Unitary Representations of Gauge Groups
Huerfano, Ruth Stella
I generalize to the case of gauge groups over non-trivial principal bundles representations that I. M. Gelfand, M. I. Graev and A. M. Versik constructed for current groups. The gauge group of the principal G-bundle P over M, (G a Lie group with an euclidean structure, M a compact, connected and oriented manifold), as the smooth sections of the associated group bundle is presented and studied in chapter I. Chapter II describes the symmetric algebra associated to a Hilbert space, its Hilbert structure, a convenient exponential and a total set that later play a key role in the construction of the representation. Chapter III is concerned with the calculus needed to make the space of Lie algebra valued 1-forms a Gaussian L^2-space. This is accomplished by studying general projective systems of finitely measurable spaces and the corresponding systems of sigma -additive measures, all of these leading to the description of a promeasure, a concept modeled after Bourbaki and classical measure theory. In the case of a locally convex vector space E, the corresponding Fourier transform, family of characters and the existence of a promeasure for every quadratic form on E^' are established, so the Gaussian L^2-space associated to a real Hilbert space is constructed. Chapter III finishes by exhibiting the explicit Hilbert space isomorphism between the Gaussian L ^2-space associated to a real Hilbert space and the complexification of its symmetric algebra. In chapter IV taking as a Hilbert space H the L^2-space of the Lie algebra valued 1-forms on P, the gauge group acts on the motion group of H defining in an straight forward fashion the representation desired.
Remarks on unitary representations of Poincare group
International Nuclear Information System (INIS)
Burzynski, A.
1979-01-01
In this paper the elementary review of methods and notions using in the theory of unitary representations of Poincare group is included. The Poincare group is a basic group for relativistic quantum mechanics. Our aim is to introduce the reader into some problems of quantum physics, which are difficult approachable for beginners. (author)
Theory of the unitary representations of compact groups
International Nuclear Information System (INIS)
Burzynski, A.; Burzynska, M.
1979-01-01
An introduction contains some basic notions used in group theory, Lie group, Lie algebras and unitary representations. Then we are dealing with compact groups. For these groups we show the problem of reduction of unitary representation of Wigner's projection operators, Clebsch-Gordan coefficients and Wigner-Eckart theorem. We show (this is a new approach) the representations reduction formalism by using superoperators in Hilbert-Schmidt space. (author)
Introduction to orthogonal, symplectic and unitary representations of finite groups
Riehm, Carl R
2011-01-01
Orthogonal, symplectic and unitary representations of finite groups lie at the crossroads of two more traditional subjects of mathematics-linear representations of finite groups, and the theory of quadratic, skew symmetric and Hermitian forms-and thus inherit some of the characteristics of both. This book is written as an introduction to the subject and not as an encyclopaedic reference text. The principal goal is an exposition of the known results on the equivalence theory, and related matters such as the Witt and Witt-Grothendieck groups, over the "classical" fields-algebraically closed, rea
Unitary group representations in Fock spaces with generalized exchange properties
International Nuclear Information System (INIS)
Liguori, A.
1994-09-01
The notion of second R-quantization is investigated, - a suitable deformation of the standard second quantization which properly takes into account the non-trivial exchange properties characterizing generalized statistics. The R-quantization of a class of unitary one-particle representations relevant for the description of symmetries is also performed. The Euclidean covariance of anyons is analyzed in this context. (author). 11 refs
All unitary ray representations of the conformal group SU(2,2) with positive energy
International Nuclear Information System (INIS)
Mack, G.
1975-12-01
We find all those unitary irreducible representations of the infinitely - sheeted covering group G tilde of the conformal group SU(2,2)/Z 4 which have positive energy P 0 >= O. They are all finite component field representations and are labelled by dimension d and a finite dimensional irreducible representation (j 1 , j 2 ) of the Lorentz group SL(2C). They all decompose into a finite number of unitary irreducible representations of the Poincare subgroup with dilations. (orig.) [de
Positive-definite functions and unitary representations of locally compact groups in a Hilbert space
International Nuclear Information System (INIS)
Gali, I.M.; Okb el-Bab, A.S.; Hassan, H.M.
1977-08-01
It is proved that the necessary and sufficient condition for the existence of an integral representation of a group of unitary operators in a Hilbert space is that it is positive-definite and continuous in some topology
An Integral Representation of Standard Automorphic L Functions for Unitary Groups
Directory of Open Access Journals (Sweden)
Yujun Qin
2007-01-01
Full Text Available Let F be a number field, G a quasi-split unitary group of rank n. We show that given an irreducible cuspidal automorphic representation π of G(A, its (partial L function LS(s,π,σ can be represented by a Rankin-Selberg-type integral involving cusp forms of π, Eisenstein series, and theta series.
Projective unitary-antiunitary representations of the Shubnikov space groups
International Nuclear Information System (INIS)
Broek, P.M. van den.
1979-01-01
Some mathematical aspects of the symmetry of a physical system in quantum mechanics are examined with special emphasis on the symmetry groups of charged particles in crystalline solids, the Shuknikov space groups. (Auth.)
Unitary representations of the fundamental group of orbifolds
Indian Academy of Sciences (India)
in Theorem 1.2 are topological, taking values in rational cohomological ..... this is the fundamental group defined using Galois theory of covering stacks of Y .... natural action of G := Z/mZ on T given by the action of Gm on L; by the choice of the.
International Nuclear Information System (INIS)
Kent, R.D.; Schlesinger, M.
1987-01-01
For the purpose of computing matrix elements of quantum mechanical operators in complex N-particle systems it is necessary that as much of each irreducible representation be stored in high-speed memory as possible in order to achieve the highest possible rate of computations. A graph theoretic approach to the representation of N-particle systems involving arbitrary single-particle spin is presented. The method involves a generalization of a technique employed by Shavitt in developing the graphical group approach (GUGA) to electronic spin-orbitals. The methods implemented in GENDRT and DRTDIM overcome many deficiencies inherent in other approaches, particularly with respect to utilization of memory resources, computational efficiency in the recognition and evaluation of non-zero matrix elements of certain group theoretic operators and complete labelling of all the basis states of the permutation symmetry (S N ) adapted irreducible representations of SU(n) groups. (orig.)
Kobayashi, T
2002-01-01
Based on an embedding formula of the CAR algebra into the Cuntz algebra ${\\mathcal O}_{2^p}$, properties of the CAR algebra are studied in detail by restricting those of the Cuntz algebra. Various $\\ast$-endomorphisms of the Cuntz algebra are explicitly constructed, and transcribed into those of the CAR algebra. In particular, a set of $\\ast$-endomorphisms of the CAR algebra into its even subalgebra are constructed. According to branching formulae, which are obtained by composing representations and $\\ast$-endomorphisms, it is shown that a KMS state of the CAR algebra is obtained through the above even-CAR endomorphisms from the Fock representation. A $U(2^p)$ action on ${\\mathcal O}_{2^p}$ induces $\\ast$-automorphisms of the CAR algebra, which are given by nonlinear transformations expressed in terms of polynomials in generators. It is shown that, among such $\\ast$-automorphisms of the CAR algebra, there exists a family of one-parameter groups of $\\ast$-automorphisms describing time evolutions of fermions, i...
Collective pairing states and non-unitary representations of the quasi-spin group
International Nuclear Information System (INIS)
Lorazo, B.
1975-01-01
Some months ago, a parameter-dependent (psub(i))-quasi-spin group was presented by the author. The interest for considering such a group was partly suggested by the possibility of describing, with a reasonable accuracy, the ground state of even spherical nuclei with one closed shell by a n-pair wave function [Σsub(i)psub(i)Ssub(+)sup(i)] sup(n)/0> depending upon the real parameters psub(i) (the operators Ssub(+)sup(i) are the one-orbit quasi-spin operators). It was stated that the formalism would provide the exact mathematical framework to discuss the generalized seniority quantum number. The relevance of this point of view has been vigorously questioned. For the author of the present paper, the arguments given are based on misinterpretation of some unconventional and possibly ambiguous aspects of the work. Proof is given below that group theoretical considerations can effectively be used in place of standard commutator techniques. (Auth.)
Harmonic Analysis and Group Representation
Figa-Talamanca, Alessandro
2011-01-01
This title includes: Lectures - A. Auslander, R. Tolimeri - Nilpotent groups and abelian varieties, M Cowling - Unitary and uniformly bounded representations of some simple Lie groups, M. Duflo - Construction de representations unitaires d'un groupe de Lie, R. Howe - On a notion of rank for unitary representations of the classical groups, V.S. Varadarajan - Eigenfunction expansions of semisimple Lie groups, and R. Zimmer - Ergodic theory, group representations and rigidity; and, Seminars - A. Koranyi - Some applications of Gelfand pairs in classical analysis.
International Nuclear Information System (INIS)
Guenaydin, M.; Saclioglu, C.
1981-06-01
We give a construction of the Lie algebras of the non-compact groups appearing in four dimensional supergravity theories in terms of boson operators. Our construction parallels very closely their emergence in supergravity and is an extension of the well-known construction of the Lie algebras of the non-compact groups Sp(2n,IR) and SO(2n) from boson operators transforming like a fundamental representation of their maximal compact subgroup U(n). However this extension is non-trivial only for n >= 4 and stops at n = 8 leading to the Lie algebras of SU(4) x SU(1,1), SU(5,1), SO(12) and Esub(7(7)). We then give a general construction of an infinite class of unitary irreducible representations of the respective non-compact groups (except for Esub(7(7)) and SO(12) obtained from the extended construction). We illustrate our construction with the examples of SU(5,1) and SO(12). (orig.)
DU and UD-invariants of unitary groups
International Nuclear Information System (INIS)
Aguilera-Navarro, M.C.K.
1977-01-01
Four distint ways of obtaining the eigenvalues of unitary groups, in any irreducible representation, are presented. The invariants are defined according to two different contraction conventions. Their eigenvalue can be given in terms of two classes of special partial hooks associated with the young diagram characterizing the irreducible representation considered
Unitary Transformations in 3 D Vector Representation of Qutrit States
2018-03-12
ARL-TR-8330 ● MAR 2018 US Army Research Laboratory Unitary Transformations in 3- D Vector Representation of Qutrit States by...return it to the originator. ARL-TR-8330 ● MAR 2018 US Army Research Laboratory Unitary Transformations in 3- D Vector...2018 2. REPORT TYPE Technical Report 3. DATES COVERED June–December 2017 4. TITLE AND SUBTITLE Unitary Transformations in 3- D Vector
Unitary representations of basic classical Lie superalgebras
International Nuclear Information System (INIS)
Gould, M.D.; Zhang, R.B.
1990-01-01
We have obtained all the finite-dimensional unitary irreps of gl(mvertical stroken) and C(n), which also exhaust such irreps of all the basic classical Lie superalgebras. The lowest weights of such irreps are worked out explicitly. It is also shown that the contravariant and covariant tensor irreps of gl(mvertical stroken) are unitary irreps of type (1) and type (2) respectively, explaining the applicability of the Young diagram method to these two types of tensor irreps. (orig.)
Multiqubit Clifford groups are unitary 3-designs
Zhu, Huangjun
2017-12-01
Unitary t -designs are a ubiquitous tool in many research areas, including randomized benchmarking, quantum process tomography, and scrambling. Despite the intensive efforts of many researchers, little is known about unitary t -designs with t ≥3 in the literature. We show that the multiqubit Clifford group in any even prime-power dimension is not only a unitary 2-design, but also a 3-design. Moreover, it is a minimal 3-design except for dimension 4. As an immediate consequence, any orbit of pure states of the multiqubit Clifford group forms a complex projective 3-design; in particular, the set of stabilizer states forms a 3-design. In addition, our study is helpful in studying higher moments of the Clifford group, which are useful in many research areas ranging from quantum information science to signal processing. Furthermore, we reveal a surprising connection between unitary 3-designs and the physics of discrete phase spaces and thereby offer a simple explanation of why no discrete Wigner function is covariant with respect to the multiqubit Clifford group, which is of intrinsic interest in studying quantum computation.
Group and representation theory
Vergados, J D
2017-01-01
This volume goes beyond the understanding of symmetries and exploits them in the study of the behavior of both classical and quantum physical systems. Thus it is important to study the symmetries described by continuous (Lie) groups of transformations. We then discuss how we get operators that form a Lie algebra. Of particular interest to physics is the representation of the elements of the algebra and the group in terms of matrices and, in particular, the irreducible representations. These representations can be identified with physical observables. This leads to the study of the classical Lie algebras, associated with unitary, unimodular, orthogonal and symplectic transformations. We also discuss some special algebras in some detail. The discussion proceeds along the lines of the Cartan-Weyl theory via the root vectors and root diagrams and, in particular, the Dynkin representation of the roots. Thus the representations are expressed in terms of weights, which are generated by the application of the elemen...
Biased Monte Carlo algorithms on unitary groups
International Nuclear Information System (INIS)
Creutz, M.; Gausterer, H.; Sanielevici, S.
1989-01-01
We introduce a general updating scheme for the simulation of physical systems defined on unitary groups, which eliminates the systematic errors due to inexact exponentiation of algebra elements. The essence is to work directly with group elements for the stochastic noise. Particular cases of the scheme include the algorithm of Metropolis et al., overrelaxation algorithms, and globally corrected Langevin and hybrid algorithms. The latter are studied numerically for the case of SU(3) theory
Karpilovsky, G
1994-01-01
This third volume can be roughly divided into two parts. The first part is devoted to the investigation of various properties of projective characters. Special attention is drawn to spin representations and their character tables and to various correspondences for projective characters. Among other topics, projective Schur index and projective representations of abelian groups are covered. The last topic is investigated by introducing a symplectic geometry on finite abelian groups. The second part is devoted to Clifford theory for graded algebras and its application to the corresponding theory
Primary fields in a unitary representation of Virasoro algebras
International Nuclear Information System (INIS)
Sasaki, R.; Yamanaka, I.
1985-08-01
A unitary representation of Virasoro algebras with the central charge c = 1 - 6/(N + 1)(N + 2) is constructed explicitly in terms of a colored (two color) coset space (the complex projective space CP sup(N-1)) quark model. By utilizing the explicit forms of the Virasoro generators Lsub(m), we derive a general method of constructing the primary fields (fields with well-defined conformal transformation properties) of the above Virasoro algebras. (author)
International Nuclear Information System (INIS)
Gunaydin, Murat; Pavlyk, Oleksandr
2005-01-01
We study the minimal unitary representations of noncompact exceptional groups that arise as U-duality groups in extended supergravity theories. First we give the unitary realizations of the exceptional group E 8(-24) in SU*(8) as well as SU(6,2) covariant bases. E 8(-24) has E 7 x SU(2) as its maximal compact subgroup and is the U-duality group of the exceptional supergravity theory in d=3. For the corresponding U-duality group E 8(8) of the maximal supergravity theory the minimal realization was given. The minimal unitary realizations of all the lower rank noncompact exceptional groups can be obtained by truncation of those of E 8(-24) and E 8(8) . By further truncation one can obtain the minimal unitary realizations of all the groups of the 'Magic Triangle'. We give explicitly the minimal unitary realizations of the exceptional subgroups of E 8(-24) as well as other physically interesting subgroups. These minimal unitary realizations correspond, in general, to the quantization of their geometric actions as quasi-conformal groups. (author)
A unified approach to the minimal unitary realizations of noncompact groups and supergroups
International Nuclear Information System (INIS)
Guenaydin, Murat; Pavlyk, Oleksandr
2006-01-01
We study the minimal unitary representations of non-compact groups and supergroups obtained by quantization of their geometric realizations as quasi-conformal groups and supergroups. The quasi-conformal groups G leave generalized light-cones defined by a quartic norm invariant and have maximal rank subgroups of the form H x SL(2, R) such that G/H x SL(2, R) are para-quaternionic symmetric spaces. We give a unified formulation of the minimal unitary representations of simple non-compact groups of type A 2 , G 2 , D 4 , F 4 , E 6 , E 7 , E 8 and Sp(2n, R). The minimal unitary representations of Sp(2n, R) are simply the singleton representations and correspond to a degenerate limit of the unified construction. The minimal unitary representations of the other noncompact groups SU(m, n), SO(m, n), SO*(2n) and SL(m, R) are also given explicitly. We extend our formalism to define and construct the corresponding minimal representations of non-compact supergroups G whose even subgroups are of the form H x SL(2, R). If H is noncompact then the supergroup G does not admit any unitary representations, in general. The unified construction with H simple or Abelian leads to the minimal representations of G(3), F(4) and O Sp(n|2, R) (in the degenerate limit). The minimal unitary representations of O Sp(n|2, R) with even subgroups SO(n) x SL(2, R) are the singleton representations. We also give the minimal realization of the one parameter family of Lie superalgebras D(2, 1; σ)
Deformations of polyhedra and polygons by the unitary group
Energy Technology Data Exchange (ETDEWEB)
Livine, Etera R. [Laboratoire de Physique, ENS Lyon, CNRS-UMR 5672, 46 Allée d' Italie, Lyon 69007, France and Perimeter Institute, 31 Caroline St N, Waterloo, Ontario N2L 2Y5 (Canada)
2013-12-15
We introduce the set of framed (convex) polyhedra with N faces as the symplectic quotient C{sup 2N}//SU(2). A framed polyhedron is then parametrized by N spinors living in C{sup 2} satisfying suitable closure constraints and defines a usual convex polyhedron plus extra U(1) phases attached to each face. We show that there is a natural action of the unitary group U(N) on this phase space, which changes the shape of faces and allows to map any (framed) polyhedron onto any other with the same total (boundary) area. This identifies the space of framed polyhedra to the Grassmannian space U(N)/ (SU(2)×U(N−2)). We show how to write averages of geometrical observables (polynomials in the faces' area and the angles between them) over the ensemble of polyhedra (distributed uniformly with respect to the Haar measure on U(N)) as polynomial integrals over the unitary group and we provide a few methods to compute these integrals systematically. We also use the Itzykson-Zuber formula from matrix models as the generating function for these averages and correlations. In the quantum case, a canonical quantization of the framed polyhedron phase space leads to the Hilbert space of SU(2) intertwiners (or, in other words, SU(2)-invariant states in tensor products of irreducible representations). The total boundary area as well as the individual face areas are quantized as half-integers (spins), and the Hilbert spaces for fixed total area form irreducible representations of U(N). We define semi-classical coherent intertwiner states peaked on classical framed polyhedra and transforming consistently under U(N) transformations. And we show how the U(N) character formula for unitary transformations is to be considered as an extension of the Itzykson-Zuber to the quantum level and generates the traces of all polynomial observables over the Hilbert space of intertwiners. We finally apply the same formalism to two dimensions and show that classical (convex) polygons can be described in
Generalized unitaries and the Picard group
Indian Academy of Sciences (India)
some explicit calculations of that type.) So the range of this .... when we restrict our attention to generalized unitaries and full modules, that is, to modules. E for which BE = B. For every ..... without dividing out equivalence classes. But there is no ...
Matrix Elements of One- and Two-Body Operators in the Unitary Group Approach (I)-Formalism
Institute of Scientific and Technical Information of China (English)
DAI Lian-Rong; PAN Feng
2001-01-01
The tensor algebraic method is used to derive general one- and two-body operator matrix elements within the Un representations, which are useful in the unitary group approach to the configuration interaction problems of quantum many-body systems.
Asymptotical representation of discrete groups
International Nuclear Information System (INIS)
Mishchenko, A.S.; Mohammad, N.
1995-08-01
If one has a unitary representation ρ: π → U(H) of the fundamental group π 1 (M) of the manifold M then one can do may useful things: 1. To construct a natural vector bundle over M; 2. To construct the cohomology groups with respect to the local system of coefficients; 3. To construct the signature of manifold M with respect to the local system of coefficients; and others. In particular, one can write the Hirzebruch formula which compares the signature with the characteristic classes of the manifold M, further based on this, find the homotopy invariant characteristic classes (i.e. the Novikov conjecture). Taking into account that the family of known representations is not sufficiently large, it would be interesting to extend this family to some larger one. Using the ideas of A.Connes, M.Gromov and H.Moscovici a proper notion of asymptotical representation is defined. (author). 7 refs
Massive and massless supersymmetry: Multiplet structure and unitary irreducible representations
International Nuclear Information System (INIS)
Jarvis, P.D.
1976-01-01
UIR's of the supersymmetry algebra for the massive and massless cases are analyzed covariantly (without the use of induced representations) in terms of their component spins. For the massive case normalized basis vectors vertical-barp 2 >0, j 0 ; sigma; pjlambda> are constructed, where j 0 is the ''superspin'' and sigma is an additional quantum number serving to distinguish the different vertical-barpjlambda>, the constituent p 2 >0, spin-j UIR's of the Poincare group. For the massless case, normalized basis vectors vertical-barp 2 =0, lambda 0 ; plambda> are similarly constructed, where lambda 0 is the ''superhelicity.'' Matrix elements of the supersymmetry generators, in these bases, are explicitly given. The ''sigma basis'' is used to define weight diagrams for the massive UIR's of supersymmetry, and their properties are briefly described. Eigenfunctions ω/sub sigma/(theta) are also defined, and their connection with the reduction of higher spin massive superfields PHI/subJ/(x,theta) is discussed. Finally, it is shown how gauge dependence necessarily arises with certain massless superfields. The massless scalar superfield, both gauge-dependent and gauge-independent, is discussed as an example
Group representations, error bases and quantum codes
Energy Technology Data Exchange (ETDEWEB)
Knill, E
1996-01-01
This report continues the discussion of unitary error bases and quantum codes. Nice error bases are characterized in terms of the existence of certain characters in a group. A general construction for error bases which are non-abelian over the center is given. The method for obtaining codes due to Calderbank et al. is generalized and expressed purely in representation theoretic terms. The significance of the inertia subgroup both for constructing codes and obtaining the set of transversally implementable operations is demonstrated.
An Informal Overview of the Unitary Group Approach
International Nuclear Information System (INIS)
Sonnad, V.; Escher, J.; Kruse, M.; Baker, R.
2016-01-01
The Unitary Groups Approach (UGA) is an elegant and conceptually unified approach to quantum structure calculations. It has been widely used in molecular structure calculations, and holds the promise of a single computational approach to structure calculations in a variety of different fields. We explore the possibility of extending the UGA to computations in atomic and nuclear structure as a simpler alternative to traditional Racah algebra-based approaches. We provide a simple introduction to the basic UGA and consider some of the issues in using the UGA with spin-dependent, multi-body Hamiltonians requiring multi-shell bases adapted to additional symmetries. While the UGA is perfectly capable of dealing with such problems, it is seen that the complexity rises dramatically, and the UGA is not at this time, a simpler alternative to Racah algebra-based approaches.
The unitary-group formulation of quantum chemistry
International Nuclear Information System (INIS)
Campbell, L.L.
1990-01-01
The major part of this dissertation establishes group theoretical techniques that are applicable to the quantum-mechanical many-body atomic and molecular problems. Several matrix element evaluation methods for many-body states are developed. The generator commutation method using generator states is presented for the first time as a complete algorithm, and a computer implementation of the method is developed. A major result of this work is the development of a new method of calculation called the freeon tensor product (FTP) method. This method is much simpler and for many purposes superior to the GUGA procedure (graphical unitary group approach), widely used in configuration interaction calculations. This dissertation is also concerned with the prediction of atomic spectra. In principle spectra can be computed by the methods of ab initio quantum chemistry. In practice these computations are difficult, expensive, time consuming, and not uniformly successful. In this dissertation, the author employs a semi-empirical group theoretical analysis of discrete spectra is the exact analog of the Fourier analysis of continuous functions. In particular, he focuses on the spectra of atoms with incomplete p, d, and f shells. The formulas and techniques are derived in a fashion that apply equally well for more complex systems, as well as the isofreeon model of spherical nuclei
International Nuclear Information System (INIS)
Guenaydin, Murat; Pavlyk, Oleksandr
2005-01-01
We study the symmetries of generalized spacetimes and corresponding phase spaces defined by Jordan algebras of degree three. The generic Jordan family of formally real Jordan algebras of degree three describe extensions of the minkowskian spacetimes by an extra 'dilatonic' coordinate, whose rotation, Lorentz and conformal groups are SO(d-1), SO(d-1,1) x SO(1,1) and SO(d,2) x SO(2,1), respectively. The generalized spacetimes described by simple Jordan algebras of degree three correspond to extensions of minkowskian spacetimes in the critical dimensions (d = 3,4,6,10) by a dilatonic and extra commuting spinorial coordinates, respectively. Their rotation, Lorentz and conformal groups are those that occur in the first three rows of the Magic Square. The Freudenthal triple systems defined over these Jordan algebras describe conformally covariant phase spaces. Following hep-th/0008063, we give a unified geometric realization of the quasiconformal groups that act on their conformal phase spaces extended by an extra 'cocycle' coordinate. For the generic Jordan family the quasiconformal groups are SO(d+2,4), whose minimal unitary realizations are given. The minimal unitary representations of the quasiconformal groups F 4(4) , E 6(2) , E 7(-5) and E 8(-24) of the simple Jordan family were given in our earlier work
Directory of Open Access Journals (Sweden)
Tomas eVeloz
2015-11-01
Full Text Available Quantum models of concept combinations have been successful in representing various experimental situations that cannot be accommodated by traditional models based on classical probability or fuzzy set theory. In many cases, the focus has been on producing a representation that fits experimental results to validate quantum models. However, these representations are not always consistent with the cognitive modeling principles. Moreover, some important issues related to the representation of concepts such as the dimensionality of the realization space, the uniqueness of solutions, and the compatibility of measurements, have been overlooked.In this paper, we provide a dimensional analysis of the realization space for the two-sector Fock space model for conjunction of concepts focusing on the first and second sectors separately. We then introduce various representation of concepts that arise from the use of unitary operators in the realization space. In these concrete representations, a pair of concepts and their combination are modeled by a single conceptual state, and by a collection of exemplar-dependent operators. Therefore, they are consistent with cognitive modeling principles. %Moreover, we show that each representation is unique up to change of basis. This framework not only provides a uniform approach to model an entire data set, but, because all measurement operators are expressed in the same basis, allows us to address the question of compatibility of measurements. In particular, we present evidence that it may be possible to predict non-commutative effects from partial measurements of conceptual combinations.
Veloz, Tomas; Desjardins, Sylvie
2015-01-01
Quantum models of concept combinations have been successful in representing various experimental situations that cannot be accommodated by traditional models based on classical probability or fuzzy set theory. In many cases, the focus has been on producing a representation that fits experimental results to validate quantum models. However, these representations are not always consistent with the cognitive modeling principles. Moreover, some important issues related to the representation of concepts such as the dimensionality of the realization space, the uniqueness of solutions, and the compatibility of measurements, have been overlooked. In this paper, we provide a dimensional analysis of the realization space for the two-sector Fock space model for conjunction of concepts focusing on the first and second sectors separately. We then introduce various representation of concepts that arise from the use of unitary operators in the realization space. In these concrete representations, a pair of concepts and their combination are modeled by a single conceptual state, and by a collection of exemplar-dependent operators. Therefore, they are consistent with cognitive modeling principles. This framework not only provides a uniform approach to model an entire data set, but, because all measurement operators are expressed in the same basis, allows us to address the question of compatibility of measurements. In particular, we present evidence that it may be possible to predict non-commutative effects from partial measurements of conceptual combinations.
Uniformly bounded representations of the Lorentz groups
International Nuclear Information System (INIS)
Brega, A.O.
1982-01-01
For the Lorentz group G = SO/sub e/(n + 1, 1)(ngreater than or equal to 2) the author constructs a family of uniformly bounded representations by means of analytically continuing a certain normalization of the unitary principal series. The method the author uses relies on an analysis of various operators under a Mellin transform and extends earlier work of E.N. Wilson. In a series of papers Kunze and Stein initiated the theory of uniformly bounded representations of semisimple Lie groups; the starting point is the unitary principal series T(sigma,s) obtained in a certain subgroup M of G and a purely imaginary number s. From there Kunze and Stein constructed families of representations R(sigma,s) depending analytically on a parameter s in a domain D of C containing the imaginary axis which are unitarily equilvalent to T(sigma,s) for s contained in the set of imaginary numbers and whose operator norms are uniformly bounded for each s in D. In the case of the Lorentz groups SO/sub e/(n + 1, 1)(ngreater than or equal to2) and the trivial representation 1 of M, E.N. Wilson obtained such a family R(1,s) for the domain D = [s contained in the set of C: absolute value Re(s) Vertical Bar2]. For this domain D and for any representation sigma of M the author provides a family R(sigma,s) of uniformly bounded representations analytically continuing T(sigma,s), thereby generalizing Wilson's work. The author has also investigated certain symmetry properties of the representations R(sigma,s) under the action of the Weyl group. The trivial representation is Weyl group invariant and the family R(1,s) obtained by Wilson satisfies R(1,s) = R(1,-s) reflecting this. Obtained was the analogous result R(sigma,s) = R(sigma,-s) for some well known representations sigma that are Weyl group invariant. This involves the explicit computation of certain constants arising in the Fourier transforms of intertwining operators
Smooth vectors and Weyl-Pedersen calculus for representations of nilpotent Lie groups
Beltita, Ingrid; Beltita, Daniel
2009-01-01
We present some recent results on smooth vectors for unitary irreducible representations of nilpotent Lie groups. Applications to the Weyl-Pedersen calculus of pseudo-differential operators with symbols on the coadjoint orbits are also discussed.
Quantum theory, groups and representations an introduction
Woit, Peter
2017-01-01
This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific ...
