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21,344
A modular functor which is universal for quantum computation
 Comm. Math. Phys
"... Abstract: We show that the topological modular functor from Witten–Chern–Simons theory is universal for quantum computation in the sense that a quantum circuit computation can be efficiently approximated by an intertwining action of a braid on the functor’s state space. A computational model based o ..."
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Cited by 117 (18 self)
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on Chern–Simons theory at a fifth root of unity is defined and shown to be polynomially equivalent to the quantum circuit model. The chief technical advance: the density of the irreducible sectors of the Jones representation has topological implications which will be considered elsewhere. 1.
Irreducibility of some spectral determinants
, 2010
"... This is a complement to our paper arXiv:0802.1461. We study irreducibility of spectral determinants of some oneparametric eigenvalue problems in dimension one with polynomial potentials. ..."
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Cited by 10 (7 self)
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This is a complement to our paper arXiv:0802.1461. We study irreducibility of spectral determinants of some oneparametric eigenvalue problems in dimension one with polynomial potentials.
Topological sectors and a dichotomy in conformal field theory
 Commun. Math. Phys
"... Let A be a local conformal net of factors on S 1 with the split property. We provide a topological construction of soliton representations of the nfold tensor product A ⊗ · · · ⊗ A, that restrict to true representations of the cyclic orbifold (A ⊗ · · · ⊗ A) Zn. We prove a quantum index the ..."
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Cited by 46 (21 self)
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theorem for our sectors relating the Jones index to a topological degree. Then A is not completely rational iff the symmetrized tensor product (A ⊗ A) flip has an irreducible representation with infinite index. This implies the following dichotomy: if all irreducible sectors of A have a conjugate sector
Sector
, 2012
"... T L U The Forest Service of the U.S. Department of Agriculture is dedicated to the principle of multiple use management of the Nation’s forest resources for sustained yields of wood, water, forage, wildlife, and recreation. Through forestry research, cooperation with the States and private forest ow ..."
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Cited by 2 (0 self)
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T L U The Forest Service of the U.S. Department of Agriculture is dedicated to the principle of multiple use management of the Nation’s forest resources for sustained yields of wood, water, forage, wildlife, and recreation. Through forestry research, cooperation with the States and private forest owners, and management of the national forests and national grasslands, it strives— as directed by Congress—to provide increasingly greater service to a growing Nation. The U.S. Department of Agriculture (USDA) prohibits discrimination in all its programs and activities on the basis of race, color, national origin, sex, religion, age, disability, sexual orientation, marital status, family status, status as a parent (in education and training programs and activities), because all or part of an individual’s income is derived from any public assistance program, or retaliation. (Not all prohibited bases apply to all programs or activities). If you require this information in alternative format (Braille, large print, audiotape, etc.), contact the USDA’s TARGET Center at
STRICTLY IRREDUCIBLE MAPS AND STRONG
"... Any space X in which no nonvoid open subset is meager is called a Baire space. In this paper, we will consider only T Baire spaces. Given a space X, we will use O(X) 2 to denote the set of all open subsets of X. If F(X) is any family of subsets of X, F+(X) will denote F(X) \ {~}. Thus the expression ..."
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Any space X in which no nonvoid open subset is meager is called a Baire space. In this paper, we will consider only T Baire spaces. Given a space X, we will use O(X) 2 to denote the set of all open subsets of X. If F(X) is any family of subsets of X, F+(X) will denote F(X) \ {~}. Thus the expression U E O+(X) indicates that U is a,nonvoid open subset of X. We will denote the collection of meager subsets of X by M(X). For any A C X, M(A) will denote the set of meager points of A, i.e., the set of all x E X such that for some open neighborhood U of x, UnA is meager. M(A) is an open subset of X and A n M(A) is meager in X. * This paper was submitted while I was a graduate student at the University of Delaware. I am grateful to Professor John C. Oxtoby of Bryn Mawr who graciously read the first version of this paper and offered some helpful comments. In particular, I would like to mention that the original version of Lemma 2.2 was incorrect. I also wish to thank the referee for his many helpful comments, correc tions, and considerable patience; he will see his influence. r trust Professor Oxtoby will see the influence of his work. 372 Wilson We will denote X\M(A), the set of nonmeager points of A,
Multiinterval subfactors and modularity of representations in conformal field theory
 Commun. Math. Phys
"... Dedicated to John E. Roberts on the occasion of his sixtieth birthday We describe the structure of the inclusions of factors A(E) ⊂A(E ′ ) ′ associated with multiintervals E ⊂ R for a local irreducible net A of von Neumann algebras on the real line satisfying the split property and Haag duality. I ..."
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Cited by 112 (37 self)
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(E ′ ) ′ coincides with the global index associated with all irreducible sectors, the braiding symmetry associated with all sectors is nondegenerate, namely the representations of A form a modular tensor category, and every sector is a direct sum of sectors with finite dimension. The superselection structure
Charge Superselection Sectors for QCD on the Lattice
, 2008
"... We study quantum chromodynamics (QCD) on a finite lattice Λ in the Hamiltonian approach. First, we present the field algebra AΛ as comprising a gluonic part, with basic building block being the crossed product C ∗algebra C(G) ⊗α G, and a fermionic (CARalgebra) part generated by the quark fields. B ..."
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Cited by 9 (6 self)
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that there exist unitary operators (charge carrying fields), which intertwine between irreducible sectors leading to a classification of irreducible representations in terms of the Z3valued global boundary flux. By the global Gauss law, these 3 inequivalent charge superselection sectors can be labeled in terms
Results 1  10
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21,344