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Topic: Irrep

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	Superselection sector - Wikipedia, the free encyclopedia
		A reducible unitary representation of O is decomposable into the direct sum of inequivalent irreducible unitary representations of O (I'll explain why they have to be inequivalent in a moment).
		Observables map a state in each irrep into another state in the same irrep.
		The relative phase of a superposition of nonzero states from different irreps is not observable (the expectation values of the observables can't distinguish between them).
	en.wikipedia.org /wiki/Superselection_sector (591 words)

	[No title]
		The subspace $\irrep d \subset \calv$ of degree-$d$ homogeneous polynomials is an irreducible $\sltc$ representation.
		The restriction $\cbra {\irrep l} {\irrep j} p \to \irrep {l + j - 2p}$ is a nonzero map for $0 \le p \le \min(l,j)$, and the corresponding linear map $\irrep l \otimes \irrep j \to \irrep {l + j -2p}$ is the $\sltc$-equivariant projection implicit in the Clebsch-Gordan formula eq.(\eqlab{cgformula}).
		Similarly, the restriction of a symplectic map $h: V \to V$ to $\irrep j \subset V$ is the identity map multiplied by $\kappa_j = \pm 1$.
	www.ma.utexas.edu /mp_arc/html/papers/94-197 (3691 words)

	[No title]
		Example: Branch[31,7] = [10, 13, 17, 21] means that the 31st irrep of E7 decomposes as the sum of the 10th, 13th, 17th, and 21st irreps of E6.
		For each k from 1 up to the top rank n, and for each irrep j of W[k-1] that occurs in the i-th irrep of W[k], (i.e., for each j in Branch[i,k]), Semi[j,i,k] is a rescaling factor for rationalizing the i-th irrep of W[k-1] in the j-th irrep of W[k].
		The rows and columns of the matrices for the i-th irrep of W[n] may be represented by chains in the Bratteli diagram; i.e., (n+1)-tuples [i[0],...,i[n]], where i[0]=1, i[n]=i, and i[k-1] is an item of Branch[i[k],k] for each k=1,...,n.
	www.math.lsa.umich.edu /~jrs/data/models/data/READ_ME (441 words)

	Exact Solutions: No Symmetry Breaking (Site not responding. Last check: 2007-10-07)
		The N particle density operator that minimizes the standard energy functional belongs to an irrep of the full 1 particle symmetry group of the Hamiltonian (of course it also belongs to irreps of any p-particle symmetry group of the Hamiltonian as well).
		If the dimension of the irrep that the minimizing N particle density operator belongs to is greater than one, then a set of degenerate ground states - pure and ensemble exists.
		Even if the minimizing N particle density operator belongs to a 1D irrep, the FORDO belongs to a reducible representation that in general includes multidimensional irreps.
	www.personal.psu.edu /faculty/b/q/bqw/san98/sld032.htm (121 words)

	[No title]
		returns: char irr_labs an array of labels (strings) which denote the irreps for the point group in which the molecule is considered, _regardless_ of whether there exist any symmetry orbitals which transform as that irrep**.
		The eigenvectors should be stored with the column index denoting mos and the row index denoting sos: this means that scf_vector[i][j] is the contribution of the ith so to the jth mo. returns: nothing.
		arguments: int irrep the number of the irrep to which the symmetry block belongs (this includes irreps with orbspi[irrep] == 0) n.b.
	vergil.chemistry.gatech.edu /psi/devel/libs/libfile30.txt (3020 words)

	Representation theory of finite groups (Site not responding. Last check: 2007-10-07)
		The conclusion, then, is that the number of conjugacy classes of G is the same as the number of inequivalent irreps of G. Corollary: If two reps have the same characters, then they are equivalent.
		To see this, note that the conjugate rep of the irrep is equivalent to the dual irrep with the Hilbert space norm acting as the intertwiner.
		The zeroth indicator is the dimension of the irrep, the first indicator would be 1 for the trivial representation and zero for the other irreps.
	www.worldhistory.com /wiki/R/Representation-theory-of-finite-groups.htm (1893 words)

	Hartree-Fock Wavefunction Stability Analysis (Site not responding. Last check: 2007-10-07)
		Only for instabilities whose direct product is the totally symmetric irrep (irrep 1) will the wavefunction maintain the symmetry of the molecular framework.
		The number of instabilities in each irrep is given along with their eigenvalue and classification.
		Because instabilities in other than the totally symmetric irrep reduce the symmetry of the wavefunction, only those in irrep 1 can be followed.
	www.osc.edu /PET/CCM/skeleton/software/manuals/aces2-man/node29.html (895 words)

	Spinor -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-07)
		for, there is an (additional info and facts about irrep) irrep whose (An artifact that is heavy) weights are all possible combinations of
		There is also another irrep whose weights are all possible combinations of
		The (A union of two disjoint sets in which every element is the sum of an element from each of the disjoint sets) direct sum of both Weyl spinors is a Dirac spinor.
	www.absoluteastronomy.com /encyclopedia/s/sp/spinor.htm (1153 words)