International Nuclear Information System (INIS)
Govil, Karan; Gunaydin, Murat
2013-01-01
Quantization of the geometric quasiconformal realizations of noncompact groups and supergroups leads directly to their minimal unitary representations (minreps). Using quasiconformal methods massless unitary supermultiplets of superconformal groups SU(2,2|N) and OSp(8 ⁎ |2n) in four and six dimensions were constructed as minreps and their U(1) and SU(2) deformations, respectively. In this paper we extend these results to SU(2) deformations of the minrep of N=4 superconformal algebra D(2,1;λ) in one dimension. We find that SU(2) deformations can be achieved using n pair of bosons and m pairs of fermions simultaneously. The generators of deformed minimal representations of D(2,1;λ) commute with the generators of a dual superalgebra OSp(2n ⁎ |2m) realized in terms of these bosons and fermions. We show that there exists a precise mapping between symmetry generators of N=4 superconformal models in harmonic superspace studied recently and minimal unitary supermultiplets of D(2,1;λ) deformed by a pair of bosons. This can be understood as a particular case of a general mapping between the spectra of quantum mechanical quaternionic Kähler sigma models with eight super symmetries and minreps of their isometry groups that descends from the precise mapping established between the 4d, N=2 sigma models coupled to supergravity and minreps of their isometry groups.
Diffeomorphism Group Representations in Relativistic Quantum Field Theory
Energy Technology Data Exchange (ETDEWEB)
Goldin, Gerald A. [Rutgers Univ., Piscataway, NJ (United States); Sharp, David H. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-12-20
We explore the role played by the di eomorphism group and its unitary representations in relativistic quantum eld theory. From the quantum kinematics of particles described by representations of the di eomorphism group of a space-like surface in an inertial reference frame, we reconstruct the local relativistic neutral scalar eld in the Fock representation. An explicit expression for the free Hamiltonian is obtained in terms of the Lie algebra generators (mass and momentum densities). We suggest that this approach can be generalized to elds whose quanta are spatially extended objects.
Factorial representations of path groups
International Nuclear Information System (INIS)
Albeverio, S.; Hoegh-Krohn, R.; Testard, D.; Vershik, A.
1983-11-01
We give the reduction of the energy representation of the group of mappings from I = [ 0,1 ], S 1 , IRsub(+) or IR into a compact semi simple Lie group G. For G = SU(2) we prove the factoriality of the representation, which is of type III in the case I = IR
Gaussian elimination in split unitary groups with an application to public-key cryptography
Directory of Open Access Journals (Sweden)
Ayan Mahalanobis
2017-07-01
Full Text Available Gaussian elimination is used in special linear groups to solve the word problem. In this paper, we extend Gaussian elimination to split unitary groups. These algorithms have an application in building a public-key cryptosystem, we demonstrate that.
Unitary symmetry, combinatorics, and special functions
Energy Technology Data Exchange (ETDEWEB)
Louck, J.D.
1996-12-31
From 1967 to 1994, Larry Biedenham and I collaborated on 35 papers on various aspects of the general unitary group, especially its unitary irreducible representations and Wigner-Clebsch-Gordan coefficients. In our studies to unveil comprehensible structures in this subject, we discovered several nice results in special functions and combinatorics. The more important of these will be presented and their present status reviewed.
Unitary representations of some infinite-dimensional Lie algebras motivated by string theory on AdS3
International Nuclear Information System (INIS)
Andreev, Oleg
1999-01-01
We consider some unitary representations of infinite-dimensional Lie algebras motivated by string theory on AdS 3 . These include examples of two kinds: the A,D,E type affine Lie algebras and the N=4 superconformal algebra. The first presents a new construction for free field representations of affine Lie algebras. The second is of a particular physical interest because it provides some hints that a hybrid of the NSR and GS formulations for string theory on AdS 3 exists
On the representations of Poincare group associated with unstable particles
International Nuclear Information System (INIS)
Exner, RP.
1983-01-01
The problem of relativistically-covariant description of unstable particles is reexamined. We follow the approach which associates a unitary reducible representation of Poincare group with a larger isolated system, and compare it with the one ascribing a non-unitary irreducible representation to the unstable particle alone. It is shown that the problem roots in choice of the subspace Hsub(u) of the state Hilbert space which could be related to the unstable particle. Translational invariance of Hsub(u) is proved to be incompatible with unitarity of the boosts. Further we propose a concrete choice of Hsub(u) and argue that in most cases of the actual experimental arrangements, this subspace is effectively one-dimensional. A correct slow-down for decay of a moving particle is obtained
Topology of unitary groups and the prime orders of binomial coefficients
Duan, HaiBao; Lin, XianZu
2017-09-01
Let $c:SU(n)\\rightarrow PSU(n)=SU(n)/\\mathbb{Z}_{n}$ be the quotient map of the special unitary group $SU(n)$ by its center subgroup $\\mathbb{Z}_{n}$. We determine the induced homomorphism $c^{\\ast}:$ $H^{\\ast}(PSU(n))\\rightarrow H^{\\ast}(SU(n))$ on cohomologies by computing with the prime orders of binomial coefficients
International Nuclear Information System (INIS)
Quesne, C.
1986-01-01
In the present series of papers, the coherent states of Sp(2d,R), corresponding to the positive discrete series irreducible representations 1 +n/2> encountered in physical applications, are analyzed in detail with special emphasis on those of Sp(4,R) and Sp(6,R). The present paper discusses the unitary-operator coherent states, as defined by Klauder, Perelomov, and Gilmore. These states are parametrized by the points of the coset space Sp(2d,R)/H, where H is the stability group of the Sp(2d,R) irreducible representation lowest weight state, chosen as the reference state, and depends upon the relative values of lambda 1 ,...,lambda/sub d/, subject to the conditions lambda 1 > or =lambda 2 > or = x x x > or =lambda/sub d/> or =0. A parametrization of Sp(2d,R)/H corresponding to a factorization of the latter into a product of coset spaces Sp(2d,R)/U(d) and U(d)/H is chosen. The overlap of two coherent states is calculated, the action of the Sp(2d,R) generators on the coherent states is determined, and the explicit form of the unity resolution relation satisfied by the coherent states in the representation space of the irreducible representation is obtained. The Hilbert space of analytic functions arising from the coherent state representation is studied in detail. Finally, some applications of the formalism developed in the present paper are outlined
Symmetric group representations and Z
Adve, Anshul; Yong, Alexander
2017-01-01
We discuss implications of the following statement about the representation theory of symmetric groups: every integer appears infinitely often as an irreducible character evaluation, and every nonnegative integer appears infinitely often as a Littlewood-Richardson coefficient and as a Kronecker coefficient.
DEFF Research Database (Denmark)
Möllers, Jan
2013-01-01
(\\pi)\\subseteq\\mathfrak{p}_{\\mathbb{C}}^*$. The associated variety $Ass(\\pi)$ is the closure of a single nilpotent $K_{\\mathbb{C}}$-orbit $\\mathcal{O}^{K_{\\mathbb{C}}}\\subseteq\\mathfrak{p}_{\\mathbb{C}}^*$ which corresponds by the Kostant-Sekiguchi correspondence to a nilpotent coadjoint $G$-orbit $\\mathcal{O}^G\\subseteq\\mathfrak{g}^*$. The known Schr\\"odinger...... model of $\\pi$ is a realization on $L^2(\\mathcal{O})$, where $\\mathcal{O}\\subseteq\\mathcal{O}^G$ is a Lagrangian submanifold. We construct an intertwining operator from the Schr\\"odinger model to the new Fock model, the generalized Segal-Bargmann transform, which gives a geometric quantization...... and as integral kernel of the Segal-Bargmann transform. As a corollary to our construction we also obtain the integral kernel of the unitary inversion operator in the Schr\\"odinger model in terms of a multivariable $J$-Bessel function....
International Nuclear Information System (INIS)
Joos, H.; Schaefer, M.
1987-01-01
The symmetry group of staggered lattice fermions is discussed as a discrete subgroup of the symmetry group of the Dirac-Kaehler equation. For the representation theory of this group, G. Mackey's generalization of E.P. Wigner's procedure for the construction of unitary representations of groups with normal subgroups is used. A complete classification of these irreducible representations by ''momentum stars'', ''flavour orbits'' and ''reduced spins'' is given. (orig.)
Collective pairing states and nonunitary representations of the quasi-spin group
International Nuclear Information System (INIS)
Lorazo, B.
1975-06-01
A mathematical proof is given of the intimate connection of the physical generalized seniority states (i.e. states the excitation energy spectra of which does not depend upon the number of particles) with states transforming according to non-unitary representations of the quasi-spin group [fr
On irreducible representations of the ultrahyperbolic BMS group
International Nuclear Information System (INIS)
McCarthy, Patrick J.; Melas, Evangelos
2003-01-01
The ordinary Bondi-Metzner-Sachs (BMS) group B is the common asymptotic symmetry group of all asymptotically flat Lorentzian space-times. As such, B is the best candidate for the universal symmetry group of General Relativity. However, in studying quantum gravity, space-times with signatures other than the usual Lorentzian one, and complex space-times, are frequently considered. Generalisations of B appropriate to these other signatures have been defined earlier. Here, the generalisation B(2,2) appropriate to the ultrahyperbolic signature (+,+,-,-) is described in detail, and the irreducible unitary representations (IRs) of B(2,2) are analysed. It is proved that all induced IRs of B(2,2) arise from IRs of compact 'little groups'. These little groups, which are closed subgroups of K=SO(2)xSO(2), are classified here in detail, with particular attention paid to those of infinite order
Representation Theory of Algebraic Groups and Quantum Groups
Gyoja, A; Shinoda, K-I; Shoji, T; Tanisaki, Toshiyuki
2010-01-01
Invited articles by top notch expertsFocus is on topics in representation theory of algebraic groups and quantum groupsOf interest to graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics
International Nuclear Information System (INIS)
Saxe, P.; Fox, D.J.; Schaefer, H.F. III; Handy, N.C.
1982-01-01
A new method for the approximate solution of Schroedinger's equation for many electron molecular systems is outlined. The new method is based on the unitary group approach (UGA) and exploits in particular the shape of loops appearing in Shavitt's graphical representation for the UGA. The method is cast in the form of a direct CI, makes use of Siegbahn's external space simplifications, and is suitable for very large configuration interaction (CI) wave functions. The ethylene molecule was chosen, as a prototype of unsaturated organic molecules, for the variational study of genuine many (i.e.,>2) body correlation effects. With a double zeta plus polarization basis set, the largest CI included all valence electron single and double excitations with respect to a 703 configuration natural orbital reference function. This variational calculation, involving 1 046 758 spin- and space-adapted 1 A/sub g/ configurations, was carried out on a minicomputer. Triple excitations are found to contribute 2.3% of the correlation energy and quadruple excitations 6.4%
International Nuclear Information System (INIS)
Giovannini, N.
1977-01-01
A complete description of the projective unitary/antiunitary representations of the general covariance group for a charged (relativistic) particle moving in an external (classical), e.m. field is given. This group was derived in a previous paper, independently of any equation of motion, on the basis of some simple physical assumptions. The physical consequences of these results are then discussed and it is shown how they open some new perspectives. (Auth.)
A remark on the unitary group of a tensor product of n finite ...
Indian Academy of Sciences (India)
By using the method of quantum circuits in the theory of quantum computing as outlined in Nielsen and Chuang [2] and using a key lemma of Jaikumar [1] we show that every unitary operator on the tensor product H = H 1 ⊗ H 2 ⊗ … ⊗ H n can be expressed as a composition of a finite number of unitary operators living on ...
Braid group representation on quantum computation
Energy Technology Data Exchange (ETDEWEB)
Aziz, Ryan Kasyfil, E-mail: kasyfilryan@gmail.com [Department of Computational Sciences, Bandung Institute of Technology (Indonesia); Muchtadi-Alamsyah, Intan, E-mail: ntan@math.itb.ac.id [Algebra Research Group, Bandung Institute of Technology (Indonesia)
2015-09-30
There are many studies about topological representation of quantum computation recently. One of diagram representation of quantum computation is by using ZX-Calculus. In this paper we will make a diagrammatical scheme of Dense Coding. We also proved that ZX-Calculus diagram of maximally entangle state satisfies Yang-Baxter Equation and therefore, we can construct a Braid Group representation of set of maximally entangle state.
Klein Topological Field Theories from Group Representations
Directory of Open Access Journals (Sweden)
Sergey A. Loktev
2011-07-01
Full Text Available We show that any complex (respectively real representation of finite group naturally generates a open-closed (respectively Klein topological field theory over complex numbers. We relate the 1-point correlator for the projective plane in this theory with the Frobenius-Schur indicator on the representation. We relate any complex simple Klein TFT to a real division ring.
Analytic vectors and irreducible representations of nilpotent Lie groups and algebras
International Nuclear Information System (INIS)
Arnal, D.
1978-01-01
Let U be a unitary irreducible locally faithful representation of a nilpotent Lie group G, V the universal enveloping algebra of G, M a simple module on V with kernel ker dU, then there exists an automorphism of V keeping ker dU invariant such that, after transport of structure, M is isomorphic to a submodule of the space of analytic vectors for U. (Auth.)
Sen, Avijit; Sen, Sangita; Samanta, Pradipta Kumar; Mukherjee, Debashis
2015-04-05
We present here a comprehensive account of the formulation and pilot applications of the second-order perturbative analogue of the recently proposed unitary group adapted state-specific multireference coupled cluster theory (UGA-SSMRCC), which we call as the UGA-SSMRPT2. We also discuss the essential similarities and differences between the UGA-SSMRPT2 and the allied SA-SSMRPT2. Our theory, like its parent UGA-SSMRCC formalism, is size-extensive. However, because of the noninvariance of the theory with respect to the transformation among the active orbitals, it requires the use of localized orbitals to ensure size-consistency. We have demonstrated the performance of the formalism with a set of pilot applications, exploring (a) the accuracy of the potential energy surface (PES) of a set of small prototypical difficult molecules in their various low-lying states, using natural, pseudocanonical and localized orbitals and compared the respective nonparallelity errors (NPE) and the mean average deviations (MAD) vis-a-vis the full CI results with the same basis; (b) the efficacy of localized active orbitals to ensure and demonstrate manifest size-consistency with respect to fragmentation. We found that natural orbitals lead to the best overall PES, as evidenced by the NPE and MAD values. The MRMP2 results for individual states and of the MCQDPT2 for multiple states displaying avoided curve crossings are uniformly poorer as compared with the UGA-SSMRPT2 results. The striking aspect of the size-consistency check is the complete insensitivity of the sum of fragment energies with given fragment spin-multiplicities, which are obtained as the asymptotic limit of super-molecules with different coupled spins. © 2015 Wiley Periodicals, Inc.
Clifford theory for group representations
Karpilovsky, G
1989-01-01
Let N be a normal subgroup of a finite group G and let F be a field. An important method for constructing irreducible FG-modules consists of the application (perhaps repeated) of three basic operations: (i) restriction to FN. (ii) extension from FN. (iii) induction from FN. This is the `Clifford Theory' developed by Clifford in 1937. In the past twenty years, the theory has enjoyed a period of vigorous development. The foundations have been strengthened and reorganized from new points of view, especially from the viewpoint of graded rings and crossed products.The purpos
International Nuclear Information System (INIS)
Ketov, S.V.
1996-01-01
The simplest free-field realizations of the exceptional non-linear (quadratically generated, or W-type) N=8 and N=7 superconformal algebras with Spin(7) and G 2 affine currents, respectively, are investigated. Both the N=8 and N=7 algebras are found to admit unitary and highest-weight irreducible representations in terms of a single free boson and free fermions in 8 of Spin(7) or 7 of G 2 , respectively, at level k=1 and the corresponding central charges c 8 =26/5 and c 7 =5. (orig.)
The representations of Lie groups and geometric quantizations
International Nuclear Information System (INIS)
Zhao Qiang
1998-01-01
In this paper we discuss the relation between representations of Lie groups and geometric quantizations. A series of representations of Lie groups are constructed by geometric quantization of coadjoint orbits. Particularly, all representations of compact Lie groups, holomorphic discrete series of representations and spherical representations of reductive Lie groups are constructed by geometric quantizations of elliptic and hyperbolic coadjoint orbits. (orig.)
A course in finite group representation theory
Webb, Peter
2016-01-01
This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.
International Nuclear Information System (INIS)
Ibort, A; Man'ko, V I; Marmo, G; Simoni, A; Ventriglia, F
2009-01-01
A natural extension of the Wigner function to the space of irreducible unitary representations of the Weyl-Heisenberg group is discussed. The action of the automorphisms group of the Weyl-Heisenberg group onto Wigner functions and their generalizations and onto symplectic tomograms is elucidated. Some examples of physical systems are considered to illustrate some aspects of the characterization of the Wigner functions as solutions of differential equations
Representations of the infinite symmetric group
Borodin, Alexei
2016-01-01
Representation theory of big groups is an important and quickly developing part of modern mathematics, giving rise to a variety of important applications in probability and mathematical physics. This book provides the first concise and self-contained introduction to the theory on the simplest yet very nontrivial example of the infinite symmetric group, focusing on its deep connections to probability, mathematical physics, and algebraic combinatorics. Following a discussion of the classical Thoma's theorem which describes the characters of the infinite symmetric group, the authors describe explicit constructions of an important class of representations, including both the irreducible and generalized ones. Complete with detailed proofs, as well as numerous examples and exercises which help to summarize recent developments in the field, this book will enable graduates to enhance their understanding of the topic, while also aiding lecturers and researchers in related areas.
On Parametrization of the Linear GL(4,C) and Unitary SU(4) Groups in Terms of Dirac Matrices
Red'Kov, Victor M.; Bogush, Andrei A.; Tokarevskaya, Natalia G.
2008-02-01
Parametrization of 4 × 4-matrices G of the complex linear group GL(4,C) in terms of four complex 4-vector parameters (k,m,n,l) is investigated. Additional restrictions separating some subgroups of GL(4,C) are given explicitly. In the given parametrization, the problem of inverting any 4 × 4 matrix G is solved. Expression for determinant of any matrix G is found: det G = F(k,m,n,l). Unitarity conditions G+ = G-1 have been formulated in the form of non-linear cubic algebraic equations including complex conjugation. Several simplest solutions of these unitarity equations have been found: three 2-parametric subgroups G1, G2, G3 - each of subgroups consists of two commuting Abelian unitary groups; 4-parametric unitary subgroup consis! ting of a product of a 3-parametric group isomorphic SU(2) and 1-parametric Abelian group. The Dirac basis of generators Λk, being of Gell-Mann type, substantially differs from the basis λi used in the literature on SU(4) group, formulas relating them are found - they permit to separate SU(3) subgroup in SU(4). Special way to list 15 Dirac generators of GL(4,C) can be used {Λk} = {μiÅνjÅ(μiVνj = KÅL ÅM )}, which permit to factorize SU(4) transformations according to S = eiaμ eibνeikKeilLeimM, where two first factors commute with each other and are isomorphic to SU(2) group, the three last ones are 3-parametric groups, each of them consisting of three Abelian commuting unitary subgroups. Besides, the structure of fifteen Dirac matrices Λk permits to separate twenty 3-parametric subgroups in SU(4) isomorphic to SU(2); those subgroups might be used as bigger elementary blocks in constructing of a general transformation SU(4). It is shown how one can specify the present approach for the pseudounitary group SU(2,2) and SU(3,1).
Wigner functions for noncommutative quantum mechanics: A group representation based construction
Energy Technology Data Exchange (ETDEWEB)
Chowdhury, S. Hasibul Hassan, E-mail: shhchowdhury@gmail.com [Chern Institute of Mathematics, Nankai University, Tianjin 300071 (China); Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8 (Canada); Ali, S. Twareque, E-mail: twareque.ali@concordia.ca [Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8 (Canada)
2015-12-15
This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions, and star-products, following a technique developed earlier, viz, using the unitary irreducible representations of the group G{sub NC}, which is the three fold central extension of the Abelian group of ℝ{sup 4}. These representations have been exhaustively studied in earlier papers. The group G{sub NC} is identified with the kinematical symmetry group of noncommutative quantum mechanics of a system with two degrees of freedom. The Wigner functions studied here reflect different levels of non-commutativity—both the operators of position and those of momentum not commuting, the position operators not commuting and finally, the case of standard quantum mechanics, obeying the canonical commutation relations only.
Method for the determination of Clebsch-Gordan coefficients of finite magnetic groups
van den Broek, P.M.; Horowitz, L.P.; Ne'eman, Y.
1980-01-01
A recent method for the determination of Clebsch-Gordan coefficients of finite magnetic groups is generalised to magnetic groups. Discussion is restricted to unitary-anti-unitary representations of type I.
Analytic factorization of Lie group representations
DEFF Research Database (Denmark)
Gimperlein, Heiko; Krötz, Bernhard; Lienau, Christoph
2012-01-01
For every moderate growth representation (p,E)(p,E) of a real Lie group G on a Fréchet space, we prove a factorization theorem of Dixmier–Malliavin type for the space of analytic vectors E¿E¿. There exists a natural algebra of superexponentially decreasing analytic functions A(G)A(G), such that E......¿=¿(A(G))E¿E¿=¿(A(G))E¿. As a corollary we obtain that E¿E¿ coincides with the space of analytic vectors for the Laplace–Beltrami operator on G....
Gessner, Manuel; Breuer, Heinz-Peter
2013-04-01
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of complex open quantum systems, employing arguments from ensemble theory. We further generalize these results to arbitrary eigenvalue distributions, allowing a detailed comparison of typical regular and chaotic systems with the help of concepts from random matrix theory. To illustrate the physical relevance and the general applicability of our results we present a series of examples related to the fields of open quantum systems and nonequilibrium quantum thermodynamics. These include the effect of initial correlations, the average quantum dynamical maps, the generic dynamics of system-environment pure state entanglement and, finally, the equilibration of generic open and closed quantum systems.
Induced representations of the affine group and intertwining operators: I. Analytical approach
International Nuclear Information System (INIS)
Elmabrok, Abdelhamid S; Hutník, Ondrej
2012-01-01
We analyze the construction and origin of unitary operators describing the structure of the space of continuous wavelet transforms inside the space L 2 (G,dν L ) of all square-integrable functions on the affine group G with respect to the left-invariant Haar measure from the viewpoint of induced representations of G. We show that these operators are, in fact, intertwining operators among pairs of induced representations of the affine group G. A characterization of the space of wavelet transforms using the Cauchy–Riemann-type equations is given. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)
Unitary unified field theories
International Nuclear Information System (INIS)
Sudarshan, E.C.G.
1976-01-01
This is an informal exposition of some recent developments. Starting with an examination of the universality of electromagnetic and weak interactions, the attempts at their unification are outlined. The theory of unitary renormalizable self-coupled vector mesons with dynamical sources is formulated for a general group. With masses introduced as variable parameters it is shown that the theory so defined is indeed unitary. Diagrammatic rules are developed in terms of a chosen set of fictitious particles. A number of special examples are outlined including a theory with strongly interacting vector and axial vector mesons and weak mesons. Applications to weak interactions of strange particles is briefly outlined. (Auth.)
Evenly distributed unitaries: On the structure of unitary designs
International Nuclear Information System (INIS)
Gross, D.; Audenaert, K.; Eisert, J.
2007-01-01
We clarify the mathematical structure underlying unitary t-designs. These are sets of unitary matrices, evenly distributed in the sense that the average of any tth order polynomial over the design equals the average over the entire unitary group. We present a simple necessary and sufficient criterion for deciding if a set of matrices constitutes a design. Lower bounds for the number of elements of 2-designs are derived. We show how to turn mutually unbiased bases into approximate 2-designs whose cardinality is optimal in leading order. Designs of higher order are discussed and an example of a unitary 5-design is presented. We comment on the relation between unitary and spherical designs and outline methods for finding designs numerically or by searching character tables of finite groups. Further, we sketch connections to problems in linear optics and questions regarding typical entanglement
An introduction to group representation theory
Keown, R D M
1975-01-01
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat
International Nuclear Information System (INIS)
Brooks, B.R.
1979-09-01
The Graphical Unitary Group Approach (GUGA) was cast into an extraordinarily powerful form by restructuring the Hamiltonian in terms of loop types. This restructuring allows the adoption of the loop-driven formulation which illuminates vast numbers of previously unappreciated relationships between otherwise distinct Hamiltonian matrix elements. The theoretical/methodological contributions made here include the development of the loop-driven formula generation algorithm, a solution of the upper walk problem used to develop a loop breakdown algorithm, the restriction of configuration space employed to the multireference interacting space, and the restructuring of the Hamiltonian in terms of loop types. Several other developments are presented and discussed. Among these developments are the use of new segment coefficients, improvements in the loop-driven algorithm, implicit generation of loops wholly within the external space adapted within the framework of the loop-driven methodology, and comparisons of the diagonalization tape method to the direct method. It is also shown how it is possible to implement the GUGA method without the time-consuming full (m 5 ) four-index transformation. A particularly promising new direction presented here involves the use of the GUGA methodology to obtain one-electron and two-electron density matrices. Once these are known, analytical gradients (first derivatives) of the CI potential energy are easily obtained. Several test calculations are examined in detail to illustrate the unique features of the method. Also included is a calculation on the asymmetric 2 1 A' state of SO 2 with 23,613 configurations to demonstrate methods for the diagonalization of very large matrices on a minicomputer. 6 figures, 6 tables
Magnetic translation groups in an n-dimensional torus and their representations
International Nuclear Information System (INIS)
Tanimura, Shogo
2002-01-01
A charged particle in a uniform magnetic field in a two-dimensional torus has a discrete noncommutative translation symmetry instead of a continuous commutative translation symmetry. We study topology and symmetry of a particle in a magnetic field in a torus of arbitrary dimensions. The magnetic translation group (MTG) is defined as a group of translations that leave the gauge field invariant. We show that the MTG in an n-dimensional torus is isomorphic to a central extension of a cyclic group Z ν 1 x···xZ ν 2l xT m by U(1) with 2l+m=n. We construct and classify irreducible unitary representations of the MTG in a three-torus and apply the representation theory to three examples. We briefly describe a representation theory for a general n-torus. The MTG in an n-torus can be regarded as a generalization of the so-called noncommutative torus
The endoscopic classification of representations orthogonal and symplectic groups
Arthur, James
2013-01-01
Within the Langlands program, endoscopy is a fundamental process for relating automorphic representations of one group with those of another. In this book, Arthur establishes an endoscopic classification of automorphic representations of orthogonal and symplectic groups G. The representations are shown to occur in families (known as global L-packets and A-packets), which are parametrized by certain self-dual automorphic representations of an associated general linear group GL(N). The central result is a simple and explicit formula for the multiplicity in the automorphic discrete spectrum of G
A Possible Neural Representation of Mathematical Group Structures.
Pomi, Andrés
2016-09-01
Every cognitive activity has a neural representation in the brain. When humans deal with abstract mathematical structures, for instance finite groups, certain patterns of activity are occurring in the brain that constitute their neural representation. A formal neurocognitive theory must account for all the activities developed by our brain and provide a possible neural representation for them. Associative memories are neural network models that have a good chance of achieving a universal representation of cognitive phenomena. In this work, we present a possible neural representation of mathematical group structures based on associative memory models that store finite groups through their Cayley graphs. A context-dependent associative memory stores the transitions between elements of the group when multiplied by each generator of a given presentation of the group. Under a convenient election of the vector basis mapping the elements of the group in the neural activity, the input of a vector corresponding to a generator of the group collapses the context-dependent rectangular matrix into a virtual square permutation matrix that is the matrix representation of the generator. This neural representation corresponds to the regular representation of the group, in which to each element is assigned a permutation matrix. This action of the generator on the memory matrix can also be seen as the dissection of the corresponding monochromatic subgraph of the Cayley graph of the group, and the adjacency matrix of this subgraph is the permutation matrix corresponding to the generator.
Fan, Hong-Yi; Chen, Jun-Hua
2002-08-01
We find that the coherent state projection operator representation of symplectic transformation constitutes a loyal group representation of symplectic group. The result of successively applying squeezing operators on number state can be easily derived. The project supported by National Natural Science Foundation of China under Grant No. 10575057 and the President Foundation of the Chinese Academy of Sciences
On the Representation Theory of the Ultrahyperbolic BMS group UHB(2, 2). I. General Results
International Nuclear Information System (INIS)
Melas, Evangelos
2015-01-01
The Bondi-Metzner-Sachs (BMS) group B is the common asymptotic group of all asymptotically flat (lorentzian) space-times, and is the best candidate for the universal symmetry group of General Relativity (G.R.). B admits generalizations to real space-times of any signature, to complex space-times, and supersymmetric generalizations for any space- time dimension. With this motivation McCarthy constructed the strongly continuous unitary irreducible representations (IRs) of B some time ago, and he identified B(2,2) as the generalization of B appropriate to the to the 'ultrahyperbolic signature' (+,+,−,−) and asymptotic flatness in null directions. We continue this programme by introducing a new group UHB(2, 2) in the group theoretical study of ultrahyperbolic G.R. which happens to be a proper subgroup of B(2, 2). In this short paper we report on the first general results on the representation theory of UHB(2, 2). In particular the main general results are that the all little groups of UHB(2, 2) are compact and that the Wigner-Mackey's inducing construction is exhaustive despite the fact that UHB(2, 2) is not locally compact in the employed Hilbert topology. At the end of the paper we comment on the significance of these results
First results on the representation theory of the Ultrahyperbolic BMS group UHB(2, 2)
International Nuclear Information System (INIS)
Melas, Evangelos
2016-01-01
The Bondi–Metzner–Sachs (BMS) group B is the common asymptotic group of all asymptotically flat (lorentzian) space–times, and is the best candidate for the universal symmetry group of General Relativity (G.R.). B admits generalizations to real space–times of any signature, to complex space–times, and supersymmetric generalizations for any space— time dimension. With this motivation McCarthy constructed the strongly continuous unitary irreducible representations (IRs) of B some time ago, and he identified B(2,2) as the generalization of B appropriate to the to the ultrahyperbolic signature (+,+,−,−) and asymptotic flatness in null directions. We continue this programme by introducing a new group UHB(2, 2) in the group theoretical study of ultrahyperbolic G.R. which happens to be a proper subgroup of B(2, 2). We report on the first general results on the representation theory of UHB(2, 2). In particular the main general results are that the all little groups of UHB(2, 2) are compact and that the Wigner–Mackeys inducing construction is exhaustive despite the fact that UHB(2, 2) is not locally compact in the employed Hilbert topology. (paper)
Representations of the ultrahyperbolic BMS group UHB(2, 2). I. General Results
International Nuclear Information System (INIS)
Melas, Evangelos
2015-01-01
The ordinary Bondi—Metzner—Sachs (BMS) group B is the common asymptotic symmetry group of all radiating, asymptotically flat, Lorentzian space—times. As such, B is the best candidate for the universal symmetry group of General Relativity (G.R.). However, in studying quantum gravity, space—times with signatures other than the usual Lorentzian one, and complex space-times, are frequently considered. Generalisations of B appropriate to these other signatures have been defined earlier. In particular, the generalisation B(2, 2) appropriate to the ultrahyperbolic signature (+,+, —,—) has been described in detail, and the study of its irreducible unitary representations (IRs) of B(2, 2) has been initiated. We continue this programme by introducing a new group UHB(2, 2) in the group theoretical study of ultrahyperbolic G.R. which happens to be a proper subgroup of B(2, 2). In this paper we report on the first general results on the representation theory of UHB(2, 2). In particular the main general results are that the all little groups of UHB(2, 2) are compact and that the Wigner—Mackey's inducing construction is exhaustive despite the fact that UHB(2, 2) is not locally compact in the employed Hilbert topology. (paper)
Special functions and the theory of group representations
Vilenkin, N Ja
1968-01-01
A standard scheme for a relation between special functions and group representation theory is the following: certain classes of special functions are interpreted as matrix elements of irreducible representations of a certain Lie group, and then properties of special functions are related to (and derived from) simple well-known facts of representation theory. The book combines the majority of known results in this direction. In particular, the author describes connections between the exponential functions and the additive group of real numbers (Fourier analysis), Legendre and Jacobi polynomials and representations of the group SU(2), and the hypergeometric function and representations of the group SL(2,R), as well as many other classes of special functions.
