
print "test coupling_9j",coupling_9j((2,0,2),(1,0,1),(1,0,1))
############################################################################################################################################################################################
def multJ(J,M):