	SCM: ADF User's Guide
		In an unrestricted calculation, two sequences of numbers must be specified for each irrep; the sequences are separated by a double slash (//).
		Note that this is not meaningfull in an unrestricted Spin-Orbit coupled calculation using the (non-)collinear approximation, where one should use one sequence of occupation numbers for each irrep.
		(the only irrep in nosym), but not the representations belonging to the input point group symmetry.
	www.scm.com /Doc/Doc2004.01/ADFUsersGuide/page104.html (1158 words)

	Elementary Particles
		An irrep of a product of a bunch of groups is the same as a tensor product of irreps of these groups.
		This representation is not irreducible: it is a direct sum of two irreps, the left-handed and right-handed massless spin-1 irreps.
		Again ignoring ISpin (3,1), all the gauge bosons correspond to real irreps of G. Let's call the direct sum of all these irreps the gauge boson representation of G, or G for short.
	math.ucr.edu /home/baez/qg-spring2003/elementary (1488 words)

	MPQC: sc::SOBasis Class Reference (Site not responding. Last check: 2007-10-07)
		Return the number of functions in the given irrep.
		Return the offset for the first function of the given irrep.
		Returns the number of functions in the shell in a given irrep.
	www.mpqc.org /mpqc-html/classsc_1_1SOBasis.html (219 words)

	[No title] (Site not responding. Last check: 2007-10-07)
		= (0,-1) (1110010010010010010000000000000000000000000000000000000000000000) %%Listed as irreps of the left-moving gauge group: %%"Irrep d : h" indicates massless states in a d-dimensional irrep %%having space-time helicity h.
		%%"from ()" indicates the sector containing the massless state %%which is the highest weight of the irrep.
		) Irrep 3:-1/2: (((2) (0) (0) (0) (0) (0))) from (1) Irrep 3:-1/2: (((2) (0) (0) (0) (0) (0))) from (1) Irrep 3:-1/2: (((2) (0) (0) (0) (0) (0))) from (1) Irrep 3:-1/2: (((2) (0) (0) (0) (0) (0))) from (1) Irrep 3:-1: (((2) (0) (0) (0) (0) (0))) from (
	fnth37.fnal.gov /strings/Models/fourdim/n=4b.myo (957 words)

	Hypercharge and Weak Isospin
		You can read these irreps off the elementary particle chart at the end of this handout.
		on this irrep, corresponding to weak isospin and hypercharge.
		As indicated in the chart at the end of this handout, this is the first member of the standard basis of the irrep
	math.ucr.edu /home/baez/qg-spring2003/hypercharge (1190 words)

	IDENTITY
		One of two mutually exclusive cases arise: either (A) all of the energy-degenerate states have the same irrep label or (B) the states are partitioned among several irreps.
		Because every irrep label corresponds to an energy label and the former are often degenerate, group theory forces energy degeneracy.
		The object is to produce a group, L, for which the observed degeneracy is normal; to reveal the single irrep label from L that subsumes all of the degenerate states.
	www.physics.ucla.edu /~chester/IDENTITY/6.html (2072 words)

	LIBDPD --- The Direct-Product Decomposition Library
		, the direct product of the irreducible representations (irreps) associated with the component orbital indices corresponds to the totally symmetric irrep of the given point group.
		, the irrep value for each orbital in the current subspace.
		As described above, one may need to store a given quantity in memory in a manner different from that which is used on disk.
	vergil.chemistry.gatech.edu /psi/devel/libs/libdpd.html (2350 words)

	[No title] (Site not responding. Last check: 2007-10-07)
		They must differ by a double replacement of an MO belonging to one one-dimensional irrep by an MO belonging to a different one-dimensional irrep.
		For each irrep for which IVOs are desired, set one virtual-orbital occupation number to -1, and include the appropriate open-shell energy coefficients.
		For each irrep: (if NI(LA) GT 0 and ISAVE LT 2) 5 40F2.0 AN(I), BN(I), I = 1, NI(LA) Occupation numbers of the NI(LA) MOs of this irrep.
	www.osc.edu /PET/CCM/skeleton/software/manuals/columbus5.0/scfpq.doc (1834 words)

	[No title] (Site not responding. Last check: 2007-10-07)
		= (0,0) (1110010010010010010001100110011001100110011011001100000000000000) %%Listed as irreps of the left-moving gauge group: %%"Irrep d : h" indicates massless states in a d-dimensional irrep %%having space-time helicity h.
		) Irrep 15:-1/2: (((0,0,0) (1,0,1) (0) (0) (0) (0))) from (1) Irrep 15:-1/2: (((0,0,0) (1,0,1) (0) (0) (0) (0))) from (1) Irrep 15:-1/2: (((0,0,0) (1,0,1) (0) (0) (0) (0))) from (1) Irrep 15:-1/2: (((0,0,0) (1,0,1) (0) (0) (0) (0))) from (1) Irrep 15:-1: (((0,0,0) (1,0,1) (0) (0) (0) (0))) from (
		) Irrep 3:-1/2: (((0,0,0) (0,0,0) (2) (0) (0) (0))) from (1) Irrep 3:-1/2: (((0,0,0) (0,0,0) (2) (0) (0) (0))) from (1) Irrep 3:-1/2: (((0,0,0) (0,0,0) (2) (0) (0) (0))) from (1) Irrep 3:-1/2: (((0,0,0) (0,0,0) (2) (0) (0) (0))) from (1) Irrep 3:-1: (((0,0,0) (0,0,0) (2) (0) (0) (0))) from (
	fnth37.fnal.gov /strings/Models/fourdim/24rfb.myo (883 words)