A representation independent propagator. Pt. 1. Compact Lie groups
International Nuclear Information System (INIS)
Tome, W.A.
1995-01-01
Conventional path integral expressions for propagators are representation dependent. Rather than having to adapt each propagator to the representation in question, it is shown that for compact Lie groups it is possible to introduce a propagator that is representation independent. For a given set of kinematical variables this propagator is a single function independent of any particular choice of fiducial vector, which monetheless, correctly propagates each element of the coherent state representation associated with these kinematical variables. Although the configuration space is in general curved, nevertheless the lattice phase-space path integral for the representation independent propagator has the form appropriate to flat space. To illustrate the general theory a representation independent propagator is explicitly constructed for the Lie group SU(2). (orig.)
Entanglement-continuous unitary transformations
Energy Technology Data Exchange (ETDEWEB)
Sahin, Serkan; Orus, Roman [Institute of Physics, Johannes Gutenberg University, 55099 Mainz (Germany)
2016-07-01
In this talk we present a new algorithm for quantum many-body systems using continuous unitary transformations (CUT) and tensor networks (TNs). With TNs we are able to approximate the solution to the flow equations that lie at the heart of continuous unitary transformations. We call this method Entanglement-Continuous Unitary Transformations (eCUT). It allows us to compute expectation values of local observables as well as tensor network representations of ground states and low-energy excited states. An implementation of the method is shown for 1d systems using matrix product operators. We show preliminary results for the 1d transverse-field Ising model to demonstrate the feasibility of the method.
Inequivalent coherent state representations in group field theory
Kegeles, Alexander; Oriti, Daniele; Tomlin, Casey
2018-06-01
In this paper we propose an algebraic formulation of group field theory and consider non-Fock representations based on coherent states. We show that we can construct representations with an infinite number of degrees of freedom on compact manifolds. We also show that these representations break translation symmetry. Since such representations can be regarded as quantum gravitational systems with an infinite number of fundamental pre-geometric building blocks, they may be more suitable for the description of effective geometrical phases of the theory.
Reducibility of quantum representations of mapping class groups
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Fjelstad, Jens
2010-01-01
that the quantum representations of all the mapping class groups built from the modular tensor category are reducible. In particular, for SU(N) we get reducibility for certain levels and ranks. For the quantum SU(2) Reshetikhin–Turaev theory we construct a decomposition for all even levels. We conjecture...... this decomposition is a complete decomposition into irreducible representations for high enough levels....
Studies on representation of the Lorentz group and gauge theory
International Nuclear Information System (INIS)
Hanitriarivo, R.
2002-01-01
This work is focused on studies about the representation of the Lorentz group and gauge theory. The mathematical tools required for the different studies are presented, as well as for the representation of the Lorentz group and for the gauge theory. Representation of the Lorentz group gives the possible types of fields and wave functions that describe particles: fermions are described by spinors and bosons are described by scalar or vector. Each of these entities (spinors, scalars, vectors) are characterized by their behavior under the action of Lorentz transformations.Gauge theory is used to describe the interactions between particles. [fr
Representations of the symmetric group as special cases of the boson polynomials in U(n)
International Nuclear Information System (INIS)
Biedenharn, L.C.; Louck, J.D.
1978-01-01
The set of all real, orthogonal irreps of S/sub n/ are realized explicitly and nonrecursively by specializing the boson polynomials carrying irreps of the unitary group. This realization makes use of a 'calculus of patterns', which is discussed
Representations of fundamental groups of algebraic varieties
Zuo, Kang
1999-01-01
Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties. The reader should have a basic knowledge of algebraic geometry and non-linear analysis. This book can form the basis for graduate level seminars in the area of topology of algebraic varieties. It also contains present new techniques for researchers working in this area.
Quantum unitary dynamics in cosmological spacetimes
International Nuclear Information System (INIS)
Cortez, Jerónimo; Mena Marugán, Guillermo A.; Velhinho, José M.
2015-01-01
We address the question of unitary implementation of the dynamics for scalar fields in cosmological scenarios. Together with invariance under spatial isometries, the requirement of a unitary evolution singles out a rescaling of the scalar field and a unitary equivalence class of Fock representations for the associated canonical commutation relations. Moreover, this criterion provides as well a privileged quantization for the unscaled field, even though the associated dynamics is not unitarily implementable in that case. We discuss the relation between the initial data that determine the Fock representations in the rescaled and unscaled descriptions, and clarify that the S-matrix is well defined in both cases. In our discussion, we also comment on a recently proposed generalized notion of unitary implementation of the dynamics, making clear the difference with the standard unitarity criterion and showing that the two approaches are not equivalent.
Quantum unitary dynamics in cosmological spacetimes
Energy Technology Data Exchange (ETDEWEB)
Cortez, Jerónimo, E-mail: jacq@ciencias.unam.mx [Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, México D.F. 04510 (Mexico); Mena Marugán, Guillermo A., E-mail: mena@iem.cfmac.csic.es [Instituto de Estructura de la Materia, IEM-CSIC, Serrano 121, 28006 Madrid (Spain); Velhinho, José M., E-mail: jvelhi@ubi.pt [Departamento de Física, Faculdade de Ciências, Universidade da Beira Interior, R. Marquês D’Ávila e Bolama, 6201-001 Covilhã (Portugal)
2015-12-15
We address the question of unitary implementation of the dynamics for scalar fields in cosmological scenarios. Together with invariance under spatial isometries, the requirement of a unitary evolution singles out a rescaling of the scalar field and a unitary equivalence class of Fock representations for the associated canonical commutation relations. Moreover, this criterion provides as well a privileged quantization for the unscaled field, even though the associated dynamics is not unitarily implementable in that case. We discuss the relation between the initial data that determine the Fock representations in the rescaled and unscaled descriptions, and clarify that the S-matrix is well defined in both cases. In our discussion, we also comment on a recently proposed generalized notion of unitary implementation of the dynamics, making clear the difference with the standard unitarity criterion and showing that the two approaches are not equivalent.
Unitary relation for the time-dependent SU(1,1) systems
International Nuclear Information System (INIS)
Song, Dae-Yup
2003-01-01
The system whose Hamiltonian is a linear combination of the generators of SU(1,1) group with time-dependent coefficients is studied. It is shown that there is a unitary relation between the system and a system whose Hamiltonian is simply proportional to the generator of the compact subgroup of SU(1,1). The unitary relation is described by the classical solutions of a time-dependent (harmonic) oscillator. Making use of the relation, the wave functions satisfying the Schroedinger equation are given, for a general unitary representation, in terms of the matrix elements of a finite group transformation (Bargmann function). The wave functions of the harmonic oscillator with an inverse-square potential is studied in detail, and it is shown that through an integral, the model provides a way of deriving the Bargmann function for the representation of positive discrete series of SU(1,1)
Lie groups, lie algebras, and representations an elementary introduction
Hall, Brian
2015-01-01
This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compac...
Minimal representations and Freudenthal triple systems
International Nuclear Information System (INIS)
Olive, D.
2004-01-01
Unitary representations of noncompact Lie groups have long been sought in physics. The first nice concrete construction was found by Dirac in connection with the anti-de Sitter group. Some subsequent generalizations will be described, in particular the minimal representation thought to be relevant to realising duality in supergravity superstring theories. A relation to Freudenthal triple systems will be described. (author)
On the ESQ Property of Certain Representations of Metacyclic Groups
Directory of Open Access Journals (Sweden)
János Wolosz
2017-06-01
Full Text Available A group representation is said to have the ESQ property if it is isomorphic to a quotient of its own exterior square. Let us denote the semidirect product of cyclic groups $Z_p\\rtimes Z_q$ by $F_{p,q}$, where p is a prime and $q | p − 1$. We investigate whether $F_{p,q}$ has an irreducible representation with the ESQ property. Fixing one of the parameters $q$ or $p−1$, we will be able to give an asymptotic answer to this question.
International Nuclear Information System (INIS)
Bergmann, P.G.
1980-01-01
A problem of construction of the unitary field theory is discussed. The preconditions of the theory are briefly described. The main attention is paid to the geometrical interpretation of physical fields. The meaning of the conceptions of diversity and exfoliation is elucidated. Two unitary field theories are described: the Weyl conformic geometry and Calitzy five-dimensioned theory. It is proposed to consider supersymmetrical theories as a new approach to the problem of a unitary field theory. It is noted that the supergravitational theories are really unitary theories, since the fields figuring there do not assume invariant expansion
Permutation representations of the orbits of the automorphism group ...
Indian Academy of Sciences (India)
Abstract. Consider a discrete valuation ring R whose residue field is finite of car- dinality at least 3. For a finite torsion module, we consider transitive subsets O under the action of the automorphism group of the module. We prove that the associated per- mutation representation on the complex vector space C[O] is multiplicity ...
The unitary space of particle internal states
International Nuclear Information System (INIS)
Perjes, Z.
1978-09-01
A relativistic theory of particle internal properties has been developed. Suppressing space-time information, internal wave functions and -observables are constructed in a 3-complex-dimensional space. The quantum numbers of a spinning point particle in this unitary space correspond with those of a low-mass hadron. Unitary space physics is linked with space-time notions via the Penrose theory of twistors, where new flavors may be represented by many-twistor systems. It is shown here that a four-twistor particle fits into the unitary space picture as a system of two points with equal masses and oppositely pointing unitary spins. Quantum states fall into the ISU(3) irreducible representations discovered by Sparling and the author. Full details of the computation involving SU(3) recoupling techniques are given. (author)
Non-commutative representation for quantum systems on Lie groups
Energy Technology Data Exchange (ETDEWEB)
Raasakka, Matti Tapio
2014-01-27
The topic of this thesis is a new representation for quantum systems on weakly exponential Lie groups in terms of a non-commutative algebra of functions, the associated non-commutative harmonic analysis, and some of its applications to specific physical systems. In the first part of the thesis, after a review of the necessary mathematical background, we introduce a {sup *}-algebra that is interpreted as the quantization of the canonical Poisson structure of the cotangent bundle over a Lie group. From the physics point of view, this represents the algebra of quantum observables of a physical system, whose configuration space is a Lie group. We then show that this quantum algebra can be represented either as operators acting on functions on the group, the usual group representation, or (under suitable conditions) as elements of a completion of the universal enveloping algebra of the Lie group, the algebra representation. We further apply the methods of deformation quantization to obtain a representation of the same algebra in terms of a non-commutative algebra of functions on a Euclidean space, which we call the non-commutative representation of the original quantum algebra. The non-commutative space that arises from the construction may be interpreted as the quantum momentum space of the physical system. We derive the transform between the group representation and the non-commutative representation that generalizes in a natural way the usual Fourier transform, and discuss key properties of this new non-commutative harmonic analysis. Finally, we exhibit the explicit forms of the non-commutative Fourier transform for three elementary Lie groups: R{sup d}, U(1) and SU(2). In the second part of the thesis, we consider application of the non-commutative representation and harmonic analysis to physics. First, we apply the formalism to quantum mechanics of a point particle on a Lie group. We define the dual non-commutative momentum representation, and derive the phase
Non-commutative representation for quantum systems on Lie groups
International Nuclear Information System (INIS)
Raasakka, Matti Tapio
2014-01-01
The topic of this thesis is a new representation for quantum systems on weakly exponential Lie groups in terms of a non-commutative algebra of functions, the associated non-commutative harmonic analysis, and some of its applications to specific physical systems. In the first part of the thesis, after a review of the necessary mathematical background, we introduce a * -algebra that is interpreted as the quantization of the canonical Poisson structure of the cotangent bundle over a Lie group. From the physics point of view, this represents the algebra of quantum observables of a physical system, whose configuration space is a Lie group. We then show that this quantum algebra can be represented either as operators acting on functions on the group, the usual group representation, or (under suitable conditions) as elements of a completion of the universal enveloping algebra of the Lie group, the algebra representation. We further apply the methods of deformation quantization to obtain a representation of the same algebra in terms of a non-commutative algebra of functions on a Euclidean space, which we call the non-commutative representation of the original quantum algebra. The non-commutative space that arises from the construction may be interpreted as the quantum momentum space of the physical system. We derive the transform between the group representation and the non-commutative representation that generalizes in a natural way the usual Fourier transform, and discuss key properties of this new non-commutative harmonic analysis. Finally, we exhibit the explicit forms of the non-commutative Fourier transform for three elementary Lie groups: R d , U(1) and SU(2). In the second part of the thesis, we consider application of the non-commutative representation and harmonic analysis to physics. First, we apply the formalism to quantum mechanics of a point particle on a Lie group. We define the dual non-commutative momentum representation, and derive the phase space path
International Nuclear Information System (INIS)
Klimko, G.T.; Luzanov, A.V.
1988-01-01
An analysis has been made of the problem of calculating one- and two-particle spin densities, which are needed in calculations of spin-orbit and spin-spin coupling. The proposed solution is oriented toward the application of computational algorithms using unitary group representations; the solution consists of explicit expressions for the matrix elements of spin density operators in terms of the means of products of spin-free generators. This has eliminated a serious problem encountered previously in determining spin characteristics of molecules within the framework of unitary formalism
Fock model and Segal-Bargmann transform for minimal representations of Hermitian Lie groups
DEFF Research Database (Denmark)
Hilgert, Joachim; Kobayashi, Toshiyuki; Möllers, Jan
2012-01-01
For any Hermitian Lie group G of tube type we construct a Fock model of its minimal representation. The Fock space is defined on the minimal nilpotent K_C-orbit X in p_C and the L^2-inner product involves a K-Bessel function as density. Here K is a maximal compact subgroup of G, and g......_C=k_C+p_C is a complexified Cartan decomposition. In this realization the space of k-finite vectors consists of holomorphic polynomials on X. The reproducing kernel of the Fock space is calculated explicitly in terms of an I-Bessel function. We further find an explicit formula of a generalized Segal-Bargmann transform which...... intertwines the Schroedinger and Fock model. Its kernel involves the same I-Bessel function. Using the Segal--Bargmann transform we also determine the integral kernel of the unitary inversion operator in the Schroedinger model which is given by a J-Bessel function....
Energy Technology Data Exchange (ETDEWEB)
Lorenzen, R.
2007-03-15
Starting from the assumption of modular P{sub 1}CT symmetry in quantum field theory a representation of the universal covering of the Poincar'e group is constructed in terms of pairs of modular conjugations. The modular conjugations are associated with field algebras of unbounded operators localised in wedge regions. It turns out that an essential step consists in characterising the universal covering group of the Lorentz group by pairs of wedge regions, in conjunction with an analysis of its geometrical properties. In this thesis two approaches to this problem are developed in four spacetime dimensions. First a realisation of the universal covering as the quotient space over the set of pairs of wedge regions is presented. In spite of the intuitive definition, the necessary properties of a covering space are not straightforward to prove. But the geometrical properties are easy to handle. The second approach takes advantage of the well-known features of spin groups, given as subgroups of Clifford algebras. Characterising elements of spin groups by pairs of wedge regions is possible in an elegant manner. The geometrical analysis is performed by means of the results achieved in the first approach. These geometrical properties allow for constructing a representation of the universal cover of the Lorentz group in terms of pairs of modular conjugations. For this representation the derivation of the spin-statistics theorem is straightforward, and a PCT operator can be defined. Furthermore, it is possible to transfer the results to nets of field algebras in algebraic quantum field theory with ease. Many of the usual assumptions in quantum field theory like the spectrum condition or the existence of a covariant unitary representation, as well as the assumption on the quantum field to have only finitely many components, are not required. For the standard axioms, the crucial assumption of modular P{sub 1}CT symmetry constitutes no loss of generality because it is a
International Nuclear Information System (INIS)
Lorenzen, R.
2007-03-01
Starting from the assumption of modular P 1 CT symmetry in quantum field theory a representation of the universal covering of the Poincar'e group is constructed in terms of pairs of modular conjugations. The modular conjugations are associated with field algebras of unbounded operators localised in wedge regions. It turns out that an essential step consists in characterising the universal covering group of the Lorentz group by pairs of wedge regions, in conjunction with an analysis of its geometrical properties. In this thesis two approaches to this problem are developed in four spacetime dimensions. First a realisation of the universal covering as the quotient space over the set of pairs of wedge regions is presented. In spite of the intuitive definition, the necessary properties of a covering space are not straightforward to prove. But the geometrical properties are easy to handle. The second approach takes advantage of the well-known features of spin groups, given as subgroups of Clifford algebras. Characterising elements of spin groups by pairs of wedge regions is possible in an elegant manner. The geometrical analysis is performed by means of the results achieved in the first approach. These geometrical properties allow for constructing a representation of the universal cover of the Lorentz group in terms of pairs of modular conjugations. For this representation the derivation of the spin-statistics theorem is straightforward, and a PCT operator can be defined. Furthermore, it is possible to transfer the results to nets of field algebras in algebraic quantum field theory with ease. Many of the usual assumptions in quantum field theory like the spectrum condition or the existence of a covariant unitary representation, as well as the assumption on the quantum field to have only finitely many components, are not required. For the standard axioms, the crucial assumption of modular P 1 CT symmetry constitutes no loss of generality because it is a consequence of
On the fermionic Heisenberg group and its Q-representation
International Nuclear Information System (INIS)
Frydryszak, A.
1992-01-01
A nonstandard way of representing the canonical anticommutation relations is presented. It is connected with a generalization of the Heisenberg group to a graded phase space. It is shown how Grassmann harmonic analysis can be performed and what are the Q-representations of such a generalized Heisenberg group. As in the conventional case, the Schroedinger and Bargmann-Fock realizations were shown to exist. Grassmann-Hermite polynomials are obtained via the generalized Bargmann transform and new Grassmann-Laguerre polynomials are introduced. (author). 10 refs
Sen, Sangita; Shee, Avijit; Mukherjee, Debashis
2018-02-01
The orbital relaxation attendant on ionization is particularly important for the core electron ionization potential (core IP) of molecules. The Unitary Group Adapted State Universal Coupled Cluster (UGA-SUMRCC) theory, recently formulated and implemented by Sen et al. [J. Chem. Phys. 137, 074104 (2012)], is very effective in capturing orbital relaxation accompanying ionization or excitation of both the core and the valence electrons [S. Sen et al., Mol. Phys. 111, 2625 (2013); A. Shee et al., J. Chem. Theory Comput. 9, 2573 (2013)] while preserving the spin-symmetry of the target states and using the neutral closed-shell spatial orbitals of the ground state. Our Ansatz invokes a normal-ordered exponential representation of spin-free cluster-operators. The orbital relaxation induced by a specific set of cluster operators in our Ansatz is good enough to eliminate the need for different sets of orbitals for the ground and the core-ionized states. We call the single configuration state function (CSF) limit of this theory the Unitary Group Adapted Open-Shell Coupled Cluster (UGA-OSCC) theory. The aim of this paper is to comprehensively explore the efficacy of our Ansatz to describe orbital relaxation, using both theoretical analysis and numerical performance. Whenever warranted, we also make appropriate comparisons with other coupled-cluster theories. A physically motivated truncation of the chains of spin-free T-operators is also made possible by the normal-ordering, and the operational resemblance to single reference coupled-cluster theory allows easy implementation. Our test case is the prediction of the 1s core IP of molecules containing a single light- to medium-heavy nucleus and thus, in addition to demonstrating the orbital relaxation, we have addressed the scalar relativistic effects on the accuracy of the IPs by using a hierarchy of spin-free Hamiltonians in conjunction with our theory. Additionally, the contribution of the spin-free component of the two
Sen, Sangita; Shee, Avijit; Mukherjee, Debashis
2018-02-07
The orbital relaxation attendant on ionization is particularly important for the core electron ionization potential (core IP) of molecules. The Unitary Group Adapted State Universal Coupled Cluster (UGA-SUMRCC) theory, recently formulated and implemented by Sen et al. [J. Chem. Phys. 137, 074104 (2012)], is very effective in capturing orbital relaxation accompanying ionization or excitation of both the core and the valence electrons [S. Sen et al., Mol. Phys. 111, 2625 (2013); A. Shee et al., J. Chem. Theory Comput. 9, 2573 (2013)] while preserving the spin-symmetry of the target states and using the neutral closed-shell spatial orbitals of the ground state. Our Ansatz invokes a normal-ordered exponential representation of spin-free cluster-operators. The orbital relaxation induced by a specific set of cluster operators in our Ansatz is good enough to eliminate the need for different sets of orbitals for the ground and the core-ionized states. We call the single configuration state function (CSF) limit of this theory the Unitary Group Adapted Open-Shell Coupled Cluster (UGA-OSCC) theory. The aim of this paper is to comprehensively explore the efficacy of our Ansatz to describe orbital relaxation, using both theoretical analysis and numerical performance. Whenever warranted, we also make appropriate comparisons with other coupled-cluster theories. A physically motivated truncation of the chains of spin-free T-operators is also made possible by the normal-ordering, and the operational resemblance to single reference coupled-cluster theory allows easy implementation. Our test case is the prediction of the 1s core IP of molecules containing a single light- to medium-heavy nucleus and thus, in addition to demonstrating the orbital relaxation, we have addressed the scalar relativistic effects on the accuracy of the IPs by using a hierarchy of spin-free Hamiltonians in conjunction with our theory. Additionally, the contribution of the spin-free component of the two
Group Representations and Intergroup Bias: Positive Affect, Similarity, and Group Size.
Dovidio, John F.; And Others
1995-01-01
Examined how social appearance and affective factors can influence social categorization and intergroup bias. Positive affect increased the extent to which subjects formed inclusive group representations, anticipating that the members of two groups would feel like one. Subjects in dissimilarly dressed groups expected the members to feel less like…
Leptonic unitary triangles and boomerangs
International Nuclear Information System (INIS)
Dueck, Alexander; Rodejohann, Werner; Petcov, Serguey T.
2010-01-01
We review the idea of leptonic unitary triangles and extend the concept of the recently proposed unitary boomerangs to the lepton sector. Using a convenient parametrization of the lepton mixing, we provide approximate expressions for the side lengths and the angles of the six different triangles and give examples of leptonic unitary boomerangs. Possible applications of the leptonic unitary boomerangs are also briefly discussed.
Application of group representation theory to symmetric structures
International Nuclear Information System (INIS)
Miller, A.G.
1980-01-01
Structures with symmetry occur in various problems, such as static and dynamic elastic response, and it is possible to gain partial information about their behaviour from their symmetry alone, using group representation theory. Due to the nature of the method, no numerical results other than the vanishing of certain quantities can be derived, but subsequent numerical calculations may be greatly shortened, and in simple structures, be rendered trivial. Among the applications to simple structures, those of interest in a nuclear context include, hexagonal tubes, bending of a circular tube under hexagonal loading patterns, and hexagonal arrays of fuel pins. (author)
Three lectures on quantum groups: Representations, duality, real forms
International Nuclear Information System (INIS)
Dobrev, V.K.
1992-07-01
Quantum groups appeared first as quantum algebra, i.e. as one parameter deformations of the numerical enveloping algebras of complex Lie algebras, in the study of the algebraic aspects of quantum integrable systems. Then quantum algebras related to triparametric solutions of the quantum Yang-Baxter equation were axiomatically introduced as (pseudo) quasi-triangular Hopf algebras. Later, a theory of formal deformations has been developed and the notion of quasi-Hopf algebra has been introduced. In other approaches to quantum groups the objects are called quantum matrix groups and are Hopf algebras in chirality to the quantum algebras. The representations of U q (G), the chirality and the real forms associated to these approaches are discussed here. Refs
International Nuclear Information System (INIS)
Fox, D.J.
1983-10-01
Analytic derivatives of the potential energy for Self-Consistent-Field (SCF) wave functions have been developed in recent years and found to be useful tools. The first derivative for configuration interaction (CI) wave functions is also available. This work details the extension of analytic methods to energy second derivatives for CI wave functions. The principal extension required for second derivatives is evaluation of the first order change in the CI wave function with respect to a nuclear perturbation. The shape driven graphical unitary group approach (SDGUGA) direct CI program was adapted to evaluate this term via the coupled-perturbed CI equations. Several iterative schemes are compared for use in solving these equations. The pilot program makes no use of molecular symmetry but the timing results show that utilization of molecular symmetry is desirable. The principles for defining and solving a set of symmetry adapted equations are discussed. Evaluation of the second derivative also requires the solution of the second order coupled-perturbed Hartree-Fock equations to obtain the correction to the molecular orbitals due to the nuclear perturbation. This process takes a consistently higher percentage of the computation time than for the first order equations alone and a strategy for its reduction is discussed
Response to the Comment by G. Emch on projective group representations in quaternionic Hilbert space
International Nuclear Information System (INIS)
Adler, S.L.
1996-01-01
We discuss the differing definitions of complex and quaternionic projective group representations employed by us and by Emch. The definition of Emch (termed here a strong projective representation) is too restrictive to accommodate quaternionic Hilbert space embeddings of complex projective representations. Our definition (termed here a weak projective representation) encompasses such embeddings, and leads to a detailed theory of quaternionic, as well as complex, projective group representations. copyright 1996 American Institute of Physics
International Nuclear Information System (INIS)
Audenaert, Koenraad M R; Scheel, Stefan
2008-01-01
In this paper, we provide necessary and sufficient conditions for a completely positive trace-preserving (CPT) map to be decomposable into a convex combination of unitary maps. Additionally, we set out to define a proper distance measure between a given CPT map and the set of random unitary maps, and methods for calculating it. In this way one could determine whether non-classical error mechanisms such as spontaneous decay or photon loss dominate over classical uncertainties, for example, in a phase parameter. The present paper is a step towards achieving this goal
Optimal quantum learning of a unitary transformation
International Nuclear Information System (INIS)
Bisio, Alessandro; Chiribella, Giulio; D'Ariano, Giacomo Mauro; Facchini, Stefano; Perinotti, Paolo
2010-01-01
We address the problem of learning an unknown unitary transformation from a finite number of examples. The problem consists in finding the learning machine that optimally emulates the examples, thus reproducing the unknown unitary with maximum fidelity. Learning a unitary is equivalent to storing it in the state of a quantum memory (the memory of the learning machine) and subsequently retrieving it. We prove that, whenever the unknown unitary is drawn from a group, the optimal strategy consists in a parallel call of the available uses followed by a 'measure-and-rotate' retrieving. Differing from the case of quantum cloning, where the incoherent 'measure-and-prepare' strategies are typically suboptimal, in the case of learning the 'measure-and-rotate' strategy is optimal even when the learning machine is asked to reproduce a single copy of the unknown unitary. We finally address the problem of the optimal inversion of an unknown unitary evolution, showing also in this case the optimality of the 'measure-and-rotate' strategies and applying our result to the optimal approximate realignment of reference frames for quantum communication.
Quantum group and Manin plane related to a coloured braid group representation
International Nuclear Information System (INIS)
Basu Mallick, B.
1993-07-01
By considering 'coloured' braid group representation we have obtained a quantum group, which reduces to the standards GL q (2) and GL pq (2) cases at some particular limits of the 'colour' parameters. In spite of quite complicated nature, all of these new quantum group relations can be expressed neatly in the Heisenberg-Weyl form, for a nontrivial choice of the basis elements. Furthermore, it is possible to associate invariant Manin planes, parametrized by the 'colour' variables, with such quantum group structure. (author). 26 refs
Kato, Yasuhiko; Kamii, Constance; Ozaki, Kyoko; Nagahiro, Mariko
2002-01-01
Interviews 60 Japanese children between the ages of 3 and 7 years to investigate the relationship between levels of abstraction and representation. Indicates that abstraction and representation are closely related. Implies that educators need to focus more on the mental relationships children make because the meaning children can give to…
Meeus, Joke; Duriez, Bart; Vanbeselaere, Norbert; Boen, Filip
2010-01-01
Two studies investigated whether the content of in-group identity affects the relation between in-group identification and ethnic prejudice. The first study among university students, tested whether national identity representations (i.e. ethnic vs. civic) moderate or mediate the relation between Flemish in-group identification and ethnic prejudice. A moderation hypothesis is supported when those higher in identification who subscribe to a more ethnic representation display higher ethnic prej...
Quantum control and representation theory
International Nuclear Information System (INIS)
Ibort, A; Perez-Pardo, J M
2009-01-01
A new notion of controllability for quantum systems that takes advantage of the linear superposition of quantum states is introduced. We call such a notion von Neumann controllability, and it is shown that it is strictly weaker than the usual notion of pure state and operator controllability. We provide a simple and effective characterization of it by using tools from the theory of unitary representations of Lie groups. In this sense, we are able to approach the problem of control of quantum states from a new perspective, that of the theory of unitary representations of Lie groups. A few examples of physical interest and the particular instances of compact and nilpotent dynamical Lie groups are discussed
Wibeck, Victoria
2014-02-01
This paper explores social representations of climate change, investigating how climate change is discussed by Swedish laypeople interacting in focus group interviews. The analysis focuses on prototypical examples and metaphors, which were key devices for objectifying climate change representations. The paper analyzes how the interaction of focus group participants with other speakers, ideas, arguments, and broader social representations shaped their representations of climate change. Climate change was understood as a global but distant issue with severe consequences. There was a dynamic tension between representations of climate change as a gradual vs. unpredictable process. Implications for climate change communication are discussed.
Optimal unitary dilation for bosonic Gaussian channels
International Nuclear Information System (INIS)
Caruso, Filippo; Eisert, Jens; Giovannetti, Vittorio; Holevo, Alexander S.
2011-01-01
A general quantum channel can be represented in terms of a unitary interaction between the information-carrying system and a noisy environment. In this paper the minimal number of quantum Gaussian environmental modes required to provide a unitary dilation of a multimode bosonic Gaussian channel is analyzed for both pure and mixed environments. We compute this quantity in the case of pure environment corresponding to the Stinespring representation and give an improved estimate in the case of mixed environment. The computations rely, on one hand, on the properties of the generalized Choi-Jamiolkowski state and, on the other hand, on an explicit construction of the minimal dilation for arbitrary bosonic Gaussian channel. These results introduce a new quantity reflecting ''noisiness'' of bosonic Gaussian channels and can be applied to address some issues concerning transmission of information in continuous variables systems.
Group representations via geometric quantization of the momentum map
International Nuclear Information System (INIS)
Mladenov, I.M.; Tsanov, V.V.
1992-09-01
In this paper, we treat a general method of quantization of Hamiltonian systems whose flow is a subgroup (not necessarily closed) of a torus acting freely and symplectically on the phase space. The quantization of some classes of completely integrable systems as well as the Borel-Weil-Bott version of representation theory are special cases. (author). 14 refs
Reflection Positive Stochastic Processes Indexed by Lie Groups
Jorgensen, Palle E. T.; Neeb, Karl-Hermann; Ólafsson, Gestur
2016-06-01
Reflection positivity originates from one of the Osterwalder-Schrader axioms for constructive quantum field theory. It serves as a bridge between euclidean and relativistic quantum field theory. In mathematics, more specifically, in representation theory, it is related to the Cartan duality of symmetric Lie groups (Lie groups with an involution) and results in a transformation of a unitary representation of a symmetric Lie group to a unitary representation of its Cartan dual. In this article we continue our investigation of representation theoretic aspects of reflection positivity by discussing reflection positive Markov processes indexed by Lie groups, measures on path spaces, and invariant gaussian measures in spaces of distribution vectors. This provides new constructions of reflection positive unitary representations.
Some applications of the representation theory of finite groups. A partial reduction methof
Zanten, Arend Jan van
1972-01-01
In this thesis we study the representation theory of finite groups and more specifically some aspects of the theory of characters. The technique of symmetrization and/or antisymmetrization of Kronecker powers of representations, which is well-known for the general linear group is applied here to
Unbounded representations of symmetry groups in gauge quantum field theory. II. Integration
International Nuclear Information System (INIS)
Voelkel, A.H.
1986-01-01
Within the gauge quantum field theory of the Wightman--Garding type, the integration of representations of Lie algebras is investigated. By means of the covariance condition (substitution rules) for the basic fields, it is shown that a form skew-symmetric representation of a Lie algebra can be integrated to a form isometric and in general unbounded representation of the universal covering group of a corresponding Lie group provided the conditions (Nelson, Sternheimer, etc.), which are well known for the case of Hilbert or Banach representations, hold. If a form isometric representation leaves the subspace from which the physical Hilbert space is obtained via factorization and completion invariant, then the same is proved to be true for its differential. Conversely, a necessary and sufficient condition is derived for the transmission of the invariance of this subspace under a form skew-symmetric representation of a Lie algebra to its integral
Representations of braid group obtained from quantum sl(3) enveloping algebra
International Nuclear Information System (INIS)
Ma Zhongqi.
1989-07-01
The quantum Clebsch-Gordan coefficients for the coproduct 6x6 of the quantum sl(3) enveloping algebra are computed. Based on the representation 6, the representation of the braid group and the corresponding link polynomial are obtained. The link polynomials based on the representations of the quantum sl(3) enveloping algebra with one row Young tableau are discussed. (author). 11 refs, 3 tabs
A group property for the coherent state representation of fermionic squeezing operators
Fan, Hong-yi; Li, Chao
2004-06-01
For the two-mode fermionic squeezing operators we find that their coherent state projection operator representation make up a loyal representation, which is homomorphic to an SO(4) group, though the fermionic coherent states are not mutual orthogonal. Thus the result of successively operating with many fermionic squeezing operators on a state can be equivalent to a single operation. The fermionic squeezing operators are mappings of orthogonal transformations in Grassmann number pseudo-classical space in the fermionic coherent state representation.
A group property for the coherent state representation of fermionic squeezing operators
International Nuclear Information System (INIS)
Fan Hongyi; Li Chao
2004-01-01
For the two-mode fermionic squeezing operators we find that their coherent state projection operator representation make up a loyal representation, which is homomorphic to an SO(4) group, though the fermionic coherent states are not mutual orthogonal. Thus the result of successively operating with many fermionic squeezing operators on a state can be equivalent to a single operation. The fermionic squeezing operators are mappings of orthogonal transformations in Grassmann number pseudo-classical space in the fermionic coherent state representation
Directory of Open Access Journals (Sweden)
Inger Edfors
2015-05-01
Full Text Available Genetics and organic chemistry are areas of science that students regard as difficult to learn. Part of this difficulty is derived from the disciplines having representations as part of their discourses. In order to optimally support students’ meaning-making, teachers need to use representations to structure the meaning-making experience in thoughtful ways that consider the variation in students’ prior knowledge. Using a focus group setting, we explored 43 university students’ reasoning on representations in introductory chemistry and genetics courses. Our analysis of eight focus group discussions revealed how students can construct somewhat bewildered relations with disciplinary-specific representations. The students stated that they preferred familiar representations, but without asserting the meaning-making affordances of those representations. Also, the students were highly aware of the affordances of certain representations, but nonetheless chose not to use those representations in their problem solving. We suggest that an effective representation is one that, to some degree, is familiar to the students, but at the same time is challenging and not too closely related to “the usual one”. The focus group discussions led the students to become more aware of their own and others ways of interpreting different representations. Furthermore, feedback from the students’ focus group discussions enhanced the teachers’ awareness of the students’ prior knowledge and limitations in students’ representational literacy. Consequently, we posit that a focus group setting can be used in a university context to promote both student meaning-making and teacher professional development in a fruitful way.
International Nuclear Information System (INIS)
Deenen, J.; Quesne, C.
1985-01-01
Both non-Hermitian Dyson and Hermitian Holstein--Primakoff representations of the Sp(2d,R) algebra are obtained when the latter is restricted to a positive discrete series irreducible representation 1 +n/2>. For such purposes, some results for boson representations, recently deduced from a study of the Sp(2d,R) partially coherent states, are combined with some standard techniques of boson expansion theories. The introduction of Usui operators enables the establishment of useful relations between the various boson representations. Two Dyson representations of the Sp(2d,R) algebra are obtained in compact form in terms of ν = d(d+1)/2 pairs of boson creation and annihilation operators, and of an extra U(d) spin, characterized by the irreducible representation [lambda 1 xxxlambda/sub d/]. In contrast to what happens when lambda 1 = xxx = lambda/sub d/ = lambda, it is shown that the Holstein--Primakoff representation of the Sp(2d,R) algebra cannot be written in such a compact form for a generic irreducible representation. Explicit expansions are, however, obtained by extending the Marumori, Yamamura, and Tokunaga method of boson expansion theories. The Holstein--Primakoff representation is then used to prove that, when restricted to the Sp(2d,R) irreducible representation 1 +n/2>, the dn-dimensional harmonic oscillator Hamiltonian has a U(ν) x SU(d) symmetry group
Real representations of Lie groups and a theorem of H. Pittie
International Nuclear Information System (INIS)
Freitas, R.
1992-01-01
In this paper, we prove a structure theorem of the real representation ring RO(T) as a module over the real representation ring RO(G), where G is a compact, connected and simply connected Lie group and T is a maximal torus of G. This provides a real version to a theorem of H. Pittie. (author). 24 refs
International Nuclear Information System (INIS)
Marion, J.
1984-01-01
The introduction of the concepts of energy machinery and energy structure of a manifold allows to construct a large class of energy representations of gauge groups including, as a very particular case, the ones known up to now. A synthesis of earlier works allows to give a sufficient condition for the irreducibility of these representations. (orig./HSI)
National Research Council Canada - National Science Library
Little, Daniel
2006-01-01
...). The reason this is so is due to hierarchies that we take for granted. By hierarchies I mean that there is a layer of representation of us as individuals, as military professional, as members of a military unit and as citizens of an entire nation...
Global unitary fixing and matrix-valued correlations in matrix models
International Nuclear Information System (INIS)
Adler, Stephen L.; Horwitz, Lawrence P.
2003-01-01
We consider the partition function for a matrix model with a global unitary invariant energy function. We show that the averages over the partition function of global unitary invariant trace polynomials of the matrix variables are the same when calculated with any choice of a global unitary fixing, while averages of such polynomials without a trace define matrix-valued correlation functions, that depend on the choice of unitary fixing. The unitary fixing is formulated within the standard Faddeev-Popov framework, in which the squared Vandermonde determinant emerges as a factor of the complete Faddeev-Popov determinant. We give the ghost representation for the FP determinant, and the corresponding BRST invariance of the unitary-fixed partition function. The formalism is relevant for deriving Ward identities obeyed by matrix-valued correlation functions
Unitary Transformation in Quantum Teleportation
International Nuclear Information System (INIS)
Wang Zhengchuan
2006-01-01
In the well-known treatment of quantum teleportation, the receiver should convert the state of his EPR particle into the replica of the unknown quantum state by one of four possible unitary transformations. However, the importance of these unitary transformations must be emphasized. We will show in this paper that the receiver cannot transform the state of his particle into an exact replica of the unknown state which the sender wants to transfer if he has not a proper implementation of these unitary transformations. In the procedure of converting state, the inevitable coupling between EPR particle and environment which is needed by the implementation of unitary transformations will reduce the accuracy of the replica.
2006-09-01
two weeks to arrive. Source: http://beergame.mit.edu/ Permission Granted – MIT Supply Chain Forum 2005 Professor Sterman –Sloan School of...Management - MITSource: http://web.mit.edu/jsterman/www/ SDG /beergame.html Rules of Engagement The MIT Beer Game Simulation 04-04 Slide Number 10 Professor...Sterman –Sloan School of Management - MITSource: http://web.mit.edu/jsterman/www/ SDG /beergame.html What is the Significance of Representation
Some double-valued representations of the linear groups
International Nuclear Information System (INIS)
Ne'eman, Y.
1983-01-01
We review the mathematical theory of SL(n,R) and its double-covering group anti SL(n,R), especially for n = 2, 3, 4. After discussing a variety of physical applications, we show that anti SL(3,R) provides holonomic curved space (world) spinors with an infinite number of components. We construct the relevant holononic manifield and discuss the gravitational interaction of a proton as an example. 41 references
On the mixed symmetry irreducible representations of the Poincare group in the BRST approach
International Nuclear Information System (INIS)
Burdik, C.; Pashnev, A.; Tsulaya, M.
2001-01-01
The Lagrangian description of irreducible massless representations of the Poincare group with the corresponding Young tableaux having two rows along with some explicit examples including the notoph and Weyl tensor is given. For this purpose the method of the BRST constructions is used adopted to the systems of the second class constraints by the construction of auxiliary representations of the algebras of constraints in terms of Verma modules
Energy Technology Data Exchange (ETDEWEB)
Larouche, M [Departement de Mathematiques et Statistique, Universite de Montreal, 2920 chemin de la Tour, Montreal, Quebec H3T 1J4 (Canada); Lemire, F W [Department of Mathematics, University of Windsor, Windsor, Ontario (Canada); Patera, J, E-mail: larouche@dms.umontreal.ca, E-mail: lemire@uwindsor.ca, E-mail: patera@crm.umontreal.ca [Centre de Recherches Mathematiques, Universite de Montreal, CP 6128-Centre ville, Montreal, Quebec H3C 3J7 (Canada)
2011-10-14
In this paper, we present a new, uniform and comprehensive description of centralizers of the maximal regular subgroups in compact simple Lie groups of all types and ranks. The centralizer is either a direct product of finite cyclic groups, a continuous group of rank 1, or a product, not necessarily direct, of a continuous group of rank 1 with a finite cyclic group. Explicit formulas for the action of such centralizers on irreducible representations of the simple Lie algebras are given. (paper)
The Impact of Merger Status and Relative Representation on Identification with a Merger Group
Directory of Open Access Journals (Sweden)
Filip Boen
2005-12-01
Full Text Available This experiment tested to what extent identification with a new merger group is determined by the status of that merger group and by the relative representation of the pre-merger ingroup. One hundred university students were assigned to a team of 'inductive' thinkers, and were later merged with a team of 'deductive' thinkers to form a team of 'analyst' thinkers. The status of the merger group (low, high and the relative representation of the ingroup into the novel merger group (low, high were manipulated. Participants identified more with the merger group in the high than in the low status condition, and they identified more in the high than in the low representation condition. The predicted interaction between relative representation and merger status was not significant. However, relative representation did interact with participants' pre-merger identification: Pre- and post-merger identification were positively related when the ingroup was highly represented, but 'negatively' when the ingroup was lowly represented.
On integral representation of the Clebsh-Gordan coefficients of SU(3) group
International Nuclear Information System (INIS)
Mal'tsev, V.M.
1985-01-01
The projection of arbitrary quark-gluon state on a singlet representation of SU(3) group is considered. It is given by an integral on the group. In this case the square of a Clebsch-Gordan coefficient is evaluated as the eight-fold integral over corresponding Eulerian angles
Factoriality of representations of the group of paths on SU(n)
International Nuclear Information System (INIS)
Albeverio, S.
We prove factoriality in the cyclic component of the vacuum for the energy representation of SU(n)-valued paths groups. The main tool is a lemma concerning generic pairs of Cartan subalgebras in the Lie algebra su(n) of SU(n) groups. (orig.)
International Nuclear Information System (INIS)
Dobrev, V.K.
1986-11-01
Let G be a real linear connected semisimple Lie group. We present a canonical construction of the differential operators intertwining elementary (≡ generalized principal series) representations of G. The results are easily extended to real linear reductive Lie groups. (author). 20 refs
Group-sparse representation with dictionary learning for medical image denoising and fusion.
Li, Shutao; Yin, Haitao; Fang, Leyuan
2012-12-01
Recently, sparse representation has attracted a lot of interest in various areas. However, the standard sparse representation does not consider the intrinsic structure, i.e., the nonzero elements occur in clusters, called group sparsity. Furthermore, there is no dictionary learning method for group sparse representation considering the geometrical structure of space spanned by atoms. In this paper, we propose a novel dictionary learning method, called Dictionary Learning with Group Sparsity and Graph Regularization (DL-GSGR). First, the geometrical structure of atoms is modeled as the graph regularization. Then, combining group sparsity and graph regularization, the DL-GSGR is presented, which is solved by alternating the group sparse coding and dictionary updating. In this way, the group coherence of learned dictionary can be enforced small enough such that any signal can be group sparse coded effectively. Finally, group sparse representation with DL-GSGR is applied to 3-D medical image denoising and image fusion. Specifically, in 3-D medical image denoising, a 3-D processing mechanism (using the similarity among nearby slices) and temporal regularization (to perverse the correlations across nearby slices) are exploited. The experimental results on 3-D image denoising and image fusion demonstrate the superiority of our proposed denoising and fusion approaches.
Social representations about criminals and crimes in various professional groups of young people
Directory of Open Access Journals (Sweden)
Yakushenko A.V.
2014-12-01
Full Text Available Describes a study whose purpose was to study the peculiarities of social representations of crime and criminals in different groups of students. The sample included 88 people aged 18 to 27 years, divided into four groups, depending on the subject of professionalization - psychologists, lawyers, journalists, representatives of technical professions. The study is based on the ideas of the theory of social representations proposed S.Moskovisi. The main method of study was a survey in a variant form, including an associative technique, the technique of "incomplete sentences", as well as open and closed questions. Associations were analyzed using analysis of prototypical proposed P.Verzhesom. The results obtained by Method "offers Incomplete" were to machine-using content analysis. Testable hypothesis regarding the specifics of professional social representations in various student groups received polnouyu or partial empirical support.
Energy Technology Data Exchange (ETDEWEB)
Sikora, W
1974-10-15
A description of magnetic structures based on the use of representations of space groups is given. Representations of the space groups were established for each compound on the basis of experimental data by the method of projection operators. The compounds contained in the list are collected according to crystal systems, alphabetically within each system. The description of each compound consists of the four parts. The first part contain the chemical symbol of the compound, the second its space group. The next part contains the chemical symbol of the magnetic atom and its positions in Wychoff notation with the number of equivalent positions in the crystal unit cell. The main description of a compound magnetic structure is given in the fourth part. It contains: K vector defined in the reciprocal space, the representation according to which a magnetic structure is transformed and the axial vector function S which describes the magnetic structure.
Symplectic Group Representation of the Two-Mode Squeezing Operator in the Coherent State Basis
Fan, Hong-Yi; Chen, Jun-Hua
2003-11-01
We find that the coherent state projection operator representation of the two-mode squeezing operator constitutes a loyal group representation of symplectic group, which is a remarkable property of the coherent state. As a consequence, the resultant effect of successively applying two-mode squeezing operators are equivalent to a single squeezing in the two-mode Fock space. Generalization of this property to the 2n-mode case is also discussed. The project supported by National Natural Science Foundation of China under Grant No. 10575057
Unitary Supermultiplets of $OSp(8^{*}|4)$ and the $AdS_{7}/CFT_{6}$ Duality
Günaydin, M; Gunaydin, Murat; Takemae, Seiji
2000-01-01
We study the unitary supermultiplets of the N=4 d=7 anti-de Sitter (AdS_7) superalgebra OSp(8^*|4), with the even subalgebra SO(6,2) X USp(4), which is the symmetry superalgebra of M-theory on AdS_7 X S^4. We give a complete classification of the positive energy doubleton and massless supermultiplets of OSp(8^*|4) . The ultra-short doubleton supermultiplets do not have a Poincaré limit in AdS_7 and correspond to superconformal field theories on the boundary of AdS_7 which can be identified with d=6 Minkowski space. We show that the six dimensional Poincare mass operator vanishes identically for the doubleton representations. By going from the compact U(4) basis of SO^*(8)=SO(6,2) to the noncompact basis SU^*(4)XD (d=6 Lorentz group times dilatations) one can associate the positive (conformal) energy representations of SO^*(8) with conformal fields transforming covariantly under the Lorentz group in d=6. The oscillator method used for the construction of the unitary supermultiplets of OSp(8^*|4) can be given ...
Kokkonen, Andrej; Karlsson, David
2017-12-01
The interests of historically disadvantaged groups risk being overlooked if they are not present in the decision-making process. However, a mere presence in politics does not guarantee political success. Often groups need allies to promote their interests successfully. We argue that one way to identify such allies is to judge politicians by whether they have friends in historically disadvantaged groups, as intergroup friendships have been shown to make people understand and feel empathy for outgroups. In other words, intergroup friendships may function as an important complement to descriptive representation. We test our argument with a unique survey that asks all elected political representatives in Sweden's 290 municipalities (response rate 79 per cent) about their friendship ties to, and their representation of, five historically disadvantaged groups: women, immigrants, youths, pensioners and blue-collar workers. We find a strong correlation between representatives' friendship ties to these groups and their commitment to represent them. The correlation is especially strong for youths and blue-collar workers, which likely can be explained by the fact that these groups usually lack crucial political resources (such as experience and education). We conclude that friendship ties function as an important complement to descriptive representation for achieving substantive representation. © London School of Economics and Political Science 2017.
Directory of Open Access Journals (Sweden)
Kokurina, Irina G.
2014-03-01
Full Text Available The paper examines the differences in the social representations of happiness among optimists and pessimists in the group of socially active, educated young members of the international youth organization Association Internationale des Etudiants en Sciences Economiques et Commerciales . To assess the degree of optimism and pessimism we used the Satisfaction With Life Scale (SWLS developed by E. Diener, while social representation, divided into the nucleus and peripheral zones, were examined using Verges’ technique within the framework of the concept of social mindsets offered by S. Moskovichi. It has been shown that, irrespective of the optimism or pessimism of the participants, the nucleus of their representations of happiness contains such a value as love. However, only in optimists’ representations is this value combined in the nucleus with the values of family and friendship. In the pessimists’ nucleus zone of the representation of happiness, love is presented as an independent value, primarily associated with striking emotional experiences, which has aspects of psychological addiction. Considerable differences between optimists and pessimists have also been found in the peripheral zone of the representation of happiness. Only optimists have such associations as “knowledge”, “children”, and “faith” in their peripheral area. In our opinion, the major scale of differences between optimists and pessimists is formed by the factor of sociocentricity and egocentricity.
Unitary Evolution as a Uniqueness Criterion
Cortez, J.; Mena Marugán, G. A.; Olmedo, J.; Velhinho, J. M.
2015-01-01
It is well known that the process of quantizing field theories is plagued with ambiguities. First, there is ambiguity in the choice of basic variables describing the system. Second, once a choice of field variables has been made, there is ambiguity concerning the selection of a quantum representation of the corresponding canonical commutation relations. The natural strategy to remove these ambiguities is to demand positivity of energy and to invoke symmetries, namely by requiring that classical symmetries become unitarily implemented in the quantum realm. The success of this strategy depends, however, on the existence of a sufficiently large group of symmetries, usually including time-translation invariance. These criteria are therefore generally insufficient in non-stationary situations, as is typical for free fields in curved spacetimes. Recently, the criterion of unitary implementation of the dynamics has been proposed in order to select a unique quantization in the context of manifestly non-stationary systems. Specifically, the unitarity criterion, together with the requirement of invariance under spatial symmetries, has been successfully employed to remove the ambiguities in the quantization of linearly polarized Gowdy models as well as in the quantization of a scalar field with time varying mass, propagating in a static background whose spatial topology is either of a d-sphere (with d = 1, 2, 3) or a three torus. Following Ref. 3, we will see here that the symmetry and unitarity criteria allows for a complete removal of the ambiguities in the quantization of scalar fields propagating in static spacetimes with compact spatial sections, obeying field equations with an explicitly time-dependent mass, of the form ddot φ - Δ φ + s(t)φ = 0 . These results apply in particular to free fields in spacetimes which, like e.g. in the closed FRW models, are conformal to a static spacetime, by means of an exclusively time-dependent conformal factor. In fact, in such
On the labeling and symmetry adaptation of the solvable finite groups representations
International Nuclear Information System (INIS)
Caride, A.O.; Zanette, S.I.; Nogueira, S.R.A.
1987-01-01
We propose a method to simultaneously perform a symmetry adaptation and a labeling of the bases of the irreducible representations of the solvable finite groups. It is performed by difining a self-adjoint operator with ligenvalues which evidence the descent in symmetry of the group-subgroups sequences. We also prove two theorems on the canonicity of the cpomposition series of the solvable groups. (author) [pt
Piaget's Egocentrism: A Unitary Construct?
Ruthven, Avis J.; Cunningham, William L.
In order to determine whether egocentrism can be conceptualized as a unitary construct, 100 children (51 four-year-olds, 37 five-year-olds, and 12 six-year-olds) were administered a visual/spatial perspective task, a cognitive/communicative task, and an affective task. All tasks were designed to measure different facets of egocentrism. The 50…
Effective hamiltonian within the microscopic unitary nuclear model
International Nuclear Information System (INIS)
Avramenko, V.I.; Blokhin, A.L.
1989-01-01
Within the microscopic version of the unitary collective model with the horizontal mixing the effective Hamiltonian for 18 O and 18 Ne nuclei is constructed. The algebraic structure of the Hamiltonian is compared to the familiar phenomenological ones with the SU(3)-mixing terms which describe the coupled rotational and vibrational spectra. The Hamiltonian, including central nuclear and Coulomb interaction, is diagonalized on the basis of three SU(3) irreducible representations with two orbital symmetries. 32 refs.; 2 figs.; 4 tabs
Representations of the q-deformed algebras Uq (so2,1) and Uq (so3,1)
International Nuclear Information System (INIS)
Gavrilik, O.M.; Klimyk, A.U.
1993-01-01
Representations of algebra U q (so 2 ,1) are studied. This algebra is a q-deformation of the universal enveloping algebra U(so 2 ,1) of the Lie algebra of the group SO 0 (2,1) and differs from the quantum algebra U q (SU 1 ,1). Classifications of irreducible representations and of infinitesimally irreducible representations of U q (SU 1 ,1). The sets of irreducible representations and of infinitesimally unitary irreducible representations of the algebra U q (so 3 ,1) are given. We also consider representations of U q (so n ,1) which are of class 1 with respect to subalgebra U q (so n ). (author). 22 refs
q-deformed differential operator algebra and new braid group representation
International Nuclear Information System (INIS)
Wang Luyu; Dai Jianghui; Zhang Jun
1991-01-01
It is proved that the q-deformed differential operator algebra introduced is consistent with quantum hyperplane described by Wess and Zumino. At the same time, a new braid group representation associated with sl q (2) is obtained by adding the terms of weight conservation to the standard universal R-matrix. (author). 10 refs
Group Representation of the Prompt Fission Neutron Spectrum of {sup 252}Cf
Energy Technology Data Exchange (ETDEWEB)
Croft, S.; Miller, K. A. [Safeguards Science and Technology Group (N-1), Nuclear Nonproliferation Division, Los Alamos National Laboratory, Los Alamos(United States)
2011-12-15
We review the spectral representation used for the prompt fission neutron spectrum of 252Cf in the International Organization for Standardization document ISO 8529-1. We find corrections to Table A.2, the discrete group structure form, of this report are needed. We describe the approach to generating replacement values and provide a new tabulation.
Representation of Coordination Mechanisms in IMS Learning Design to Support Group-based Learning
Miao, Yongwu; Burgos, Daniel; Griffiths, David; Koper, Rob
2007-01-01
Miao, Y., Burgos, D., Griffiths, D., & Koper, R. (2008). Representation of Coordination Mechanisms in IMS Learning Design to Support Group-based Learning. In L. Lockyer, S. Bennet, S. Agostinho & B. Harper (Eds.), Handbook of Research on Learning Design and Learning Objects: Issues, Applications and
On the Elliptic Nonabelian Fourier Transform for Unipotent Representations of p-Adic Groups
Ciubotaru, D.; Opdam, E.; Cogdell, J.; Kim, J.-L.; Zhu, C.-B.
2017-01-01
In this paper, we consider the relation between two nonabelian Fourier transforms. The first one is defined in terms of the Langlands-Kazhdan-Lusztig parameters for unipotent elliptic representations of a split p-adic group and the second is defined in terms of the pseudocoefficients of these
On the representation of symmetry group transformation operators in the interaction picture
International Nuclear Information System (INIS)
Jorjadze, G.P.; Khvedelidze, A.M.; Kvinikhidze, A.H.
1987-01-01
The representation similar to that of Dyson, is obtained in the form of a chronologically (antichronologically) ordered exponent for operators of any symmetry group transformations of an interacting quantum field system. The exponent is given by an integral of the interaction Hamiltonian density in Dirac's picture. The domain of integration is determined by the symmetry transformation considered. 3 refs.; 2 figs
A comment on continuous spin representations of the Poincare group and perturbative string theory
Energy Technology Data Exchange (ETDEWEB)
Font, A. [Departamento de Fisica, Centro de Fisica Teorica y Computacional, Facultad de Ciencias, Universidad Central de Venezuela, Caracas (Venezuela, Bolivarian Republic of); Quevedo, F. [Abdus Salam ICTP, Trieste (Italy); DAMTP/CMS, University of Cambridge, Wilberforce Road, Cambridge (United Kingdom); Theisen, S. [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Golm (Germany)
2014-11-04
We make a simple observation that the massless continuous spin representations of the Poincare group are not present in perturbative string theory constructions. This represents one of the very few model-independent low-energy consequences of these models. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Representations of the Poincare group, position operator and the bi-local model
International Nuclear Information System (INIS)
Sohkawa, Tohru
1978-01-01
We propose two types of representations of the Poincare group which give general frameworks for introduction of internal degrees of freedom of a particle. The bi-local model recently proposed by Takabayasi is constructed through our frameworks. In this study, new covariant and non-covariant position operators are introduced and discussed. (author)
Representation theory of 2-groups on finite dimensional 2-vector spaces
Elgueta, Josep
2004-01-01
In this paper, the 2-category $\\mathfrak{Rep}_{{\\bf 2Mat}_{\\mathbb{C}}}(\\mathbb{G})$ of (weak) representations of an arbitrary (weak) 2-group $\\mathbb{G}$ on (some version of) Kapranov and Voevodsky's 2-category of (complex) 2-vector spaces is studied. In particular, the set of equivalence classes of representations is computed in terms of the invariants $\\pi_0(\\mathbb{G})$, $\\pi_1(\\mathbb{G})$ and $[\\alpha]\\in H^3(\\pi_0(\\mathbb{G}),\\pi_1(\\mathbb{G}))$ classifying $\\mathbb{G}$. Also the categ...