	on gerbes and boundary states
		In fact, there is a 1-1 correspondence between irreps of the symplectomorphism group in n dimensions (n even) and Sp(n).
		In this situation, there is always a 1-1 correspondence between g and g_0 irreps.
		In particular, when n = 2 the irreps of the group of area-preserving diffs correspond to Sp(2) = SU(2); a spin j irrep is carried by a totally symmetric tensor field with j indices.
	www.pych-one.com /new-5655015-4397.html (9954 words)

	ON QUANTUM THEORETICAL ORIGINS OF NEWTONIAN TIME
		Every carrier space, for given n, supports an IRREP of su(2), [Section XIV] hence the group SU(2), which is, of course, not true for any SU(n) where n > 2.
		By a complex extension then also a finite dimensional IRREP of algebra sl(2, C) and group SL(2, C), all of which are usually associated with the spin (n-1)/2 and mass zero.
		Such a Hilbert space is that often used for the construction of the all the finite dimensional IRREPS of sl(2, C).
	graham.main.nc.us /~bhammel/PHYS/newtqtime.html (15363 words)

	SCM: Theory: Multiplet Energies
		Each 'irrep occups' record specifies the occupations for the indicated irrep in the usual way (see for instance the occupations key).
		The irrep labels must correspond to the AOC point group symmetry used in the AOC calculation, not the point group symmetry used in the SLATERDETERMINANTS calculation!
		Note that in an unrestricted calculations, occupations numbers must be given for both spins, using the double slash (//) to separate the occupations for spin-alpha and spin-beta.
	www.scm.com /Doc/Doc2004.01/Theory/page7.html (507 words)

	Zindo - Commands--Standalone Mode
		The first shell is filled by aufbau, the second shell has 4 MOs of irrep 1, 3 of irrep 2, 2 of irrep 3, and 1 of irrep 4.
		The irrep for each MO should be based on the character tables shown above.
		Note: If the CI is done on more than one irrep, then the CI specification lines must be repeated for each irrep considered.
	www.scripps.edu /rc/softwaredocs/msi/insight2K/zindo/E_Cmds_SA.html (6505 words)

	The Shania Forums - Need Up! font??? Get it here! (Site not responding. Last check: 2007-10-07)
		It's called irrep and you can download it here:
		irrep from the drop-down menu and off you go...start writing with the "Shania-font"!
		You shouldn't have had to look very far or long.
	www.shaniaforums.com /printthread.php?t=21778&pp=50 (889 words)

	Amazon.com: Quantum Mechanics 1: Foundations (Oxford Chemistry Primers, 48): Books: N. J. B. Green (Site not responding. Last check: 2007-10-07)
		Green "As stated in the introduction, at the scale of atoms and molecules nature does not behave in the same way as macroscopic objects..." (more)
		As stated in the introduction, at the scale of atoms and molecules nature does not behave in the same way as macroscopic objects.
		totally symmetric irrep, each irrep, dimensional irrep, representative matrices, polarizability operator, representative matrix, direct product representation, figure axis, molecular point group, orbital approximation, vibrational wavefunctions, symmetry operations, two wavefunctions, dipole moment operator, improper rotations, electronic wavefunctions, methane molecule, repulsion energy, nuclear coordinates, reduction formula, normal coordinates, correct symmetry, ammonia molecule, potential energy curve, symmetry operators
	www.amazon.com /exec/obidos/tg/detail/-/0198557612?v=glance (911 words)

	scf.c File Reference
		Note: since it only looks at the first element in each column, it will not work for matrices where that element can be zero by symmetry.
		So, this function is only helpful when called for an irrep block at a time.
		Generated on Sat Jan 11 12:28:18 2003 for PSI by
	www.psicode.org /doc/libs/doxygen/html/scf_8c.html (118 words)

	Basic Instructions and Rules
		The number of non-zero entries in Tensors must equal the number of entries in Irrep--add zeros as needed.
		The sum of all enties in Tensors must equal the sum of all entries in Irrep--in SU(N) a constant can be added to all entries of the irrep without changing the irrep.
		Start with the first red code in each example and press enter to see the results.
	www.physics.uiowa.edu /~wklink/Racah/Example-1.mw (398 words)

	rd_scf_ptrs.c File Reference (Site not responding. Last check: 2007-10-07)
		/ [5] = Number of orbitals per irrep for non-zero occupancies /
		/ [6] = Number of closed shells per irrep with non-zero occ /
		/ [7] = Number of open shells per irrep with non-zero occ /
	zopyros.ccqc.uga.edu /~kenny/psi-doc/rd__scf__ptrs_8c.html (225 words)

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