Teleportation of M-Qubit Unitary Operations
Institute of Scientific and Technical Information of China (English)
郑亦庄; 顾永建; 郭光灿
2002-01-01
We discuss teleportation of unitary operations on a two-qubit in detail, then generalize the bidirectional state teleportation scheme from one-qubit to M-qubit unitary operations. The resources required for the optimal implementation of teleportation of an M-qubit unitary operation using a bidirectional state teleportation scheme are given.
Morales-Chicas, Jessica; Graham, Sandra
2017-09-01
This study examined the association between change in ethnic group representation from elementary to middle school and Latino students' school belonging and achievement. The ethnic diversity of students' middle school was examined as a moderator. Participants were 1,825 Latino sixth graders from 26 ethnically diverse urban middle schools. Hierarchical regression analyses showed that a change in ethnic representation toward fewer Latinos in middle school than elementary school was related to less perceived belonging and lower achievement in schools with low ethnic diversity. There were no mean differences as a function of declining representation in more diverse middle schools, suggesting that greater school diversity was protective. Findings highlight the importance of examining school ethnic context, especially across the middle school transition. © 2016 The Authors. Journal of Research on Adolescence © 2016 Society for Research on Adolescence.
Gelfand-Dikii Hamiltonian operator and co-ad joint representation of the Volterra group
International Nuclear Information System (INIS)
Lebedev, D.R.; Manin, Yu.I.
1978-01-01
It is shown that the Gelfand-Dikii Hamiltonian structure is an analogue of a very special class of finite-dimensional symplectic structures, namely, the Kirillow structures on the orbits of the co-adjoint representation of the Lie groups. The Lie group is represented by the Volterra operators. The main interest lies in the possibility of application of the ideology of ''geometric quantization'' to the Lax equations
A bound for the Schur index of irreducible representations of finite groups
Energy Technology Data Exchange (ETDEWEB)
Kiselev, D D [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2013-08-31
We construct an optimal bound for the Schur index of irreducible complex representations of finite groups over the field of rational numbers, when only the prime divisors of the order of the group are known. We study relationships with compatible and universally compatible extensions of number fields. We give a simpler proof of the well-known Berman-Yamada bound for the Schur index over the field Q{sub p}. Bibliography: 7 titles.
Symmetric mixed states of n qubits: Local unitary stabilizers and entanglement classes
Energy Technology Data Exchange (ETDEWEB)
Lyons, David W.; Walck, Scott N. [Lebanon Valley College, Annville, Pennsylvania 17003 (United States)
2011-10-15
We classify, up to local unitary equivalence, local unitary stabilizer Lie algebras for symmetric mixed states of n qubits into six classes. These include the stabilizer types of the Werner states, the Greenberger-Horne-Zeilinger state and its generalizations, and Dicke states. For all but the zero algebra, we classify entanglement types (local unitary equivalence classes) of symmetric mixed states that have those stabilizers. We make use of the identification of symmetric density matrices with polynomials in three variables with real coefficients and apply the representation theory of SO(3) on this space of polynomials.
Poincare group and relativistic wave equations in 2+1 dimensions
Energy Technology Data Exchange (ETDEWEB)
Gitman, Dmitri M. [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo, SP (Brazil); Shelepin, A.L. [Moscow Institute of Radio Engenering, Electronics and Automation, Moscow (Russian Federation)
1997-09-07
Using the generalized regular representation, an explicit construction of the unitary irreducible representations of the (2+1)-Poincare group is presented. A detailed description of the angular momentum and spin in 2+1 dimensions is given. On this base the relativistic wave equations for all spins (including fractional) are constructed. (author)
Symmetries and Laplacians introduction to harmonic analysis, group representations and applications
Gurarie, D
1992-01-01
Designed as an introduction to harmonic analysis and group representations,this book covers a wide range of topics rather than delving deeply into anyparticular one. In the words of H. Weyl ...it is primarily meant forthe humble, who want to learn as new the things set forth therein, rather thanfor the proud and learned who are already familiar with the subject and merelylook for quick and exact information.... The main objective is tointroduce the reader to concepts, ideas, results and techniques that evolvearound symmetry-groups, representations and Laplacians. Morespecifically, the main interest concerns geometrical objects and structures{X}, discrete or continuous, that possess sufficiently large symmetrygroup G, such as regular graphs (Platonic solids), lattices, andsymmetric Riemannian manifolds. All such objects have a natural Laplacian&Dgr;, a linear operator on functions over X, invariant underthe group action. There are many problems associated with Laplacians onX, such as continuous or discrete...
Unbounded representations of symmetry groups in gauge quantum field theory. Pt. 1
International Nuclear Information System (INIS)
Voelkel, A.H.
1983-01-01
Symmetry groups and especially the covariance (substitution rules) of the basic fields in a gauge quantum field theory of the Wightman-Garding type are investigated. By means of the continuity properties hidden in the substitution rules it is shown that every unbounded form-isometric representation U of a Lie group has a form-skew-symmetric differential deltaU with dense domain in the unphysical Hilbert space. Necessary and sufficient conditions for the existence of the closures of U and deltaU as well as for the isometry of U are derived. It is proved that a class of representations of the transition group enforces a relativistic confinement mechanism, by which some or all basic fields are confined but certain mixed products of them are not. (orig.)
Generation of symmetry coordinates for crystals using multiplier representations of the space groups
DEFF Research Database (Denmark)
Hansen, Flemming Yssing
1978-01-01
Symmetry coordinates play an important role in the normal-mode calculations of crystals. It is therefore of great importance to have a general method, which may be applied for any crystal at any wave vector, to generate these. The multiplier representations of the space groups as given by Kovalev...... and the projection-operator technique provide a basis for such a method. The method is illustrated for the nonsymmorphic D36 space group, and the theoretical background for the representations of space groups in general is reviewed and illustrated on the example above. It is desirable to perform the projection...... of symmetry coordinates in such a way that they may be used for as many wave vectors as possible. We discuss how to achieve this goal. The detailed illustrations should make it simple to apply the theory in any other case....
Unitary Housing Regimes in Transition
DEFF Research Database (Denmark)
Bengtsson, Bo; Jensen, Lotte
2013-01-01
Path dependence is strong in housing institutions and policy. In both Denmark and Sweden, today’s universal and ‘unitary’ (Kemeny) housing regimes can be traced back to institutions that were introduced fifty years back in history or more. Recently, universal and unitary housing systems...... in Scandinavia, and elsewhere, are under challenge from strong political and economic forces. These challenges can be summarized as economic cutbacks, privatization and Europeanization. Although both the Danish and the Swedish housing system are universal and unitary in character, they differ considerably...... in institutional detail. Both systems have corporatist features, however in Denmark public housing is based on local tenant democracy and control, and in Sweden on companies owned and controlled by the municipalities, combined with a centralized system of rent negotiations. In the paper the present challenges...
A 9 x 9 Matrix Representation of Birman-Wenzl-Murakami Algebra and Berry Phase in Yang-Baxter System
International Nuclear Information System (INIS)
Gou Lidan; Xue Kang; Wang Gangcheng
2011-01-01
We present a 9 x 9 S-matrix and E-matrix. A representation of specialized Birman-Wenzl-Murakami algebra is obtained. Starting from the given braid group representation S-matrix, we obtain the trigonometric solution of Yang-Baxter equation. A unitary matrix R(x, φ 1 ,φ 2 ) is generated via the Yang-Baxterization approach. Then we construct a Yang-Baxter Hamiltonian through the unitary matrix R(x, φ 1 ,φ 2 ). Berry phase of this Yang-Baxter system is investigated in detail. (general)
Wilson, S.
1977-01-01
A method is presented for the determination of the representation matrices of the spin permutation group (symmetric group), a detailed knowledge of these matrices being required in the study of the electronic structure of atoms and molecules. The method is characterized by the use of two different coupling schemes. Unlike the Yamanouchi spin algebraic scheme, the method is not recursive. The matrices for the fundamental transpositions can be written down directly in one of the two bases. The method results in a computationally significant reduction in the number of matrix elements that have to be stored when compared with, say, the standard Young tableaux group theoretical approach.
On the algebra of local unitary invariants of pure and mixed quantum states
International Nuclear Information System (INIS)
Vrana, Peter
2011-01-01
We study the structure of the inverse limit of the graded algebras of local unitary invariant polynomials using its Hilbert series. For k subsystems, we show that the inverse limit is a free algebra and the number of algebraically independent generators with homogenous degree 2m equals the number of conjugacy classes of index m subgroups in a free group on k - 1 generators. Similarly, we show that the inverse limit in the case of k-partite mixed state invariants is free and the number of algebraically independent generators with homogenous degree m equals the number of conjugacy classes of index m subgroups in a free group on k generators. The two statements are shown to be equivalent. To illustrate the equivalence, using the representation theory of the unitary groups, we obtain all invariants in the m = 2 graded parts and express them in a simple form both in the case of mixed and pure states. The transformation between the two forms is also derived. Analogous invariants of higher degree are also introduced.
Energy Technology Data Exchange (ETDEWEB)
Xiao, Hailin [Wenzhou University, College of Physics and Electronic Information Engineering, Wenzhou (China); Southeast University, National Mobile Communications Research Laboratory, Nanjing (China); Guilin University of Electronic Technology, Ministry of Education, Key Laboratory of Cognitive Radio and Information Processing, Guilin (China); Zhang, Zhongshan [University of Science and Technology Beijing, Beijing Engineering and Technology Research Center for Convergence Networks and Ubiquitous Services, Beijing (China); Chronopoulos, Anthony Theodore [University of Texas at San Antonio, Department of Computer Science, San Antonio, TX (United States)
2017-10-15
In quantum computing, nice error bases as generalization of the Pauli basis were introduced by Knill. These bases are known to be projective representations of finite groups. In this paper, we propose a group representation approach to the study of quantum stabilizer codes. We utilize this approach to define decoherence-free subspaces (DFSs). Unlike previous studies of DFSs, this type of DFSs does not involve any spatial symmetry assumptions on the system-environment interaction. Thus, it can be used to construct quantum error-avoiding codes (QEACs) that are fault tolerant automatically. We also propose a new simple construction of QEACs and subsequently develop several classes of QEACs. Finally, we present numerical simulation results encoding the logical error rate over physical error rate on the fidelity performance of these QEACs. Our study demonstrates that DFSs-based QEACs are capable of providing a generalized and unified framework for error-avoiding methods. (orig.)
Loop space representation of quantum general relativity and the group of loops
International Nuclear Information System (INIS)
Gambini, R.
1991-01-01
The action of the constraints of quantum general relativity on a general state in the loop representation is coded in terms of loop derivatives. These differential operators are related to the infinitesimal generators of the group of loops and generalize the area derivative first considered by Mandelstam. A new sector of solutions of the physical states space of nonperturbative quantum general relativity is found. (orig.)
Baryonic sources using irreducible representations of the double-covered octahedral group
International Nuclear Information System (INIS)
Basak, S.; Edwards, R.; Fiebig, R.; Fleming, G.T.; Heller, U.M.; Morningstar, C.; Richards, D.; Sato, I.; Wallace, S.
2005-01-01
Irreducible representations (IRs) of the double-covered octahedral group are used to construct lattice source and sink operators for three-quark baryons. The goal is to achieve a good coupling to higher spin states as well as ground states. Complete sets of local and nonlocal straight-link operators are explicitly shown for isospin 1/2 and 3/2 baryons. The orthogonality relations of the IR operators are confirmed in a quenched lattice simulation
Baryonic sources using irreducible representations of the double-covered octahedral group
International Nuclear Information System (INIS)
Basak, S.; Edwards, R.; Fiebig, R.; Fleming, G. T.; Heller, U. M.; Morningstar, C.; Richards, D.; Sato, I.; Wallace, S.
2004-01-01
Irreducible representations (IRs) of the double-covered octahedral group are used to construct lattice source and sink operators for three-quark baryons. The goal is to achieve a good coupling to higher spin states as well as ground states. Complete sets of local and nonlocal straight-link operators are explicitly shown for isospin 1/2 and 3/2 baryons. The orthogonality relations of the IR operators are confirmed in a quenched lattice simulation
Representation of SO(4,1) group and Hawking effect in the de-Sitter space
International Nuclear Information System (INIS)
Bogush, A.A.; Otchik, V.S.
1983-01-01
Expression relating the solution of the equation for particles with spin 1/2 to matrix elements of group SO(4, 1), is obtained. When using the relation of the Dirac equation solutions in the de Sitter space with matrix elements of representations of group SO(4, 1) the presence of the Hawking effect in the space is established. The de Sitter space is considered as 4-dimensional hyperboloid, inserted into 5-dimensional pseudo-Euclidean space. It is established, that the average number of emitted spinor particles obeys the Fermi-Dirac distribution
Hyperfunction solutions of the zero rest mass equations and representations of LIE groups
International Nuclear Information System (INIS)
Dunne, E.G.
1984-01-01
Recently, hyperfunctions have arisen in an essential way in separate results in mathematical physics and in representation theory. In the setting of the twistor program, Wells, with others, has extended the Penrose transform to hyperfunction solutions of the zero rest mass equations, showing that the fundamental isomorphisms hold for this larger space. Meanwhile, Schmid has shown the existence of a canonical globalization of a Harish-Chandra module, V, to a representation of the group. This maximal globalization may be realized as the completion of V in a locally convex vector space in the hyperfunction topology. This thesis shows that the former is a particular case of the latter where the globalization can be done by hand. This explicit globalization is then carried out for a more general case of the Radon transform on homogeneous spaces
Wigner functions for a class of semi-direct product groups
International Nuclear Information System (INIS)
Krasowska, Anna E; Ali, S Twareque
2003-01-01
Following a general method proposed earlier, we construct here Wigner functions defined on coadjoint orbits of a class of semidirect product groups. The groups in question are such that their unitary duals consist purely of representations from the discrete series and each unitary irreducible representation is associated with a coadjoint orbit. The set of all coadjoint orbits (hence UIRs) is finite and their union is dense in the dual of the Lie algebra. The simple structure of the groups and the orbits enables us to compute the various quantities appearing in the definition of the Wigner function explicitly. A large number of examples, with potential use in image analysis, is worked out
Adaptive structured dictionary learning for image fusion based on group-sparse-representation
Yang, Jiajie; Sun, Bin; Luo, Chengwei; Wu, Yuzhong; Xu, Limei
2018-04-01
Dictionary learning is the key process of sparse representation which is one of the most widely used image representation theories in image fusion. The existing dictionary learning method does not use the group structure information and the sparse coefficients well. In this paper, we propose a new adaptive structured dictionary learning algorithm and a l1-norm maximum fusion rule that innovatively utilizes grouped sparse coefficients to merge the images. In the dictionary learning algorithm, we do not need prior knowledge about any group structure of the dictionary. By using the characteristics of the dictionary in expressing the signal, our algorithm can automatically find the desired potential structure information that hidden in the dictionary. The fusion rule takes the physical meaning of the group structure dictionary, and makes activity-level judgement on the structure information when the images are being merged. Therefore, the fused image can retain more significant information. Comparisons have been made with several state-of-the-art dictionary learning methods and fusion rules. The experimental results demonstrate that, the dictionary learning algorithm and the fusion rule both outperform others in terms of several objective evaluation metrics.
Unitary Root Music and Unitary Music with Real-Valued Rank Revealing Triangular Factorization
2010-06-01
AFRL-RY-WP-TP-2010-1213 UNITARY ROOT MUSIC AND UNITARY MUSIC WITH REAL-VALUED RANK REVEALING TRIANGULAR FACTORIZATION (Postprint) Nizar...DATES COVERED (From - To) June 2010 Journal Article Postprint 08 September 2006 – 31 August 2009 4. TITLE AND SUBTITLE UNITARY ROOT MUSIC AND...UNITARY MUSIC WITH REAL-VALUED RANK REVEALING TRIANGULAR FACTORIZATION (Postprint) 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA8650-05-D-1912-0007 5c
Energy Technology Data Exchange (ETDEWEB)
Gates, D.E.A. [Jefferson Physical Laboratory, Harvard University,17 Oxford St., Cambridge, MA, 02138 (United States); Gates, James S. Jr. [Center for String and Particle Theory, Dept. of Physics, University of Maryland, 4150 Campus Dr., College Park, MD, 20472 (United States); Department of Physics and Astronomy, Dartmouth College,6127 College St., Hanover, NH, 03755 (United States); Stiffler, Kory [Department of Chemistry, Physics, and Astronomy, Indiana University Northwest, 3400 Broadway, Gary, Indiana, 46408 (United States)
2016-08-10
We present an expanded and detailed discussion of the mathematical tools required to cull and filter representations of the Coxeter Group BC{sub 4} into providing bases for the construction of minimal off-shell representations of the 4D, N = 1 spacetime supersymmetry algebra.
International Nuclear Information System (INIS)
Fradkin, E.S.; Metsaev, R.R.
1996-02-01
Using the language of highest weight representations and the light cone formalism we construct a full list of cubic amplitudes of scattering for all bosonic massless representations of the Poincare group in any even space-time dimension. (author). 29 refs
Tensor and Spin Representations of SO(4) and Discrete Quantum Gravity
Lorente, M.; Kramer, P.
Starting from the defining transformations of complex matrices for the SO(4) group, we construct the fundamental representation and the tensor and spinor representations of the group SO(4). Given the commutation relations for the corresponding algebra, the unitary representations of the group in terms of the generalized Euler angles are constructed. These mathematical results help us to a more complete description of the Barret-Crane model in Quantum Gravity. In particular a complete realization of the weight function for the partition function is given and a new geometrical interpretation of the asymptotic limit for the Regge action is presented.
Representations of Reductive Groups : in Honor of the 60th Birthday of David A. Vogan, Jr.
Trapa, Peter
2015-01-01
Over the last forty years, David Vogan has left an indelible imprint on the representation theory of reductive groups. His groundbreaking ideas have lead to deep advances in the theory of real and p-adic groups, and have forged lasting connections with other subjects, including number theory, automorphic forms, algebraic geometry, and combinatorics. Representations of Reductive Groups is an outgrowth of the conference of the same name, dedicated to David Vogan on his 60th birthday, which took place at MIT on May 19-23, 2014. This volume highlights the depth and breadth of Vogan's influence over the subjects mentioned above, and point to many exciting new directions that remain to be explored. Notably, the first article by McGovern and Trapa offers an overview of Vogan's body of work, placing his ideas in a historical context. Contributors: Pramod N. Achar, Jeffrey D. Adams, Dan Barbasch, Manjul Bhargava, Cédric Bonnafé, Dan Ciubotaru, Meinolf Geck, William Graham, Benedict H. Gross, Xuhua He, Jing-Son...
Isometric and unitary phase operators: explaining the Villain transform
International Nuclear Information System (INIS)
Hemmen, J L van; Wreszinski, Walter F
2007-01-01
The Villain transform plays a key role in spin-wave theory, a bosonization of elementary excitations in a system of extensively many Heisenberg spins. Intuitively, it is a representation of the spin operators in terms of an angle and its canonically conjugate angular momentum operator and, as such, has a few nasty boundary-condition twists. We construct an isometric phase representation of spin operators that conveys a precise mathematical meaning to the Villain transform and is related to both classical mechanics and the Pegg-Barnett-Bialynicki-Birula boson (photon) phase operators by means of suitable limits. In contrast to the photon case, unitary extensions are inadequate because they describe the wrong physics. We also discuss in some detail the application to spin-wave theory, pointing out some examples in which the isometric representation is indispensable
On Investigating GMRES Convergence using Unitary Matrices
Czech Academy of Sciences Publication Activity Database
Duintjer Tebbens, Jurjen; Meurant, G.; Sadok, H.; Strakoš, Z.
2014-01-01
Roč. 450, 1 June (2014), s. 83-107 ISSN 0024-3795 Grant - others:GA AV ČR(CZ) M100301201; GA MŠk(CZ) LL1202 Institutional support: RVO:67985807 Keywords : GMRES convergence * unitary matrices * unitary spectra * normal matrices * Krylov residual subspace * Schur parameters Subject RIV: BA - General Mathematics Impact factor: 0.939, year: 2014
A unitary correlation operator method
International Nuclear Information System (INIS)
Feldmeier, H.; Neff, T.; Roth, R.; Schnack, J.
1997-09-01
The short range repulsion between nucleons is treated by a unitary correlation operator which shifts the nucleons away from each other whenever their uncorrelated positions are within the repulsive core. By formulating the correlation as a transformation of the relative distance between particle pairs, general analytic expressions for the correlated wave functions and correlated operators are given. The decomposition of correlated operators into irreducible n-body operators is discussed. The one- and two-body-irreducible parts are worked out explicitly and the contribution of three-body correlations is estimated to check convergence. Ground state energies of nuclei up to mass number A=48 are calculated with a spin-isospin-dependent potential and single Slater determinants as uncorrelated states. They show that the deduced energy-and mass-number-independent correlated two-body Hamiltonian reproduces all ''exact'' many-body calculations surprisingly well. (orig.)
Strange statistics, braid group representations and multipoint functions in the N-component model
International Nuclear Information System (INIS)
Lee, H.C.; Ge, M.L.; Couture, M.; Wu, Y.S.
1989-01-01
The statistics of fields in low dimensions is studied from the point of view of the braid group B n of n strings. Explicit representations M R for the N-component model, N = 2 to 5, are derived by solving the Yang-Baxter-like braid group relations for the statistical matrix R, which describes the transformation of the bilinear product of two N-component fields under the transposition of coordinates. When R 2 not equal to 1 the statistics is neither Bose-Einstein nor Fermi-Dirac; it is strange. It is shown that for each N, the N + 1 parameter family of solutions obtained is the most general one under a given set of constraints including charge conservation. Extended Nth order (N > 2) Alexander-Conway relations for link polynomials are derived. They depend nonhomogeneously only on one of the N + 1 parameters. The N = 3 and 4 ones agree with those previously derived
International Nuclear Information System (INIS)
Bonora, Loriano; Bytsenko, Andrey; Elizalde, Emilio
2012-01-01
This review paper contains a concise introduction to highest weight representations of infinite-dimensional Lie algebras, vertex operator algebras and Hilbert schemes of points, together with their physical applications to elliptic genera of superconformal quantum mechanics and superstring models. The common link of all these concepts and of the many examples considered in this paper is to be found in a very important feature of the theory of infinite-dimensional Lie algebras: the modular properties of the characters (generating functions) of certain representations. The characters of the highest weight modules represent the holomorphic parts of the partition functions on the torus for the corresponding conformal field theories. We discuss the role of the unimodular (and modular) groups and the (Selberg-type) Ruelle spectral functions of hyperbolic geometry in the calculation of elliptic genera and associated q-series. For mathematicians, elliptic genera are commonly associated with new mathematical invariants for spaces, while for physicists elliptic genera are one-loop string partition function. (Therefore, they are applicable, for instance, to topological Casimir effect calculations.) We show that elliptic genera can be conveniently transformed into product expressions, which can then inherit the homology properties of appropriate polygraded Lie algebras. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker’s 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (review)
Fourier transform and the Verlinde formula for the quantum double of a finite group
Koornwinder, T.H.; Schroers, B.J.; Slingerland, J.K.; Bais, F.A.
1999-01-01
We define a Fourier transform $S$ for the quantum double $D(G)$ of a finite group $G$. Acting on characters of $D(G)$, $S$ and the central ribbon element of $D(G)$ generate a unitary matrix representation of the group $SL(2,Z)$. The characters form a ring over the integers under both the algebra
New unitary affine-Virasoro constructions
International Nuclear Information System (INIS)
Halpern, M.B.; Kiritsis, E.; Obers, N.A.; Poratti, M.; Yamron, J.P.
1990-01-01
This paper reports on a quasi-systematic investigation of the Virasoro master equation. The space of all affine-Virasoro constructions is organized by K-conjugation into affine-Virasoro nests, and an estimate of the dimension of the space shows that most solutions await discovery. With consistent ansatze for the master equation, large classes of new unitary nests are constructed, including quadratic deformation nests with continuous conformal weights, and unitary irrational central charge nests, which may dominate unitary rational central charge on compact g
Chiral unitary theory: Application to nuclear problems
Indian Academy of Sciences (India)
Chiral unitary theory: Application to nuclear problems ... Physics Department, Nara Women University, Nara, Japan. 5 ... RCNP, Osaka University, Osaka, Japan ...... We acknowledge partial financial support from the DGICYT under contract ...
Non-unitary probabilistic quantum computing
Gingrich, Robert M.; Williams, Colin P.
2004-01-01
We present a method for designing quantum circuits that perform non-unitary quantum computations on n-qubit states probabilistically, and give analytic expressions for the success probability and fidelity.
International Nuclear Information System (INIS)
Schroeck, Franklin E.
2008-01-01
The quarks have always been a puzzle, as have the particles' mass and mass/spin relations as they seemed to have no coordinates in configuration space and/or momentum space. The solution to this seems to lie in the marriage of ordinary Poincare group representations with a non-associative algebra made through a demisemidirect product. Then, the work of G. Dixon applies; so, we may obtain all the relations between masses, mass and spin, and the attribution of position and momentum to quarks--this in spite of the old restriction that the Poincare group cannot be extended to a larger group by any means (including the (semi)direct product) to get even the mass relations. Finally, we will briefly discuss a possible connection between the phase space representations of the Poincare group and the phase space representations of the object we will obtain. This will take us into Leibniz (co)homology.
Probabilistic implementation of Hadamard and unitary gates
International Nuclear Information System (INIS)
Song Wei; Yang Ming; Cao Zhuoliang
2004-01-01
We show that the Hadamard and unitary gates could be implemented by a unitary evolution together with a measurement for any unknown state chosen from a set A={ vertical bar Ψi>, vertical bar Ψ-bar i>} (i=1,2) if and only if vertical bar Ψ1>, vertical bar Ψ2>, vertical bar Ψ-bar 1>, vertical bar Ψ-bar 2> are linearly independent. We also derive the best transformation efficiencies
Entanglement quantification by local unitary operations
Energy Technology Data Exchange (ETDEWEB)
Monras, A.; Giampaolo, S. M.; Gualdi, G.; Illuminati, F. [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, CNISM, Unita di Salerno, and INFN, Sezione di Napoli-Gruppo Collegato di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy); Adesso, G.; Davies, G. B. [School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom)
2011-07-15
Invariance under local unitary operations is a fundamental property that must be obeyed by every proper measure of quantum entanglement. However, this is not the only aspect of entanglement theory where local unitary operations play a relevant role. In the present work we show that the application of suitable local unitary operations defines a family of bipartite entanglement monotones, collectively referred to as ''mirror entanglement.'' They are constructed by first considering the (squared) Hilbert-Schmidt distance of the state from the set of states obtained by applying to it a given local unitary operator. To the action of each different local unitary operator there corresponds a different distance. We then minimize these distances over the sets of local unitary operations with different spectra, obtaining an entire family of different entanglement monotones. We show that these mirror-entanglement monotones are organized in a hierarchical structure, and we establish the conditions that need to be imposed on the spectrum of a local unitary operator for the associated mirror entanglement to be faithful, i.e., to vanish in and only in separable pure states. We analyze in detail the properties of one particularly relevant member of the family, the ''stellar mirror entanglement'' associated with the traceless local unitary operations with nondegenerate spectra and equispaced eigenvalues in the complex plane. This particular measure generalizes the original analysis of S. M. Giampaolo and F. Illuminati [Phys. Rev. A 76, 042301 (2007)], valid for qubits and qutrits. We prove that the stellar entanglement is a faithful bipartite entanglement monotone in any dimension and that it is bounded from below by a function proportional to the linear entropy and from above by the linear entropy itself, coinciding with it in two- and three-dimensional spaces.
Entanglement quantification by local unitary operations
Monras, A.; Adesso, G.; Giampaolo, S. M.; Gualdi, G.; Davies, G. B.; Illuminati, F.
2011-07-01
Invariance under local unitary operations is a fundamental property that must be obeyed by every proper measure of quantum entanglement. However, this is not the only aspect of entanglement theory where local unitary operations play a relevant role. In the present work we show that the application of suitable local unitary operations defines a family of bipartite entanglement monotones, collectively referred to as “mirror entanglement.” They are constructed by first considering the (squared) Hilbert-Schmidt distance of the state from the set of states obtained by applying to it a given local unitary operator. To the action of each different local unitary operator there corresponds a different distance. We then minimize these distances over the sets of local unitary operations with different spectra, obtaining an entire family of different entanglement monotones. We show that these mirror-entanglement monotones are organized in a hierarchical structure, and we establish the conditions that need to be imposed on the spectrum of a local unitary operator for the associated mirror entanglement to be faithful, i.e., to vanish in and only in separable pure states. We analyze in detail the properties of one particularly relevant member of the family, the “stellar mirror entanglement” associated with the traceless local unitary operations with nondegenerate spectra and equispaced eigenvalues in the complex plane. This particular measure generalizes the original analysis of S. M. Giampaolo and F. Illuminati [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.76.042301 76, 042301 (2007)], valid for qubits and qutrits. We prove that the stellar entanglement is a faithful bipartite entanglement monotone in any dimension and that it is bounded from below by a function proportional to the linear entropy and from above by the linear entropy itself, coinciding with it in two- and three-dimensional spaces.
Entanglement quantification by local unitary operations
International Nuclear Information System (INIS)
Monras, A.; Giampaolo, S. M.; Gualdi, G.; Illuminati, F.; Adesso, G.; Davies, G. B.
2011-01-01
Invariance under local unitary operations is a fundamental property that must be obeyed by every proper measure of quantum entanglement. However, this is not the only aspect of entanglement theory where local unitary operations play a relevant role. In the present work we show that the application of suitable local unitary operations defines a family of bipartite entanglement monotones, collectively referred to as ''mirror entanglement.'' They are constructed by first considering the (squared) Hilbert-Schmidt distance of the state from the set of states obtained by applying to it a given local unitary operator. To the action of each different local unitary operator there corresponds a different distance. We then minimize these distances over the sets of local unitary operations with different spectra, obtaining an entire family of different entanglement monotones. We show that these mirror-entanglement monotones are organized in a hierarchical structure, and we establish the conditions that need to be imposed on the spectrum of a local unitary operator for the associated mirror entanglement to be faithful, i.e., to vanish in and only in separable pure states. We analyze in detail the properties of one particularly relevant member of the family, the ''stellar mirror entanglement'' associated with the traceless local unitary operations with nondegenerate spectra and equispaced eigenvalues in the complex plane. This particular measure generalizes the original analysis of S. M. Giampaolo and F. Illuminati [Phys. Rev. A 76, 042301 (2007)], valid for qubits and qutrits. We prove that the stellar entanglement is a faithful bipartite entanglement monotone in any dimension and that it is bounded from below by a function proportional to the linear entropy and from above by the linear entropy itself, coinciding with it in two- and three-dimensional spaces.
Polynomial approximation of non-Gaussian unitaries by counting one photon at a time
Arzani, Francesco; Treps, Nicolas; Ferrini, Giulia
2017-05-01
In quantum computation with continuous-variable systems, quantum advantage can only be achieved if some non-Gaussian resource is available. Yet, non-Gaussian unitary evolutions and measurements suited for computation are challenging to realize in the laboratory. We propose and analyze two methods to apply a polynomial approximation of any unitary operator diagonal in the amplitude quadrature representation, including non-Gaussian operators, to an unknown input state. Our protocols use as a primary non-Gaussian resource a single-photon counter. We use the fidelity of the transformation with the target one on Fock and coherent states to assess the quality of the approximate gate.
Unitary transformations in solid state physics
International Nuclear Information System (INIS)
Wagner, M.
1986-01-01
The main emphasis of this book is on the practical application of unitary transformations to problems in solid state physics. This is a method used in the field of nonadiabatic electron-phonon phenomena where the Born-Oppenheimer approximation is no longer applicable. The book is intended as a tool for those who want to apply unitary transformations quickly and on a more elementary level and also for those who want to use this method for more involved problems. The book is divided into 6 chapters. The first three chapters are concerned with presenting quick applications of unitary transformations and chapter 4 presents a more systematic procedure. The last two chapters contain the major known examples of the utilization of unitary transformations in solid state physics, including such highlights as the Froehlich and the Fulton-Gouterman transformations. The book is supplemented by extended tables of unitary transformations, whose properties and peculiarities are also listed. This tabulated material is unique and will be of great practical use to those applying the method of unitary transformations in their work. (Auth.)
On relevant boundary perturbations of unitary minimal models
International Nuclear Information System (INIS)
Recknagel, A.; Roggenkamp, D.; Schomerus, V.
2000-01-01
We consider unitary Virasoro minimal models on the disk with Cardy boundary conditions and discuss deformations by certain relevant boundary operators, analogous to tachyon condensation in string theory. Concentrating on the least relevant boundary field, we can perform a perturbative analysis of renormalization group fixed points. We find that the systems always flow towards stable fixed points which admit no further (non-trivial) relevant perturbations. The new conformal boundary conditions are in general given by superpositions of 'pure' Cardy boundary conditions
SL(2, 7) representations and their relevance to neutrino physics
Energy Technology Data Exchange (ETDEWEB)
Aliferis, G.; Vlachos, N.D. [University of Thessaloniki, Department of Nuclear and Particle Physics, Thessaloniki (Greece); Leontaris, G.K. [University of Ioannina, Physics Department, Ioannina (Greece); CERN, Department of Physics, Geneva 23 (Switzerland)
2017-06-15
The investigation of the role of finite groups in flavor physics and, particularly, in the interpretation of the neutrino data has been the subject of intensive research. Motivated by this fact, in this work we derive the three-dimensional unitary representations of the projective linear group PSL{sub 2}(7). Based on the observation that the generators of the group exhibit a Latin square pattern, we use available computational packages on discrete algebra to determine the generic properties of the group elements. We present analytical expressions and discuss several examples which reproduce the neutrino mixing angles in accordance with the experimental data. (orig.)
Random unitary operations and quantum Darwinism
International Nuclear Information System (INIS)
Balaneskovic, Nenad
2016-01-01
We study the behavior of Quantum Darwinism (Zurek, Nature Physics 5, 181-188 (2009)) within the iterative, random unitary operations qubit-model of pure decoherence (Novotn'y et al, New Jour. Phys. 13, 053052 (2011)). We conclude that Quantum Darwinism, which describes the quantum mechanical evolution of an open system from the point of view of its environment, is not a generic phenomenon, but depends on the specific form of initial states and on the type of system-environment interactions. Furthermore, we show that within the random unitary model the concept of Quantum Darwinism enables one to explicitly construct and specify artificial initial states of environment that allow to store information about an open system of interest and its pointer-basis with maximal efficiency. Furthermore, we investigate the behavior of Quantum Darwinism after introducing dissipation into the iterative random unitary qubit model with pure decoherence in accord with V. Scarani et al (Phys. Rev. Lett. 88, 097905 (2002)) and reconstruct the corresponding dissipative attractor space. We conclude that in Zurek's qubit model Quantum Darwinism depends on the order in which pure decoherence and dissipation act upon an initial state of the entire system. We show explicitly that introducing dissipation into the random unitary evolution model in general suppresses Quantum Darwinism (regardless of the order in which decoherence and dissipation are applied) for all positive non-zero values of the dissipation strength parameter, even for those initial state configurations which, in Zurek's qubit model and in the random unitary model with pure decoherence, would lead to Quantum Darwinism. Finally, we discuss what happens with Quantum Darwinism after introducing into the iterative random unitary qubit model with pure decoherence (asymmetric) dissipation and dephasing, again in accord with V. Scarani et al (Phys. Rev. Lett. 88, 097905 (2002)), and reconstruct the corresponding
Medland, A. J.; Zhu, Guowang; Gao, Jian; Sun, Jian
1996-03-01
Feature conversion, also called feature transformation and feature mapping, is defined as the process of converting features from one view of an object to another view of the object. In a relatively simple implementation, for each application the design features are automatically converted into features specific for that application. All modifications have to be made via the design features. This is the approach that has attracted most attention until now. In the ideal situation, however, conversions directly from application views to the design view, and to other applications views, are also possible. In this paper, some difficulties faced in feature conversion are discussed. A new representation scheme of feature-based parts models has been proposed for the purpose of one-way feature conversion. The parts models consist of five different levels of abstraction, extending from an assembly level and its attributes, single parts and their attributes, single features and their attributes, one containing the geometric reference element and finally one for detailed geometry. One implementation of feature conversion for rotational components within GT (Group Technology) has already been undertaken using an automated coding procedure operating on a design-feature database. This database has been generated by a feature-based design system, and the GT coding scheme used in this paper is a specific scheme created for a textile machine manufacturing plant. Such feature conversion techniques presented here are only in their early stages of development and further research is underway.
Exploring the Structure of Spatial Representations
Madl, Tamas; Franklin, Stan; Chen, Ke; Trappl, Robert; Montaldi, Daniela
2016-01-01
It has been suggested that the map-like representations that support human spatial memory are fragmented into sub-maps with local reference frames, rather than being unitary and global. However, the principles underlying the structure of these ‘cognitive maps’ are not well understood. We propose that the structure of the representations of navigation space arises from clustering within individual psychological spaces, i.e. from a process that groups together objects that are close in these spaces. Building on the ideas of representational geometry and similarity-based representations in cognitive science, we formulate methods for learning dissimilarity functions (metrics) characterizing participants’ psychological spaces. We show that these learned metrics, together with a probabilistic model of clustering based on the Bayesian cognition paradigm, allow prediction of participants’ cognitive map structures in advance. Apart from insights into spatial representation learning in human cognition, these methods could facilitate novel computational tools capable of using human-like spatial concepts. We also compare several features influencing spatial memory structure, including spatial distance, visual similarity and functional similarity, and report strong correlations between these dimensions and the grouping probability in participants’ spatial representations, providing further support for clustering in spatial memory. PMID:27347681
Orthogonality relations and supercharacter formulas of U(m|n) representations
International Nuclear Information System (INIS)
Alfaro, J.; Medina, R.; Urrutia, L.F.
1997-01-01
In this paper we obtain the orthogonality relations for the supergroup U(m|n), which are remarkably different from the ones for the U(N) case. We extend our results for ordinary representations, obtained some time ago, to the case of complex conjugated and mixed representations. Our results are expressed in terms of the Young tableaux notation for irreducible representations. We use the supersymmetric Harish - Chandra - Itzykson endash Zuber integral and the character expansion technique as mathematical tools for deriving these relations. As a byproduct we also obtain closed expressions for the supercharacters and dimensions of some particular irreducible U(m|n) representations. A new way of labeling the U(m|n) irreducible representations in terms of m+n numbers is proposed. Finally, as a corollary of our results, new identities among the dimensions of the irreducible representations of the unitary group U(N) are presented. copyright 1997 American Institute of Physics
DEFF Research Database (Denmark)
Brander, David; Rossman, Wayne; Schmitt, Nicholas
2010-01-01
We give an infinite dimensional generalized Weierstrass representation for spacelike constant mean curvature (CMC) surfaces in Minkowski 3-space $\\R^{2,1}$. The formulation is analogous to that given by Dorfmeister, Pedit and Wu for CMC surfaces in Euclidean space, replacing the group $SU_2$ with...
Effective Hamiltonian within the microscopic unitary nuclear model
International Nuclear Information System (INIS)
Filippov, G.F.; Blokhin, A.L.
1989-01-01
A technique of projecting the microscopic nuclear Hamiltonian on the SU(3)-group enveloping algebra is developed. The approach proposed is based on the effective Hamiltonian restored from the matrix elements between the coherent states of the SU(3) irreducible representations. The technique is displayed for almost magic nuclei within the mixed representation basis, and for arbitrary nuclei within the single representation. 40 refs
Multiple multicontrol unitary operations: Implementation and applications
Lin, Qing
2018-04-01
The efficient implementation of computational tasks is critical to quantum computations. In quantum circuits, multicontrol unitary operations are important components. Here, we present an extremely efficient and direct approach to multiple multicontrol unitary operations without decomposition to CNOT and single-photon gates. With the proposed approach, the necessary two-photon operations could be reduced from O( n 3) with the traditional decomposition approach to O( n), which will greatly relax the requirements and make large-scale quantum computation feasible. Moreover, we propose the potential application to the ( n- k)-uniform hypergraph state.
Identical particles, exotic statistics and braid groups
International Nuclear Information System (INIS)
Imbo, T.D.; Sudarshan, E.C.G.; Shah Imbo, C.
1990-01-01
The inequivalent quantizations of a system of n identical particles on a manifold M, dim M≥2, are in 1-1 correspondence with irreducible unitary representations of the braid group B n (M). The notion of the statistics of the particles is made precise. We give various examples where all the possible statistics for the system are determined, and find instances where the particles obey statistics different from the well-studied Bose, Fermi para- and θ-statistics. (orig.)
The SNARC effect is not a unitary phenomenon.
Basso Moro, Sara; Dell'Acqua, Roberto; Cutini, Simone
2018-04-01
Models of the spatial-numerical association of response codes (SNARC) effect-faster responses to small numbers using left effectors, and the converse for large numbers-diverge substantially in localizing the root cause of this effect along the numbers' processing chain. One class of models ascribes the cause of the SNARC effect to the inherently spatial nature of the semantic representation of numerical magnitude. A different class of models ascribes the effect's cause to the processing dynamics taking place during response selection. To disentangle these opposing views, we devised a paradigm combining magnitude comparison and stimulus-response switching in order to monitor modulations of the SNARC effect while concurrently tapping both semantic and response-related processing stages. We observed that the SNARC effect varied nonlinearly as a function of both manipulated factors, a result that can hardly be reconciled with a unitary cause of the SNARC effect.
Directory of Open Access Journals (Sweden)
Lau M. Andersen
2018-05-01
Full Text Available An important aim of an analysis pipeline for magnetoencephalographic (MEG data is that it allows for the researcher spending maximal effort on making the statistical comparisons that will answer his or her questions. The example question being answered here is whether the so-called beta rebound differs between novel and repeated stimulations. Two analyses are presented: going from individual sensor space representations to, respectively, an across-group sensor space representation and an across-group source space representation. The data analyzed are neural responses to tactile stimulations of the right index finger in a group of 20 healthy participants acquired from an Elekta Neuromag System. The processing steps covered for the first analysis are MaxFiltering the raw data, defining, preprocessing and epoching the data, cleaning the data, finding and removing independent components related to eye blinks, eye movements and heart beats, calculating participants' individual evoked responses by averaging over epoched data and subsequently removing the average response from single epochs, calculating a time-frequency representation and baselining it with non-stimulation trials and finally calculating a grand average, an across-group sensor space representation. The second analysis starts from the grand average sensor space representation and after identification of the beta rebound the neural origin is imaged using beamformer source reconstruction. This analysis covers reading in co-registered magnetic resonance images, segmenting the data, creating a volume conductor, creating a forward model, cutting out MEG data of interest in the time and frequency domains, getting Fourier transforms and estimating source activity with a beamformer model where power is expressed relative to MEG data measured during periods of non-stimulation. Finally, morphing the source estimates onto a common template and performing group-level statistics on the data are
On reducibility of mapping class group representations: the SU(N) case
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Fjelstad, Jens
2010-01-01
of examples where we can show reducibility significantly by establishing the existence of algebras with the required properties using methods developed by Fuchs, Runkel and Schweigert. As a result we show that the quantum representations are reducible in the SU(N) case, N>2, for all levels k\\in \\mathbb...
Unitary information ether and its possible applications
International Nuclear Information System (INIS)
Horodecki, R.
1991-01-01
The idea of information ether as the unitary information field is developed. It rests on the assumption that the notion of information is a fundamental category in the description of reality and that it can be defined independently from the notion of probability itself. It is shown that the information ether provides a deterministic background for the nonlinear wave hypothesis and quantum cybernetics. (orig.)
Khan, Abu M. A. S.
We study the continuous spin representation (CSR) of the Poincare group in arbitrary dimensions. In d dimensions, the CSRs are characterized by the length of the light-cone vector and the Dynkin labels of the SO(d-3) short little group which leaves the light-cone vector invariant. In addition to these, a solid angle Od-3 which specifies the direction of the light-cone vector is also required to label the states. We also find supersymmetric generalizations of the CSRs. In four dimensions, the supermultiplet contains one bosonic and one fermionic CSRs which transform into each other under the action of the supercharges. In a five dimensional case, the supermultiplet contains two bosonic and two fermionic CSRs which is like N = 2 supersymmetry in four dimensions. When constructed using Grassmann parameters, the light-cone vector becomes nilpotent. This makes the representation finite dimensional, but at the expense of introducing central charges even though the representation is massless. This leads to zero or negative norm states. The nilpotent constructions are valid only for even dimensions. We also show how the CSRs in four dimensions can be obtained from five dimensions by the combinations of Kaluza-Klein (KK) dimensional reduction and the Inonu-Wigner group contraction. The group contraction is a singular transformation. We show that the group contraction is equivalent to imposing periodic boundary condition along one direction and taking a double singular limit. In this form the contraction parameter is interpreted as the inverse KK radius. We apply this technique to both five dimensional regular massless and massive representations. For the regular massless case, we find that the contraction gives the CSR in four dimensions under a double singular limit and the representation wavefunction is the Bessel function. For the massive case, we use Majorana's infinite component theory as a model for the SO(4) little group. In this case, a triple singular limit is
Irreducible projective representations and their physical applications
Yang, Jian; Liu, Zheng-Xin
2018-01-01
An eigenfunction method is applied to reduce the regular projective representations (Reps) of finite groups to obtain their irreducible projective Reps. Anti-unitary groups are treated specially, where the decoupled factor systems and modified Schur’s lemma are introduced. We discuss the applications of irreducible Reps in many-body physics. It is shown that in symmetry protected topological phases, geometric defects or symmetry defects may carry projective Rep of the symmetry group; while in symmetry enriched topological phases, intrinsic excitations (such as spinons or visons) may carry projective Rep of the symmetry group. We also discuss the applications of projective Reps in problems related to spectrum degeneracy, such as in search of models without sign problem in quantum Monte Carlo simulations.
Niskanen, Eini; Julkunen, Petro; Säisänen, Laura; Vanninen, Ritva; Karjalainen, Pasi; Könönen, Mervi
2010-08-01
Navigated transcranial magnetic stimulation (TMS) can be used to stimulate functional cortical areas at precise anatomical location to induce measurable responses. The stimulation has commonly been focused on anatomically predefined motor areas: TMS of that area elicits a measurable muscle response, the motor evoked potential. In clinical pathologies, however, the well-known homunculus somatotopy theory may not be straightforward, and the representation area of the muscle is not fixed. Traditionally, the anatomical locations of TMS stimulations have not been reported at the group level in standard space. This study describes a methodology for group-level analysis by investigating the normal representation areas of thenar and anterior tibial muscle in the primary motor cortex. The optimal representation area for these muscles was mapped in 59 healthy right-handed subjects using navigated TMS. The coordinates of the optimal stimulation sites were then normalized into standard space to determine the representation areas of these muscles at the group-level in healthy subjects. Furthermore, 95% confidence interval ellipsoids were fitted into the optimal stimulation site clusters to define the variation between subjects in optimal stimulation sites. The variation was found to be highest in the anteroposterior direction along the superior margin of the precentral gyrus. These results provide important normative information for clinical studies assessing changes in the functional cortical areas because of plasticity of the brain. Furthermore, it is proposed that the presented methodology to study TMS locations at the group level on standard space will be a suitable tool for research purposes in population studies. 2010 Wiley-Liss, Inc.
Rom, Eldad; Mikulincer, Mario
2003-06-01
Four studies examined attachment-style differences in group-related cognitions and behaviors. In Studies 1-2, participants completed scales on group-related cognitions and emotions. In Studies 3-4, participants were divided into small groups, and their performance in group tasks as well as the cohesion of their group were assessed. Both attachment anxiety and avoidance in close relationships were associated with negative group-related cognitions and emotions. Anxiety was also related to the pursuit of closeness goals and impaired instrumental performance in group tasks. Avoidance was related to the pursuit of distance goals and deficits in socioemotional and instrumental performance. Group cohesion significantly moderated the effects of attachment anxiety. The discussion emphasizes the relevance of attachment theory within group contexts.
Vector coherent state representations and their inner products
International Nuclear Information System (INIS)
Rowe, D J
2012-01-01
Several advances have extended the power and versatility of coherent state theory to the extent that it has become a vital tool in the representation theory of Lie groups and their Lie algebras. Representative applications are reviewed and some new developments are introduced. The examples given are chosen to illustrate special features of the scalar and vector coherent state constructions and how they work in practical situations. Comparisons are made with Mackey's theory of induced representations. For simplicity, we focus on square integrable (discrete series) unitary representations although many of the techniques apply more generally, with minor adjustment. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (review)
Black hole thermodynamics based on unitary evolutions
International Nuclear Information System (INIS)
Feng, Yu-Lei; Chen, Yi-Xin
2015-01-01
In this paper, we try to construct black hole thermodynamics based on the fact that the formation and evaporation of a black hole can be described by quantum unitary evolutions. First, we show that the Bekenstein–Hawking entropy S BH may not be a Boltzmann or thermal entropy. To confirm this statement, we show that the original black hole's ‘first law’ may not simply be treated as the first law of thermodynamics formally, due to some missing metric perturbations caused by matter. Then, by including those (quantum) metric perturbations, we show that the black hole formation and evaporation can be described effectively in a unitary manner, through a quantum channel between the exterior and interior of the event horizon. In this way, the paradoxes of information loss and firewall can be resolved effectively. Finally, we show that black hole thermodynamics can be constructed in an ordinary way, by constructing statistical mechanics. (paper)
Unitary evolution between pure and mixed states
International Nuclear Information System (INIS)
Reznik, B.
1996-01-01
We propose an extended quantum mechanical formalism that is based on a wave operator d, which is related to the ordinary density matrix via ρ=dd degree . This formalism allows a (generalized) unitary evolution between pure and mixed states. It also preserves much of the connection between symmetries and conservation laws. The new formalism is illustrated for the case of a two-level system. copyright 1996 The American Physical Society
Directory of Open Access Journals (Sweden)
T Ashino
2008-11-01
Full Text Available On March 4-5, 2008, the CODATA Task Group for Exchangeable Material Data Representation to Support Research and Education held a two day seminar cum meeting at the National Physical Laboratory (NPL, New Delhi, India, with NPL materials researchers and task group members representing material activities and databases from seven countries: European Union (The Czech Republic, France, and the Netherlands, India, Korea, Japan, and the United States. The NPL seminar included presentations about the researchers' work. The Task Group meeting included presentations about current data related activities of the members. Joint discussions between NPL researchers and CODATA task group members began an exchange of viewpoints among materials data producers, users, and databases developers. The seminar cum meeting included plans to continue and expand Task Group activities at the 2008 CODATA 21st Meeting in Kyiv, Ukraine.
Representations of coherent states in non-orthogonal bases
International Nuclear Information System (INIS)
Ali, S Twareque; Roknizadeh, R; Tavassoly, M K
2004-01-01
Starting with the canonical coherent states, we demonstrate that all the so-called nonlinear coherent states, used in the physical literature, as well as large classes of other generalized coherent states, can be obtained by changes of bases in the underlying Hilbert space. This observation leads to an interesting duality between pairs of generalized coherent states, bringing into play a Gelfand triple of (rigged) Hilbert spaces. Moreover, it is shown that in each dual pair of families of nonlinear coherent states, at least one family is related to a (generally) non-unitary projective representation of the Weyl-Heisenberg group, which can then be thought of as characterizing the dual pair
International Nuclear Information System (INIS)
Roche, Ph.
2016-01-01
We recall the relation between zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of zeta function representations of groups. We compute some of these functions in the case of the finite group GL(2, _q) and PGL(2, _q). We recall the table characters of these groups for any q, compute the Frobenius-Schur indicator of their irreducible representations, and give the explicit structure of their fusion rings.
Andersen, Lau M
2018-01-01
An important aim of an analysis pipeline for magnetoencephalographic data is that it allows for the researcher spending maximal effort on making the statistical comparisons that will answer the questions of the researcher, while in turn spending minimal effort on the intricacies and machinery of the pipeline. I here present a set of functions and scripts that allow for setting up a clear, reproducible structure for separating raw and processed data into folders and files such that minimal effort can be spend on: (1) double-checking that the right input goes into the right functions; (2) making sure that output and intermediate steps can be accessed meaningfully; (3) applying operations efficiently across groups of subjects; (4) re-processing data if changes to any intermediate step are desirable. Applying the scripts requires only general knowledge about the Python language. The data analyses are neural responses to tactile stimulations of the right index finger in a group of 20 healthy participants acquired from an Elekta Neuromag System. Two analyses are presented: going from individual sensor space representations to, respectively, an across-group sensor space representation and an across-group source space representation. The processing steps covered for the first analysis are filtering the raw data, finding events of interest in the data, epoching data, finding and removing independent components related to eye blinks and heart beats, calculating participants' individual evoked responses by averaging over epoched data and calculating a grand average sensor space representation over participants. The second analysis starts from the participants' individual evoked responses and covers: estimating noise covariance, creating a forward model, creating an inverse operator, estimating distributed source activity on the cortical surface using a minimum norm procedure, morphing those estimates onto a common cortical template and calculating the patterns of activity
Directory of Open Access Journals (Sweden)
Lau M. Andersen
2018-01-01
Full Text Available An important aim of an analysis pipeline for magnetoencephalographic data is that it allows for the researcher spending maximal effort on making the statistical comparisons that will answer the questions of the researcher, while in turn spending minimal effort on the intricacies and machinery of the pipeline. I here present a set of functions and scripts that allow for setting up a clear, reproducible structure for separating raw and processed data into folders and files such that minimal effort can be spend on: (1 double-checking that the right input goes into the right functions; (2 making sure that output and intermediate steps can be accessed meaningfully; (3 applying operations efficiently across groups of subjects; (4 re-processing data if changes to any intermediate step are desirable. Applying the scripts requires only general knowledge about the Python language. The data analyses are neural responses to tactile stimulations of the right index finger in a group of 20 healthy participants acquired from an Elekta Neuromag System. Two analyses are presented: going from individual sensor space representations to, respectively, an across-group sensor space representation and an across-group source space representation. The processing steps covered for the first analysis are filtering the raw data, finding events of interest in the data, epoching data, finding and removing independent components related to eye blinks and heart beats, calculating participants' individual evoked responses by averaging over epoched data and calculating a grand average sensor space representation over participants. The second analysis starts from the participants' individual evoked responses and covers: estimating noise covariance, creating a forward model, creating an inverse operator, estimating distributed source activity on the cortical surface using a minimum norm procedure, morphing those estimates onto a common cortical template and calculating the patterns
Casimir energy between two parallel plates and projective representation of the Poincaré group
Akita, Takamaru; Matsunaga, Mamoru
2016-06-01
The Casimir effect is a physical manifestation of zero point energy of quantum vacuum. In a relativistic quantum field theory, Poincaré symmetry of the theory seems, at first sight, to imply that nonzero vacuum energy is inconsistent with translational invariance of the vacuum. In the setting of two uniform boundary plates at rest, quantum fields outside the plates have (1 +2 )-dimensional Poincaré symmetry. Taking a massless scalar field as an example, we have examined the consistency between the Poincaré symmetry and the existence of the vacuum energy. We note that, in quantum theory, symmetries are represented projectively in general and show that the Casimir energy is connected to central charges appearing in the algebra of generators in the projective representations.
Wang, Juven C; Gu, Zheng-Cheng; Wen, Xiao-Gang
2015-01-23
The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs. We find new examples of mixed gauge-gravity actions for U(1) SPTs in (4+1)D via the gravitational Chern-Simons term. Field theory representations of SPT invariants not only serve as tools for classifying SPTs, but also guide us in designing physical probes for them. In addition, our field theory representations are independently powerful for studying group cohomology within the mathematical context.
Hirose, Y; Sasaki, Y; Kinoshita, A
2001-01-01
We have previously reported the access control mechanism and audit strategy of the "patient-doctor relation and clinical situation at the point-of-care" model with multi-axial access control matrix (ACM). This mechanism overcomes the deficit of ACM in the aspect of data accessibility but does not resolve the representation of the staff's affiliate and/or plural membership in the complex real world. Care groups inside a department or inter-department clinical team plays significant clinical role but also spend great amount of time and money in the hospital. Therefore the impact of human resource assignment and cost of such stakeholders to the hospital management is huge, so that they should be accurately treated in the hospital information system. However multi-axial ACM has problems with the representation of staff groups due to static parameters such as department/license because staffs belong to a group rather temporarily and/or a medical staff may belong to plural groups. As a solution, we have designed and implemented "cascading staff-group authoring" method with "relation and situation" model and multi-axial ACM. In this mechanism, (i) a system administrator certifies "group chief certifying person" according to the request and authorization by the department director, (ii) the "group chief certifying person" certifies "group chief(s)", (iii) the "group chief" recruits its members from the medical staffs, and at the same time the "group chief" decides the profit distribution policy of this group. This will enable medical staff to access EMR according to the role he/she plays whether it is as a department staff or as a group member. This solution has worked successfully over the past few years. It provides end-users with a flexible and time-to-time staff-group authoring environment using a simple human-interfaced tool without security breach and without system administration cost. In addition, profit and cost distribution is clarified among departments and
Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories
Buican, Matthew; Laczko, Zoltan
2018-02-01
In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N =2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us Lagrangians for particular observables in certain subsectors of many "non-Lagrangian" SCFTs by sacrificing unitarity while preserving the full N =2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.
Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories.
Buican, Matthew; Laczko, Zoltan
2018-02-23
In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N=2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us Lagrangians for particular observables in certain subsectors of many "non-Lagrangian" SCFTs by sacrificing unitarity while preserving the full N=2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.
Quaternionic representation of the Coxeter group W(H4) and the polyhedra
International Nuclear Information System (INIS)
Koca, Mehmet; Al-Ajmi, Mudhahir; Koc, Ramazan
2006-01-01
The vertices of the four-dimensional polytope {3, 3, 5} and its dual {5, 3, 3} admitting the symmetry of the non-crystallographic Coxeter group W(H 4 ) of order 14,400 are represented in terms of quaternions with unit norm where the polytope {3, 3, 5} is represented by the elements of the binaryicosahedral group of quaternions of order 120. We projected the polytopes to three-dimensional Euclidean space where the quaternionic vertices are the orbits of the Coxeter group W(H 3 ), icosahedral group with inversion, where W(H 3 ) x Z 2 is one of the maximal subgroups of the Coxeter group W(H 4 ). The orbits of the icosahedral group W(H 3 ) in the polytope {3, 3, 5} are the conjugacy classes of the binary icosahedral group and represent a number of icosahedrons, dodecahedrons and one icosidodecahedron in three dimensions. The 15 orbits of the icosahedral group W(H 3 ) in the polytope {5, 3, 3} represent the dodecahedrons, icosidodecahedrons, small rhombicosidodecahedrons and some convex solids possessing the icosahedral symmetry. One of the convex solids with 60 vertices is very similar to the truncated icosahedron (soccer ball) but with two different edge lengths which can be taken as a realistic model of the C 60 molecule at extreme temperature and pressure
Quantum reading of unitary optical devices
International Nuclear Information System (INIS)
Dall'Arno, Michele; Bisio, Alessandro; D'Ariano, Giacomo Mauro
2014-01-01
We address the problem of quantum reading of optical memories, namely the retrieving of classical information stored in the optical properties of a media with minimum energy. We present optimal strategies for ambiguous and unambiguous quantum reading of unitary optical memories, namely when one's task is to minimize the probability of errors in the retrieved information and when perfect retrieving of information is achieved probabilistically, respectively. A comparison of the optimal strategy with coherent probes and homodyne detection shows that the former saves orders of magnitude of energy when achieving the same performances. Experimental proposals for quantum reading which are feasible with present quantum optical technology are reported
Quaternionic representation of the Coxeter group W(H{sub 4}) and the polyhedra
Energy Technology Data Exchange (ETDEWEB)
Koca, Mehmet [Department of Physics, College of Science, Sultan Qaboos University, PO Box 36, Al-Khod 123, Muscat (Oman); Al-Ajmi, Mudhahir [Department of Physics, College of Science, Sultan Qaboos University, PO Box 36, Al-Khod 123, Muscat (Oman); Koc, Ramazan [Department of Physics, Faculty of Engineering, University of Gaziantep, 27310 Gaziantep (Turkey)
2006-11-10
The vertices of the four-dimensional polytope {l_brace}3, 3, 5{r_brace} and its dual {l_brace}5, 3, 3{r_brace} admitting the symmetry of the non-crystallographic Coxeter group W(H{sub 4}) of order 14,400 are represented in terms of quaternions with unit norm where the polytope {l_brace}3, 3, 5{r_brace} is represented by the elements of the binaryicosahedral group of quaternions of order 120. We projected the polytopes to three-dimensional Euclidean space where the quaternionic vertices are the orbits of the Coxeter group W(H{sub 3}), icosahedral group with inversion, where W(H{sub 3}) x Z{sub 2} is one of the maximal subgroups of the Coxeter group W(H{sub 4}). The orbits of the icosahedral group W(H{sub 3}) in the polytope {l_brace}3, 3, 5{r_brace} are the conjugacy classes of the binary icosahedral group and represent a number of icosahedrons, dodecahedrons and one icosidodecahedron in three dimensions. The 15 orbits of the icosahedral group W(H{sub 3}) in the polytope {l_brace}5, 3, 3{r_brace} represent the dodecahedrons, icosidodecahedrons, small rhombicosidodecahedrons and some convex solids possessing the icosahedral symmetry. One of the convex solids with 60 vertices is very similar to the truncated icosahedron (soccer ball) but with two different edge lengths which can be taken as a realistic model of the C{sub 60} molecule at extreme temperature and pressure.
Cruwys, Tegan; Steffens, Niklas K; Haslam, S Alexander; Haslam, Catherine; Jetten, Jolanda; Dingle, Genevieve A
2016-12-01
In this research, we introduce Social Identity Mapping (SIM) as a method for visually representing and assessing a person's subjective network of group memberships. To provide evidence of its utility, we report validating data from three studies (two longitudinal), involving student, community, and clinical samples, together comprising over 400 participants. Results indicate that SIM is easy to use, internally consistent, with good convergent and discriminant validity. Each study also illustrates the ways that SIM can be used to address a range of novel research questions. Study 1 shows that multiple positive group memberships are a particularly powerful predictor of well-being. Study 2 shows that social support is primarily given and received within social groups and that only in-group support is beneficial for well-being. Study 3 shows that improved mental health following a social group intervention is attributable to an increase in group compatibility. In this way, the studies demonstrate the capacity for SIM to make a contribution both to the development of social-psychological theory and to its practical application. © 2016 The British Psychological Society.
Energy Technology Data Exchange (ETDEWEB)
Carlsson-Kanyama, A. [Swedish Defence Research Institute, Stockholm (Sweden); Ripa Julia, Isabel [Consultoria Ambiental, Logrono (Spain); Roehr, Ulrike [LIFE e.V, Berlin (Germany)
2010-08-15
This survey shows that female representation in boards and management groups of large energy companies in Germany, Spain and Sweden is far from being gender-equal. Of the 464 companies surveyed, 295 (64%) had no women at all in boards or management groups and only 5% could be considered gender-equal by having 40% or more women in such positions. Interviews with energy companies confirmed current trends that gender equality efforts within decision-making in business are weak or non-existent. The findings are discussed against the background of differences in risk perceptions among women and men, evidence of women's impact on boards and companies' performance and the substantial risks related to unabated climate change. Research is suggested for exploring potential impacts on energy companies' performance with more women in the boards when it comes to mitigation activities. (author)
Energy Technology Data Exchange (ETDEWEB)
Carlsson-Kanyama, A., E-mail: carlsson@foi.s [Swedish Defence Research Institute, Stockholm (Sweden); Ripa Julia, Isabel [Consultoria Ambiental, Logrono (Spain); Roehr, Ulrike [LIFE e.V, Berlin (Germany)
2010-08-15
This survey shows that female representation in boards and management groups of large energy companies in Germany, Spain and Sweden is far from being gender-equal. Of the 464 companies surveyed, 295 (64%) had no women at all in boards or management groups and only 5% could be considered gender-equal by having 40% or more women in such positions. Interviews with energy companies confirmed current trends that gender equality efforts within decision-making in business are weak or non-existent. The findings are discussed against the background of differences in risk perceptions among women and men, evidence of women's impact on boards and companies' performance and the substantial risks related to unabated climate change. Research is suggested for exploring potential impacts on energy companies' performance with more women in the boards when it comes to mitigation activities.
International Nuclear Information System (INIS)
Carlsson-Kanyama, A.; Ripa Julia, Isabel; Roehr, Ulrike
2010-01-01
This survey shows that female representation in boards and management groups of large energy companies in Germany, Spain and Sweden is far from being gender-equal. Of the 464 companies surveyed, 295 (64%) had no women at all in boards or management groups and only 5% could be considered gender-equal by having 40% or more women in such positions. Interviews with energy companies confirmed current trends that gender equality efforts within decision-making in business are weak or non-existent. The findings are discussed against the background of differences in risk perceptions among women and men, evidence of women's impact on boards and companies' performance and the substantial risks related to unabated climate change. Research is suggested for exploring potential impacts on energy companies' performance with more women in the boards when it comes to mitigation activities.
Meditations on the unitary rhythm of dying-grieving.
Malinski, Violet M
2012-07-01
When someone faces loss of a loved one, that person simultaneously grieves and dies a little, just as the one dying also grieves. The author's personal conceptualization of dying and grieving as a unitary rhythm is explored based primarily on her interpretation of Rogers' science of unitary human beings, along with selected examples from related nursing literature and from the emerging focus on continuing bonds in other disciplines. Examples from contemporary songwriters that depict such a unitary conceptualization are given along with personal examples. The author concludes with her description of the unitary rhythm of dying-grieving.
Moduli spaces of unitary conformal field theories
International Nuclear Information System (INIS)
Wendland, K.
2000-08-01
We investigate various features of moduli spaces of unitary conformal field theories. A geometric characterization of rational toroidal conformal field theories in arbitrary dimensions is presented and discussed in relation to singular tori and those with complex multiplication. We study the moduli space M 2 of unitary two-dimensional conformal field theories with central charge c = 2. All the 26 non-exceptional non-isolated irreducible components of M 2 are constructed that may be obtained by an orbifold procedure from toroidal theories. The parameter spaces and partition functions are calculated explicitly. All multicritical points and lines are determined, such that all but three of these 26 components are directly or indirectly connected to the space of toroidal theories in M 2 . Relating our results to those by Dixon, Ginsparg, Harvey on the classification of c = 3/2 superconformal field theories, we give geometric interpretations to all non-isolated orbifolds discussed by them and correct their statements on multicritical points within the moduli space of c = 3/2 superconformal field theories. In the main part of this work, we investigate the moduli space M of N = (4, 4) superconformal field theories with central charge c = 6. After a slight emendation of its global description we give generic partition functions for models contained in M. We explicitly determine the locations of various known models in the component of M associated to K3 surfaces
Random unitary maps for quantum state reconstruction
International Nuclear Information System (INIS)
Merkel, Seth T.; Riofrio, Carlos A.; Deutsch, Ivan H.; Flammia, Steven T.
2010-01-01
We study the possibility of performing quantum state reconstruction from a measurement record that is obtained as a sequence of expectation values of a Hermitian operator evolving under repeated application of a single random unitary map, U 0 . We show that while this single-parameter orbit in operator space is not informationally complete, it can be used to yield surprisingly high-fidelity reconstruction. For a d-dimensional Hilbert space with the initial observable in su(d), the measurement record lacks information about a matrix subspace of dimension ≥d-2 out of the total dimension d 2 -1. We determine the conditions on U 0 such that the bound is saturated, and show they are achieved by almost all pseudorandom unitary matrices. When we further impose the constraint that the physical density matrix must be positive, we obtain even higher fidelity than that predicted from the missing subspace. With prior knowledge that the state is pure, the reconstruction will be perfect (in the limit of vanishing noise) and for arbitrary mixed states, the fidelity is over 0.96, even for small d, and reaching F>0.99 for d>9. We also study the implementation of this protocol based on the relationship between random matrices and quantum chaos. We show that the Floquet operator of the quantum kicked top provides a means of generating the required type of measurement record, with implications on the relationship between quantum chaos and information gain.
Peters, Christina D.; Kranzler, John H.; Algina, James; Smith, Stephen W.; Daunic, Ann P.
2014-01-01
The aim of the current study was to examine mean-group differences on behavior rating scales and variables that may predict such differences. Sixty-five teachers completed the Clinical Assessment of Behavior-Teacher Form (CAB-T) for a sample of 982 students. Four outcome variables from the CAB-T were assessed. Hierarchical linear modeling was used…
A low-memory algorithm for finding short product representations in finite groups
Bisson, G.; Sutherland, A.V.
2012-01-01
We describe a space-efficient algorithm for solving a generalization of the subset sum problem in a finite group G, using a Pollard-¿ approach. Given an element z and a sequence of elements S, our algorithm attempts to find a subsequence of S whose product in G is equal to z. For a random sequence S
A low-memory algorithm for finding short product representations in finite groups
Bisson, G.; Sutherland, A.V.
2011-01-01
We describe a space-efficient algorithm for solving a generalization of the subset sum problem in a finite group G, using a Pollard-rho approach. Given an element z and a sequence of elements S, our algorithm attempts to find a subsequence of S whose product in G is equal to z. For a random sequence
Disintegration of positive isometric group representations on L^p-spaces
Jeu, de M.F.E.; Rozendaal, J.
2017-01-01
Let G be a Polish locally compact group acting on a Polish space X" role="presentation">X with a G-invariant probability measure μ" role="presentation">μ. We factorize the integral with respect to μ" role="presentation">μ in terms of the integrals with respect to the ergodic measures on X, and show
Peterson, Dwight J; Gözenman, Filiz; Arciniega, Hector; Berryhill, Marian E
2015-10-01
Recent studies have demonstrated that factors influencing perception, such as Gestalt grouping cues, can influence the storage of information in visual working memory (VWM). In some cases, stationary cues, such as stimulus similarity, lead to superior VWM performance. However, the neural correlates underlying these benefits to VWM performance remain unclear. One neural index, the contralateral delay activity (CDA), is an event-related potential that shows increased amplitude according to the number of items held in VWM and asymptotes at an individual's VWM capacity limit. Here, we applied the CDA to determine whether previously reported behavioral benefits supplied by similarity, proximity, and uniform connectedness were reflected as a neural savings such that the CDA amplitude was reduced when these cues were present. We implemented VWM change-detection tasks with arrays including similarity and proximity (Experiment 1); uniform connectedness (Experiments 2a and 2b); and similarity/proximity and uniform connectedness (Experiment 3). The results indicated that when there was a behavioral benefit to VWM, this was echoed by a reduction in CDA amplitude, which suggests more efficient processing. However, not all perceptual grouping cues provided a VWM benefit in the same measure (e.g., accuracy) or of the same magnitude. We also found unexpected interactions between cues. We observed a mixed bag of effects, suggesting that these powerful perceptual grouping benefits are not as predictable in VWM. The current findings indicate that when grouping cues produce behavioral benefits, there is a parallel reduction in the neural resources required to maintain grouped items within VWM.
Harmonic analysis on exponential solvable Lie groups
Fujiwara, Hidenori
2015-01-01
This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. There still are many interesting open problems, and the book contributes to the future progress of this research field. As well, various related topics are presented to motivate young researchers. The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups. This method tells us that the unitary dual of these groups is realized as the space of their coadjoint orbits. This fact is established using the Mackey theory for induced representations, and that mechanism is explained first. One of the fundamental problems in the representation theory is the irreducible decomposition of induced or restricted representations. Therefore, these decompositions are studied in detail before proceeding to various related problems: the multiplicity formula, Plancherel formulas, intertwining operators, Frobenius reciprocity, and associated alge...
Two dimentional lattice vibrations from direct product representations of symmetry groups
Directory of Open Access Journals (Sweden)
J. N. Boyd
1983-01-01
two dimensional crystals. First, the Born cyclic condition is applied to a double chain composed of coupled linear lattices to obtain a cylindrical arrangement. Then the quadratic Lagrangian function for the system is written in matrix notation. The Lagrangian is diagonalized to yield the natural frequencies of the system. The transformation to achieve the diagonalization was obtained from group theorectic considerations. Next, the techniques developed for the double chain are applied to a square lattice. The square lattice is transformed into the toroidal Ising model. The direct product nature of the symmetry group of the torus reveals the transformation to diagonalize the Lagrangian for the Ising model, and the natural frequencies for the principal directions in the model are obtained in closed form.
Composition series for representations of the generalized Lorentz group associated with a cone
Helminck, G.F.; Opimakh, A.V.
2008-01-01
Consider the cone C = {x is a member of Rn | -x(1)2+x(2)2 + ... + x(n)2 = 0, x(1) > 0}. The group G := SO(0)(1, n-1) acts through its natural action on Rn on C. This action of G induces an action of G on the differential forms of degree one. In this paper we describe the composition series of
Compactifications of the Heterotic string with unitary bundles
Energy Technology Data Exchange (ETDEWEB)
Weigand, T.
2006-05-23
In this thesis we investigate a large new class of four-dimensional supersymmetric string vacua defined as compactifications of the E{sub 8} x E{sub 8} and the SO(32) heterotic string on smooth Calabi-Yau threefolds with unitary gauge bundles and heterotic five-branes. The first part of the thesis discusses the implementation of this idea into the E{sub 8} x E{sub 8} heterotic string. After specifying a large class of group theoretic embeddings featuring unitary bundles, we analyse the effective four-dimensional N=1 supergravity upon compactification. From the gauge invariant Kaehler potential for the moduli fields we derive a modification of the Fayet-Iliopoulos D-terms arising at one-loop in string perturbation theory. From this we conjecture a one-loop deformation of the Hermitian Yang-Mills equation and introduce the idea of {lambda}-stability as the perturbatively correct stability concept generalising the notion of Mumford stability valid at tree-level. We then proceed to a definition of SO(32) heterotic vacua with unitary gauge bundles in the presence of heterotic five-branes and find agreement of the resulting spectrum with the S-dual framework of Type I/Type IIB orientifolds. A similar analysis of the effective four-dimensional supergravity is performed. Further evidence for the proposed one-loop correction to the stability condition is found by identifying the heterotic corrections as the S-dual of the perturbative part of {pi}-stability as the correct stability concept in Type IIB theory. After reviewing the construction of holomorphic stable vector bundles on elliptically fibered Calabi-Yau manifolds via spectral covers, we provide semi-realistic examples for SO(32) heterotic vacua with Pati-Salam and MSSM-like gauge sectors. We finally discuss the construction of realistic vacua with flipped SU(5) GUT and MSSM gauge group within the E{sub 8} x E{sub 8} framework, based on the embedding of line bundles into both E{sub 8} factors. Some of the appealing
Twisted Diff S sup 1 -action on loop groups and representations of the Virasoro algebra
Energy Technology Data Exchange (ETDEWEB)
Harnad, J [Montreal Univ., Quebec (Canada). Centre de Recherches Mathematiques (CRM); Kupershmidt, B A [Tennessee Univ., Tullahoma (USA). Space Inst.
1990-05-01
A modified Hamiltonian action of Diff S{sup 1} on the phase space LG{sup C}/G{sup C}, where LG is a loop group, is defined by twisting the usual action by a left translation in LG. This twisted action is shown to be generated by a nonequivariant moment map, thereby defining a classical Poisson bracket realization of a central extension of the Lie algebra diff{sub C} S{sup 1}. The resulting formula expresses the Diff S{sup 1} generators in terms of the left LG translation generators, giving a shifted modification of both the classical and quantum versions of the Sugawara formula. (orig.).
Territory in the Constitutional Standards of Unitary States
Directory of Open Access Journals (Sweden)
Marina V. Markhgeym
2017-06-01
Full Text Available The article is based on the analysis of the constitutions of seven European countries (Albania, Hungary, Greece, Spain, Malta, Poland, Sweden. The research allows to reveal general and specific approaches to consolidation of norms on territories in a state and give the characteristic of the corresponding constitutional norms. Given the authors ' comprehensive approach to the definition of the territory of the state declared constitutional norms were assessed from the perspective of the fundamental principles and constituent elements of the territory. Considering the specifics of the constitutional types of state territories authors suggest typical and variative models and determine the constitutions of unitary states, distinguished by their originality in the declared group of legal relations. The original constitutional language areas associated with the introduction at the state level, these types of areas that are not typical for other countries.
The flexible focus: whether spatial attention is unitary or divided depends on observer goals.
Jefferies, Lisa N; Enns, James T; Di Lollo, Vincent
2014-04-01
The distribution of visual attention has been the topic of much investigation, and various theories have posited that attention is allocated either as a single unitary focus or as multiple independent foci. In the present experiment, we demonstrate that attention can be flexibly deployed as either a unitary or a divided focus in the same experimental task, depending on the observer's goals. To assess the distribution of attention, we used a dual-stream Attentional Blink (AB) paradigm and 2 target pairs. One component of the AB, Lag-1 sparing, occurs only if the second target pair appears within the focus of attention. By varying whether the first-target-pair could be expected in a predictable location (always in-stream) or not (unpredictably in-stream or between-streams), observers were encouraged to deploy a divided or a unitary focus, respectively. When the second-target-pair appeared between the streams, Lag-1 sparing occurred for the Unpredictable group (consistent with a unitary focus) but not for the Predictable group (consistent with a divided focus). Thus, diametrically different outcomes occurred for physically identical displays, depending on the expectations of the observer about where spatial attention would be required.
Equivalence of quantum states under local unitary transformations
International Nuclear Information System (INIS)
Fei Shaoming; Jing Naihuan
2005-01-01
In terms of the analysis of fixed point subgroup and tensor decomposability of certain matrices, we study the equivalence of quantum bipartite mixed states under local unitary transformations. For non-degenerate case an operational criterion for the equivalence of two such mixed bipartite states under local unitary transformations is presented
Perfect state transfer in unitary Cayley graphs over local rings
Directory of Open Access Journals (Sweden)
Yotsanan Meemark
2014-12-01
Full Text Available In this work, using eigenvalues and eigenvectors of unitary Cayley graphs over finite local rings and elementary linear algebra, we characterize which local rings allowing PST occurring in its unitary Cayley graph. Moreover, we have some developments when $R$ is a product of local rings.
Unitary Quantum Relativity. (Work in Progress)
Finkelstein, David Ritz
2017-01-01
A quantum universe is expressed as a finite unitary relativistic quantum computer network. Its addresses are subject to quantum superposition as well as its memory. It has no exact mathematical model. It Its Hilbert space of input processes is also a Clifford algebra with a modular architecture of many ranks. A fundamental fermion is a quantum computer element whose quantum address belongs to the rank below. The least significant figures of its address define its spin and flavor. The most significant figures of it adress define its orbital variables. Gauging arises from the same quantification as space-time. This blurs star images only slightly, but perhaps measurably. General relativity is an approximation that splits nature into an emptiness with a high symmetry that is broken by a filling of lower symmetry. Action principles result from self-organization pf the vacuum.
Quantum Entanglement Growth under Random Unitary Dynamics
Nahum, Adam; Ruhman, Jonathan; Vijay, Sagar; Haah, Jeongwan
2017-07-01
Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the "entanglement tsunami" in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar-Parisi-Zhang (KPZ) equation. The mean entanglement grows linearly in time, while fluctuations grow like (time )1/3 and are spatially correlated over a distance ∝(time )2/3. We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i) a stochastic model of a growing surface, (ii) a "minimal cut" picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii) a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the "velocity" of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the well-studied problem of pinning of a membrane or domain wall by disorder.
Quantum Entanglement Growth under Random Unitary Dynamics
Directory of Open Access Journals (Sweden)
Adam Nahum
2017-07-01
Full Text Available Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the “entanglement tsunami” in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar-Parisi-Zhang (KPZ equation. The mean entanglement grows linearly in time, while fluctuations grow like (time^{1/3} and are spatially correlated over a distance ∝(time^{2/3}. We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i a stochastic model of a growing surface, (ii a “minimal cut” picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the “velocity” of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the well-studied problem of pinning of a membrane or domain wall by disorder.
Quantum Groups, Property (T), and Weak Mixing
Brannan, Michael; Kerr, David
2018-06-01
For second countable discrete quantum groups, and more generally second countable locally compact quantum groups with trivial scaling group, we show that property (T) is equivalent to every weakly mixing unitary representation not having almost invariant vectors. This is a generalization of a theorem of Bekka and Valette from the group setting and was previously established in the case of low dual by Daws, Skalski, and Viselter. Our approach uses spectral techniques and is completely different from those of Bekka-Valette and Daws-Skalski-Viselter. By a separate argument we furthermore extend the result to second countable nonunimodular locally compact quantum groups, which are shown in particular not to have property (T), generalizing a theorem of Fima from the discrete setting. We also obtain quantum group versions of characterizations of property (T) of Kerr and Pichot in terms of the Baire category theory of weak mixing representations and of Connes and Weiss in terms of the prevalence of strongly ergodic actions.
A new derivation of the highest-weight polynomial of a unitary lie algebra
International Nuclear Information System (INIS)
P Chau, Huu-Tai; P Van, Isacker
2000-01-01
A new method is presented to derive the expression of the highest-weight polynomial used to build the basis of an irreducible representation (IR) of the unitary algebra U(2J+1). After a brief reminder of Moshinsky's method to arrive at the set of equations defining the highest-weight polynomial of U(2J+1), an alternative derivation of the polynomial from these equations is presented. The method is less general than the one proposed by Moshinsky but has the advantage that the determinantal expression of the highest-weight polynomial is arrived at in a direct way using matrix inversions. (authors)
International Nuclear Information System (INIS)
Malik, R. P.; Srinivas, N.; Bhanja, T.
2016-01-01
We exploit the key concepts of the augmented version of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism to derive the superspace (SUSP) dual unitary operator and its Hermitian conjugate and demonstrate their utility in the derivation of the nilpotent and absolutely anticommuting (anti-)dual-BRST symmetry transformations for a set of interesting models of the Abelian 1-form gauge theories. These models are the one (0+1)-dimensional (1D) rigid rotor and modified versions of the two (1+1)-dimensional (2D) Proca as well as anomalous gauge theories and 2D model of a self-dual bosonic field theory. We show the universality of the SUSP dual unitary operator and its Hermitian conjugate in the cases of all the Abelian models under consideration. These SUSP dual unitary operators, besides maintaining the explicit group structure, provide the alternatives to the dual horizontality condition (DHC) and dual gauge invariant restrictions (DGIRs) of the superfield formalism. The derivations of the dual unitary operators and corresponding (anti-)dual-BRST symmetries are completely novel results in our present investigation.
The real symplectic groups quantum mechanics and optics
International Nuclear Information System (INIS)
Arvind; Mukunda, N.
1995-01-01
We present a utilitarian review of the family of matrix groups Sp(2n,R), in a form suited to various applications both in optics and quantum mechanics. We contrast these groups and their geometry with the much more familiar Euclidean and unitary geometries. Both the properties of finite group elements and of the Lie algebra are studied, and special attention is paid to the so-called unitary metaplectic representation of Sp(2n,R). Global decomposition theorems, interesting subgroups and their generators are described. Turning to n-mode quantum systems, we define and study their variance matrices in general states, the implications of the Heisenberg uncertainty principles, and developed a U(n)-invariant squeezing criterion. The particular properties of Wigner distributions and Gaussian pure state wavefunctions under Sp(2n,R) action are delineated. (author). 22 refs
Operator entanglement of two-qubit joint unitary operations revisited: Schmidt number approach
Energy Technology Data Exchange (ETDEWEB)
Xia, Hui-Zhi; Li, Chao; Yang, Qing; Yang, Ming, E-mail: mingyang@ahu.edu.cn [Key Laboratory of Opto-electronic Information Acquisition and Manipulation, Ministry of Education, School of Physics and Material Science, Anhui University Hefei (China); Cao, Zhuo-Liang [School of Electronic Information Engineering, Hefei Normal University (China)
2012-08-15
The operator entanglement of two-qubit joint unitary operations is revisited. The Schmidt number, an important attribute of a two-qubit unitary operation, may have connection with the entanglement measure of the unitary operator. We find that the entanglement measure of a two-qubit unitary operators is classified by the Schmidt number of the unitary operators. We also discuss the exact relation between the operator entanglement and the parameters of the unitary operator. (author)
On the τ(2)-model in the chiral Potts model and cyclic representation of the quantum group Uq(sl2)
International Nuclear Information System (INIS)
Roan Shishyr
2009-01-01
We identify the precise relationship between the five-parameter τ (2) -family in the N-state chiral Potts model and XXZ chains with U q (sl 2 )-cyclic representation. By studying the Yang-Baxter relation of the six-vertex model, we discover a one-parameter family of L-operators in terms of the quantum group U q (sl 2 ). When N is odd, the N-state τ (2) -model can be regarded as the XXZ chain of U q (sl 2 ) cyclic representations with q N =1. The symmetry algebra of the τ (2) -model is described by the quantum affine algebra U q (sl 2 -hat) via the canonical representation. In general, for an arbitrary N, we show that the XXZ chain with a U q (sl 2 )-cyclic representation for q 2N = 1 is equivalent to two copies of the same N-state τ (2) -model. (fast track communication)
Path integral quantization of the Symplectic Leaves of the SU(2)*Poisson-Lie Group
International Nuclear Information System (INIS)
Morariu, B.
1997-01-01
The Feynman path integral is used to quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of Uq(su(2)). This is achieved by finding explicit Darboux coordinates and then using a phase space path integral. I discuss the *-structure of SU(2)* and give a detailed description of its leaves using various parameterizations and also compare the results with the path integral quantization of spin
Gauging the graded conformal group with unitary internal symmetries
International Nuclear Information System (INIS)
Ferrara, S.; Townsend, P.K.; Kaku, M.; Nieuwenhuizen Van, P.
1977-06-01
Gauge theories for extended SU(N) conformal supergravity are constructed which are invariant under local scale, chiral, proper conformal, supersymmetry and internal SU(N) transformations. The relation between intrinsic parity and symmetry properties of their generators of the internal vector mesons is established. These theories contain no cosmological constants, but technical problems inherent to higher derivative actions are pointed out
Weyl calculus in QED I. The unitary group
Amour, L.; Lascar, R.; Nourrigat, J.
2017-01-01
In this work, we consider fixed 1/2 spin particles interacting with the quantized radiation field in the context of quantum electrodynamics. We investigate the time evolution operator in studying the reduced propagator (interaction picture). We first prove that this propagator belongs to the class of infinite dimensional Weyl pseudodifferential operators recently introduced in Amour et al. [J. Funct. Anal. 269(9), 2747-2812 (2015)] on Wiener spaces. We give a semiclassical expansion of the symbol of the reduced propagator up to any order with estimates on the remainder terms. Next, taking into account analyticity properties for the Weyl symbol of the reduced propagator, we derive estimates concerning transition probabilities between coherent states.
Unitary 4-point correlators from classical geometries
Energy Technology Data Exchange (ETDEWEB)
Bombini, Alessandro; Galliani, Andrea; Giusto, Stefano [Universita di Padova, Dipartimento di Fisica ed Astronomia ' ' Galileo Galilei' ' , Padua (Italy); I.N.F.N. Sezione di Padova, Padua (Italy); Moscato, Emanuele; Russo, Rodolfo [Queen Mary University of London, Centre for Research in String Theory, School of Physics and Astronomy, London (United Kingdom)
2018-01-15
We compute correlators of two heavy and two light operators in the strong coupling and large c limit of the D1D5 CFT which is dual to weakly coupled AdS{sub 3} gravity. The light operators have dimension two and are scalar descendants of the chiral primaries considered in arXiv:1705.09250, while the heavy operators belong to an ensemble of Ramond-Ramond ground states. We derive a general expression for these correlators when the heavy states in the ensemble are close to the maximally spinning ground state. For a particular family of heavy states we also provide a result valid for any value of the spin. In all cases we find that the correlators depend non-trivially on the CFT moduli and are not determined by the symmetries of the theory; however, they have the properties expected for correlators among pure states in a unitary theory, in particular they do not decay at large Lorentzian times. (orig.)
About the unitary discretizations of Heisenberg equations of motion
International Nuclear Information System (INIS)
Vazquez, L.
1986-01-01
In a recent paper Bender et al. (1985) have used a unitary discretization of Heisenberg equations for a one-dimensional quantum system in order to obtain information about the spectrum of the underlying continuum theory. The method consists in comparing the matrix elements between adjacent Fock states of the operators and at two steps. At the same time a very simple variational approach must be made. The purpose of this paper is to show that with unitary schemes, accurate either to order τ or τ 2 , we obtain the same spectrum results in the framework of the above method. On the other hand the same eigenvalues are obtained with a non-unitary scheme (Section II). In Section III we discuss the construction of the Hamiltonian associated to the unitary discretizations. (orig.)
Constructing a unitary title regime for the European Patent System
Rodriguez, V.F.
2011-01-01
The European Patent System without any unitary title allows Member States to retain institutional arrangements within their borders and to prevent any moves to delegate responsibility outside the national sphere. This intergovernmental patent regime suffers from fragmentation due to national
Elegant Coercion and Iran: Beyond the Unitary Actor Model
National Research Council Canada - National Science Library
Moss, J. C
2005-01-01
.... At its core, then, coercion is about state decision-making. Most theories of coercion describe states as if they were unitary actors whose decision-making results from purely rational cost-benefit calculations...
International Nuclear Information System (INIS)
Haapasalo, Erkka Theodor; Pellonpaeae, Juha-Pekka
2011-01-01
We represent quantum observables as normalized positive operator valued measures and consider convex sets of observables which are covariant with respect to a unitary representation of a locally compact Abelian symmetry group G. The value space of such observables is a transitive G-space. We characterize the extreme points of covariant observables and also determine the covariant extreme points of the larger set of all quantum observables. The results are applied to position, position difference, and time observables.
Operator Spreading in Random Unitary Circuits
Nahum, Adam; Vijay, Sagar; Haah, Jeongwan
2018-04-01
Random quantum circuits yield minimally structured models for chaotic quantum dynamics, which are able to capture, for example, universal properties of entanglement growth. We provide exact results and coarse-grained models for the spreading of operators by quantum circuits made of Haar-random unitaries. We study both 1 +1 D and higher dimensions and argue that the coarse-grained pictures carry over to operator spreading in generic many-body systems. In 1 +1 D , we demonstrate that the out-of-time-order correlator (OTOC) satisfies a biased diffusion equation, which gives exact results for the spatial profile of the OTOC and determines the butterfly speed vB. We find that in 1 +1 D , the "front" of the OTOC broadens diffusively, with a width scaling in time as t1 /2. We address fluctuations in the OTOC between different realizations of the random circuit, arguing that they are negligible in comparison to the broadening of the front within a realization. Turning to higher dimensions, we show that the averaged OTOC can be understood exactly via a remarkable correspondence with a purely classical droplet growth problem. This implies that the width of the front of the averaged OTOC scales as t1 /3 in 2 +1 D and as t0.240 in 3 +1 D (exponents of the Kardar-Parisi-Zhang universality class). We support our analytic argument with simulations in 2 +1 D . We point out that, in two or higher spatial dimensions, the shape of the spreading operator at late times is affected by underlying lattice symmetries and, in general, is not spherical. However, when full spatial rotational symmetry is present in 2 +1 D , our mapping implies an exact asymptotic form for the OTOC, in terms of the Tracy-Widom distribution. For an alternative perspective on the OTOC in 1 +1 D , we map it to the partition function of an Ising-like statistical mechanics model. As a result of special structure arising from unitarity, this partition function reduces to a random walk calculation which can be
The dual algebra of the Poincare group on Fock space
International Nuclear Information System (INIS)
Klink, W.H.; Iowa Univ., Iowa City, IA
1989-01-01
The Lie algebra of operators commuting with the Poincare group on the Fock space appropriate for a massive spinless particle is constructed in terms of raising and lowering operators indexed by a Lorentz invariant function. From the assumption that the phase operator is an element of this Lie algebra, it is shown that the scattering operator can be written as a unitary representation operator of the group associated with the Lie algebra. A simple choice of the phase operator shows that the Lorentz invariant function can be interpreted as a basic scattering amplitude, in the sense that all multiparticle scattering amplitudes can be written in terms of this basic scattering amplitude. (orig.)
Toward a self-consistent and unitary reaction network for big bang nucleosynthesis
Energy Technology Data Exchange (ETDEWEB)
Paris, Mark W.; Brown, Lowell S.; Hale, Gerald M.; Hayes-Sterbenz, Anna C.; Jungman, Gerard; Kawano, Toshihiko, E-mail: mparis@lanl.gov [Los Alamos National Laboratory, Los Alamos, New Mexico (United States); Fuller, George M.; Grohs, Evan B. [Department of Physics, University of California, San Diego, La Jolla, CA (United States); Kunieda, Satoshi [Nuclear Data Center, Japan Atomic Energy Agency, Tokai-mura Naka-gun, Ibaraki (Japan)
2014-07-01
Unitarity, the mathematical expression of the conservation of probability in multichannel reactions, is an essential ingredient in the development of accurate nuclear reaction networks appropriate for nucleosynthesis in a variety of environments. We describe our ongoing program to develop a 'unitary reaction network' for the big-bang nucleosynthesis environment and look at an example of the need and power of unitary parametrizations of nuclear scattering and reaction data. Recent attention has been focused on the possible role of the {sup 9}B compound nuclear system in the resonant destruction of {sup 7}Li during primordial nucleosynthesis. We have studied reactions in the {sup 9}B compound system with a multichannel, two-body unitary R-matrix code (EDA) using the known elastic and reaction data, in a four-channel treatment. The data include elastic {sup 6}Li({sup 3}He,{sup 3}He){sup 6}Li differential cross sections from 0.7 to 2.0 MeV, integrated reaction cross sections for energies from 0.7 to 5.0 MeV for {sup 6}Li({sup 3}He,p){sup 8}Be* and from 0.4 to 5.0 MeV for the {sup 6}Li({sup 3}He,γ){sup 7}Be reaction. Capture data have been added to the previous analysis with integrated cross section measurements from 0.7 to 0.825 MeV for {sup 6}Li({sup 3}He,γ){sup 9}B. The resulting resonance parameters are compared with tabulated values from TUNL Nuclear Data Group analyses. Previously unidentified resonances are noted and the relevance of this analysis and a unitary reaction network for big-bang nucleosynthesis are emphasized. (author)
Toward a self-consistent and unitary reaction network for big bang nucleosynthesis
International Nuclear Information System (INIS)
Paris, Mark W.; Brown, Lowell S.; Hale, Gerald M.; Hayes-Sterbenz, Anna C.; Jungman, Gerard; Kawano, Toshihiko; Fuller, George M.; Grohs, Evan B.; Kunieda, Satoshi
2014-01-01
Unitarity, the mathematical expression of the conservation of probability in multichannel reactions, is an essential ingredient in the development of accurate nuclear reaction networks appropriate for nucleosynthesis in a variety of environments. We describe our ongoing program to develop a 'unitary reaction network' for the big-bang nucleosynthesis environment and look at an example of the need and power of unitary parametrizations of nuclear scattering and reaction data. Recent attention has been focused on the possible role of the 9 B compound nuclear system in the resonant destruction of 7 Li during primordial nucleosynthesis. We have studied reactions in the 9 B compound system with a multichannel, two-body unitary R-matrix code (EDA) using the known elastic and reaction data, in a four-channel treatment. The data include elastic 6 Li( 3 He, 3 He) 6 Li differential cross sections from 0.7 to 2.0 MeV, integrated reaction cross sections for energies from 0.7 to 5.0 MeV for 6 Li( 3 He,p) 8 Be* and from 0.4 to 5.0 MeV for the 6 Li( 3 He,γ) 7 Be reaction. Capture data have been added to the previous analysis with integrated cross section measurements from 0.7 to 0.825 MeV for 6 Li( 3 He,γ) 9 B. The resulting resonance parameters are compared with tabulated values from TUNL Nuclear Data Group analyses. Previously unidentified resonances are noted and the relevance of this analysis and a unitary reaction network for big-bang nucleosynthesis are emphasized. (author)
Robust Learning Control Design for Quantum Unitary Transformations.
Wu, Chengzhi; Qi, Bo; Chen, Chunlin; Dong, Daoyi
2017-12-01
Robust control design for quantum unitary transformations has been recognized as a fundamental and challenging task in the development of quantum information processing due to unavoidable decoherence or operational errors in the experimental implementation of quantum operations. In this paper, we extend the systematic methodology of sampling-based learning control (SLC) approach with a gradient flow algorithm for the design of robust quantum unitary transformations. The SLC approach first uses a "training" process to find an optimal control strategy robust against certain ranges of uncertainties. Then a number of randomly selected samples are tested and the performance is evaluated according to their average fidelity. The approach is applied to three typical examples of robust quantum transformation problems including robust quantum transformations in a three-level quantum system, in a superconducting quantum circuit, and in a spin chain system. Numerical results demonstrate the effectiveness of the SLC approach and show its potential applications in various implementation of quantum unitary transformations.
Joule-Thomson Coefficient for Strongly Interacting Unitary Fermi Gas
International Nuclear Information System (INIS)
Liao Kai; Chen Jisheng; Li Chao
2010-01-01
The Joule-Thomson effect reflects the interaction among constituent particles of macroscopic system. For classical ideal gas, the corresponding Joule-Thomson coefficient is vanishing while it is non-zero for ideal quantum gas due to the quantum degeneracy. In recent years, much attention is paid to the unitary Fermi gas with infinite two-body scattering length. According to universal analysis, the thermodynamical law of unitary Fermi gas is similar to that of non-interacting ideal gas, which can be explored by the virial theorem P = 2E/3V. Based on previous works, we further study the unitary Fermi gas properties. The effective chemical potential is introduced to characterize the nonlinear levels crossing effects in a strongly interacting medium. The changing behavior of the rescaled Joule-Thomson coefficient according to temperature manifests a quite different behavior from that for ideal Fermi gas. (general)
Karakowsky, L; Siegel, J P
1999-08-01
Much of the research that has examined the behavioral consequences of membership in mixed-gender work groups suggests that men are more participative and influential in task-related behavior. Drawing from elements of sociological, structural, and psychological perspectives, this study examined the effects of group gender composition and gender orientation of the group's task on patterns of emergent leadership behavior. Participants were assigned to male-dominated, female-dominated, or balanced-gender groups for the purpose of discussing and generating solutions for two business-related cases--each case emphasized either male-oriented or female-oriented expertise. The findings suggest that the proportional representation of men and women in a work group, along with the gender orientation of the group's task, can significantly influence the level of leadership behavior exhibited in group activity.
Consciousness, intentionality, and community: Unitary perspectives and research.
Zahourek, Rothlyn P; Larkin, Dorothy M
2009-01-01
Consciousness and intentionality often have been related and studied together. These concepts also are readily viewed and understood for practice, research, and education in a unitary paradigm. How these ideas relate to community is less known. Considering the expansion of our capacity for communication through the World Wide Web and other technologic advances and appreciating recent research on the nonlocal character of intentionality and consciousness, it is more apparent how concepts of community can be seen in the same unitary context. The authors address these issues and review relevant nursing research.
Non-unitary probabilistic quantum computing circuit and method
Williams, Colin P. (Inventor); Gingrich, Robert M. (Inventor)
2009-01-01
A quantum circuit performing quantum computation in a quantum computer. A chosen transformation of an initial n-qubit state is probabilistically obtained. The circuit comprises a unitary quantum operator obtained from a non-unitary quantum operator, operating on an n-qubit state and an ancilla state. When operation on the ancilla state provides a success condition, computation is stopped. When operation on the ancilla state provides a failure condition, computation is performed again on the ancilla state and the n-qubit state obtained in the previous computation, until a success condition is obtained.
Cogeneration Power Plants: a Proposed Methodology for Unitary Production Cost
International Nuclear Information System (INIS)
Metalli, E.
2009-01-01
A new methodology to evaluate unitary energetic production costs in the cogeneration power plants is proposed. This methodology exploits the energy conversion factors fixed by Italian Regulatory Authority for Electricity and Gas. So it allows to settle such unitary costs univocally for a given plant, without assigning them a priori subjective values when there are two or more energy productions at the same time. Moreover the proposed methodology always ensures positive values for these costs, complying with the total generation cost balance equation. [it
K-theory for group C*-algebras and semigroup C*-algebras
Cuntz, Joachim; Li, Xin; Yu, Guoliang
2017-01-01
This book gives an account of the necessary background for group algebras and crossed products for actions of a group or a semigroup on a space and reports on some very recently developed techniques with applications to particular examples. Much of the material is available here for the first time in book form. The topics discussed are among the most classical and intensely studied C*-algebras. They are important for applications in fields as diverse as the theory of unitary group representations, index theory, the topology of manifolds or ergodic theory of group actions.
Directory of Open Access Journals (Sweden)
Akihito Soeda
2010-06-01
Full Text Available We study how two pieces of localized quantum information can be delocalized across a composite Hilbert space when a global unitary operation is applied. We classify the delocalization power of global unitary operations on quantum information by investigating the possibility of relocalizing one piece of the quantum information without using any global quantum resource. We show that one-piece relocalization is possible if and only if the global unitary operation is local unitary equivalent of a controlled-unitary operation. The delocalization power turns out to reveal different aspect of the non-local properties of global unitary operations characterized by their entangling power.
Generalizations of the BMS group and results
International Nuclear Information System (INIS)
Melas, E
2006-01-01
The ordinary Bondi-Metzner-Sachs (BMS) group B is the common asymptotic symmetry group of all radiating, asymptotically flat, Lorentzian space-times. As such, B is the best candidate for the universal symmetry group of General Relativity. However, in studying quantum gravity, space-times with signatures other than the usual Lorentzian one, and complex space-times, are frequently considered. Generalisations of B appropriate to these other signatures have been defined earlier. In particular, the generalization B(2, 2) appropriate to the ultrahyperbolic signature (+, +, -, -) has been described in detail, and the study of its irreducible unitary representations (IRs) has been initiated. The infinite little groups of B(2, 2) have been given explicitly but its finite little groups have only been partially described. All the information needed in order to construct the finite little groups is given. Possible connections with gravitational instantons are being put forward
Unitary evolution and uniqueness of the Fock quantization in flat cosmologies
International Nuclear Information System (INIS)
Marugán, G A Mena; Błas, D Martín-de; Gomar, L Castelló
2013-01-01
We study the Fock quantization of scalar fields with a time dependent mass in cosmological scenarios with flat compact spatial sections. This framework describes physically interesting situations like, e.g., cosmological perturbations in flat Friedmann-Robertson-Walker spacetimes, generally including a suitable scaling of them by a background function. We prove that the requirements of vacuum invariance under the spatial isometries and of a unitary quantum dynamics select (a) a unique canonical pair of field variables among all those related by time dependent canonical transformations which scale the field configurations, and (b) a unique Fock representation for the canonical commutation relations of this pair of variables. The proof is generalizable to any compact spatial topology in three or less dimensions, though we focus on the case of the three-torus owing to the especially relevant implications.
Energy Technology Data Exchange (ETDEWEB)
Fernandes, Julio C.L.; Vilhena, Marco T.; Bodmann, Bardo E.J., E-mail: julio.lombaldo@ufrgs.br, E-mail: mtmbvilhena@gmail.com, E-mail: bardo.bodmann@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Matematica Pura e Aplicada; Dulla, Sandra; Ravetto, Piero, E-mail: sandra.dulla@polito.it, E-mail: piero.ravetto@polito.it [Dipartimento di Energia, Politecnico di Torino, Piemonte (Italy)
2015-07-01
In this work we generalize the solution of the one-dimensional neutron transport equation to a multi- group approach in planar geometry. The basic idea of this work consists in consider the hierarchical construction of a solution for a generic number G of energy groups, starting from a mono-energetic solution. The hierarchical method follows the reasoning of the decomposition method. More specifically, the additional terms from adding energy groups is incorporated into the recursive scheme as source terms. This procedure leads to an analytical representation for the solution with G energy groups. The recursion depth is related to the accuracy of the solution, that may be evaluated after each recursion step. The authors present a heuristic analysis of stability for the results. Numerical simulations for a specific example with four energy groups and a localized pulsed source. (author)
A remark on the unitary part of contractions
International Nuclear Information System (INIS)
Duggal, B.P.
1992-07-01
Considering operators on a complex infinite dimensional Hilbert space H and denoting by T * a construction with C .O completely non-unitary part, it is proved that A T is projection which commutes with T and H (u) T = A T H. 3 refs
Establishing the Unitary Classroom: Organizational Change and School Culture.
Eddy, Elizabeth M.; True, Joan H.
1980-01-01
This paper examines the organizational changes introduced in two elementary schools to create unitary (desegregated) classrooms. The different models adopted by the two schools--departmentalization and team teaching--are considered as expressions of their patterns of interaction, behavior, and values. (Part of a theme issue on educational…
Microscopic description and excitation of unitary analog states
Energy Technology Data Exchange (ETDEWEB)
Kisslinger, L S [Carnegie-Mellon Univ., Pittsburgh, Pa. (USA); Van Giai, N [Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire
1977-12-05
A microscopic investigation in a self-consistent particle-hole model reveals approximate unitary analog states in spite of large symmetry breaking. The K-nucleus elastic scattering and (K/sup -/, ..pi../sup -/) excitation of these states are studied, showing strong surface effects.
Energy Technology Data Exchange (ETDEWEB)
Roche, Ph., E-mail: philippe.roche@univ-montp2.fr [Université Montpellier 2, CNRS, L2C, IMAG, Montpellier (France)
2016-03-15
We recall the relation between zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of zeta function representations of groups. We compute some of these functions in the case of the finite group GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q}). We recall the table characters of these groups for any q, compute the Frobenius-Schur indicator of their irreducible representations, and give the explicit structure of their fusion rings.
Directory of Open Access Journals (Sweden)
Nikos Irges
2017-11-01
Full Text Available We perform an old school, one-loop renormalization of the Abelian–Higgs model in the Unitary and Rξ gauges, focused on the scalar potential and the gauge boson mass. Our goal is to demonstrate in this simple context the validity of the Unitary gauge at the quantum level, which could open the way for an until now (mostly avoided framework for loop computations. We indeed find that the Unitary gauge is consistent and equivalent to the Rξ gauge at the level of β-functions. Then we compare the renormalized, finite, one-loop Higgs potential in the two gauges and we again find equivalence. This equivalence needs not only a complete cancellation of the gauge fixing parameter ξ from the Rξ gauge potential but also requires its ξ-independent part to be equal to the Unitary gauge result. We follow the quantum behavior of the system by plotting Renormalization Group trajectories and Lines of Constant Physics, with the former the well known curves and with the latter, determined by the finite parts of the counter-terms, particularly well suited for a comparison with non-perturbative studies.
Three particle Poincare states and SU(6) x SU(3) as a classification group for baryons
International Nuclear Information System (INIS)
Buccella, F.; Sciarrino, A.; Sorba, P.
1975-05-01
A complete set of democratic quantum numbers is introduced to classify the states of an irreducible unitary representation (IUR) of the Poincare group obtained from the decomposition of the direct products of three I.U.R. Such states are identified with the baryon states constituted of three free relativistic quarks. The transformation from current to constituent quarks is then easily reobtained. Moreover, the group SU(6) x SU(3) appears naturally as a collinear classification group for baryons. Results similar to those of the symmetric harmonic oscillator quark model are obtained [fr
Dang, Cai-Ping; Braeken, Johan; Ferrer, Emilio; Liu, Chang
2012-01-01
This study explored the controversy surrounding working memory: whether it is a unitary system providing general purpose resources or a more differentiated system with domain-specific sub-components. A total of 348 participants completed a set of 6 working memory tasks that systematically varied in storage target contents and type of information…
A mapping from the unitary to doubly stochastic matrices and symbols on a finite set
Karabegov, Alexander V.
2008-11-01
We prove that the mapping from the unitary to doubly stochastic matrices that maps a unitary matrix (ukl) to the doubly stochastic matrix (|ukl|2) is a submersion at a generic unitary matrix. The proof uses the framework of operator symbols on a finite set.
Lee, Jong-Eun Roselyn; Nass, Clifford I; Bailenson, Jeremy N
2014-04-01
Virtual environments employing avatars for self-representation-including the opportunity to represent or misrepresent social categories-raise interesting and intriguing questions as to how one's avatar-based social category shapes social identity dynamics, particularly when stereotypes prevalent in the offline world apply to the social categories visually represented by avatars. The present experiment investigated how social category representation via avatars (i.e., graphical representations of people in computer-mediated environments) affects stereotype-relevant task performance. In particular, building on and extending the Proteus effect model, we explored whether and how stereotype lift (i.e., a performance boost caused by the awareness of a domain-specific negative stereotype associated with outgroup members) occurred in virtual group settings in which avatar-based gender representation was arbitrary. Female and male participants (N=120) were randomly assigned either a female avatar or a male avatar through a process masked as a random drawing. They were then placed in a numerical minority status with respect to virtual gender-as the only virtual female (male) in a computer-mediated triad with two opposite-gendered avatars-and performed a mental arithmetic task either competitively or cooperatively. The data revealed that participants who were arbitrarily represented by a male avatar and competed against two ostensible female avatars showed strongest performance compared to others on the arithmetic task. This pattern occurred regardless of participants' actual gender, pointing to a virtual stereotype lift effect. Additional mediation tests showed that task motivation partially mediated the effect. Theoretical and practical implications for social identity dynamics in avatar-based virtual environments are discussed.
Quantum groups, roots of unity and particles on quantized Anti-de Sitter space
International Nuclear Information System (INIS)
Steinacker, H.
1997-01-01
Quantum groups in general and the quantum Anti-de Sitter group U q (so(2,3)) in particular are studied from the point of view of quantum field theory. The author shows that if q is a suitable root of unity, there exist finite-dimensional, unitary representations corresponding to essentially all the classical one-particle representations with (half) integer spin, with the same structure at low energies as in the classical case. In the massless case for spin ≥ 1, open-quotes naiveclose quotes representations are unitarizable only after factoring out a subspace of open-quotes pure gaugesclose quotes, as classically. Unitary many-particle representations are defined, with the correct classical limit. Furthermore, the author identifies a remarkable element Q in the center of U q (g), which plays the role of a BRST operator in the case of U q (so(2,3)) at roots of unity, for any spin ≥ 1. The associated ghosts are an intrinsic part of the indecomposable representations. The author shows how to define an involution on algebras of creation and anihilation operators at roots of unity, in an example corresponding to non-identical particles. It is shown how nonabelian gauge fields appear naturally in this framework, without having to define connections on fiber bundles. Integration on Quantum Euclidean space and sphere and on Anti-de Sitter space is studied as well. The author gives a conjecture how Q can be used in general to analyze the structure of indecomposable representations, and to define a new, completely reducible associative (tensor) product of representations at roots of unity, which generalizes the standard open-quotes truncatedclose quotes tensor product as well as many-particle representations
Quantum groups, roots of unity and particles on quantized Anti-de Sitter space
Energy Technology Data Exchange (ETDEWEB)
Steinacker, Harold [Univ. of California, Berkeley, CA (United States). Dept. of Physics
1997-05-23
Quantum groups in general and the quantum Anti-de Sitter group U_{q}(so(2,3)) in particular are studied from the point of view of quantum field theory. The author shows that if q is a suitable root of unity, there exist finite-dimensional, unitary representations corresponding to essentially all the classical one-particle representations with (half) integer spin, with the same structure at low energies as in the classical case. In the massless case for spin ≥ 1, "naive" representations are unitarizable only after factoring out a subspace of "pure gauges", as classically. Unitary many-particle representations are defined, with the correct classical limit. Furthermore, the author identifies a remarkable element Q in the center of U_{q}(g), which plays the role of a BRST operator in the case of U_{q}(so(2,3)) at roots of unity, for any spin ≥ 1. The associated ghosts are an intrinsic part of the indecomposable representations. The author shows how to define an involution on algebras of creation and anihilation operators at roots of unity, in an example corresponding to non-identical particles. It is shown how nonabelian gauge fields appear naturally in this framework, without having to define connections on fiber bundles. Integration on Quantum Euclidean space and sphere and on Anti-de Sitter space is studied as well. The author gives a conjecture how Q can be used in general to analyze the structure of indecomposable representations, and to define a new, completely reducible associative (tensor) product of representations at roots of unity, which generalizes the standard "truncated" tensor product as well as many-particle representations.
Massless representations and admissibility condition for higher spin superalgebras
Energy Technology Data Exchange (ETDEWEB)
Konstein, S E; Vasiliev, M A
1989-01-16
Massless particle representations of various infinite-dimensional higher spin superalgebras proposed previously are constructed. We analyse which of higher spin superalgebras obey the requirement (the admissibility condition) of possessing massless unitary representations with the same spectra of spins as predicted by the structure of gauge fields originating from these superalgebras. It is argued that those higher spin superalgebras, which obey the admissibility condition, can serve as rigid supersymmetries in nontrivial consistent gauge theories of massless fields of all spins.
The BMS group and generalized gravitational instantons
International Nuclear Information System (INIS)
Melas, Evangelos
2004-01-01
The ordinary Bondi-Metzner-Sachs (BMS) group B is the best candidate for the fundamental symmetry group of General Relativity. It has been shown that B admits generalizations to real space-times of any signature, and also to complex space-times. It has been suggested that certain continuous unitary irreducible representations (IRs) of B and of its generalizations correspond to gravitational instantons. Here I make this correspondence more precise and I take this suggestion one step further by arguing that a subclass of IRs of B and of its generalizations correspond to generalized gravitational instantons. Some of these generalized gravitational instantons involve in their definition certain subgroups of the Cartesian product group C n xC m , where C r is the cyclic group of order r. With this motivation, I give the subgroups of C n xC m explicitly
Random unitary evolution model of quantum Darwinism with pure decoherence
Balanesković, Nenad
2015-10-01
We study the behavior of Quantum Darwinism [W.H. Zurek, Nat. Phys. 5, 181 (2009)] within the iterative, random unitary operations qubit-model of pure decoherence [J. Novotný, G. Alber, I. Jex, New J. Phys. 13, 053052 (2011)]. We conclude that Quantum Darwinism, which describes the quantum mechanical evolution of an open system S from the point of view of its environment E, is not a generic phenomenon, but depends on the specific form of input states and on the type of S-E-interactions. Furthermore, we show that within the random unitary model the concept of Quantum Darwinism enables one to explicitly construct and specify artificial input states of environment E that allow to store information about an open system S of interest with maximal efficiency.
Prenominal and postnominal reduced relative clauses: arguments against unitary analyses
Directory of Open Access Journals (Sweden)
Petra Sleeman
2007-01-01
Full Text Available These last years, several analyses have been proposed in which prenominal and postnominal reduced relatives are merged in the same position. Kayne (1994 claims that both types of reduced relative clauses are the complement of the determiner. More recently, Cinque (2005 has proposed that both types are merged in the functional projections of the noun, at the left edge of the modifier system. In this paper, I argue against a unitary analysis of prenominal and postnominal participial reduced relatives.
Unitary Application of the Quantum Error Correction Codes
International Nuclear Information System (INIS)
You Bo; Xu Ke; Wu Xiaohua
2012-01-01
For applying the perfect code to transmit quantum information over a noise channel, the standard protocol contains four steps: the encoding, the noise channel, the error-correction operation, and the decoding. In present work, we show that this protocol can be simplified. The error-correction operation is not necessary if the decoding is realized by the so-called complete unitary transformation. We also offer a quantum circuit, which can correct the arbitrary single-qubit errors.
Unitary-matrix models as exactly solvable string theories
Periwal, Vipul; Shevitz, Danny
1990-01-01
Exact differential equations are presently found for the scaling functions of models of unitary matrices which are solved in a double-scaling limit, using orthogonal polynomials on a circle. For the case of the simplest, k = 1 model, the Painleve II equation with constant 0 is obtained; possible nonperturbative phase transitions exist for these models. Equations are presented for k = 2 and 3, and discussed with a view to asymptotic behavior.
Complex projection of unitary dynamics of quaternionic pure states
International Nuclear Information System (INIS)
Asorey, M.; Scolarici, G.; Solombrino, L.
2007-01-01
Quaternionic quantum mechanics has been revealed to be a very useful framework to describe quantum phenomena. In the case of two qubit compound systems we show that the complex projection of quaternionic pure states and quaternionic unitary maps permits the description of interesting phenomena such as decoherence and optimal entanglement generation. The approach, however, presents severe limitations for the case of multipartite or higher dimensional bipartite quantum systems as we point out
Information-disturbance tradeoff in estimating a unitary transformation
International Nuclear Information System (INIS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Chiribella, Giulio
2010-01-01
We address the problem of the information-disturbance tradeoff associated to the estimation of a quantum transformation and show how the extraction of information about a black box causes a perturbation of the corresponding input-output evolution. In the case of a black box performing a unitary transformation, randomly distributed according to the invariant measure, we give a complete solution of the problem, deriving the optimal tradeoff curve and presenting an explicit construction of the optimal quantum network.
Efficient learning algorithm for quantum perceptron unitary weights
Seow, Kok-Leong; Behrman, Elizabeth; Steck, James
2015-01-01
For the past two decades, researchers have attempted to create a Quantum Neural Network (QNN) by combining the merits of quantum computing and neural computing. In order to exploit the advantages of the two prolific fields, the QNN must meet the non-trivial task of integrating the unitary dynamics of quantum computing and the dissipative dynamics of neural computing. At the core of quantum computing and neural computing lies the qubit and perceptron, respectively. We see that past implementat...
Entanglement entropy of non-unitary integrable quantum field theory
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Davide Bianchini
2015-07-01
Full Text Available In this paper we study the simplest massive 1+1 dimensional integrable quantum field theory which can be described as a perturbation of a non-unitary minimal conformal field theory: the Lee–Yang model. We are particularly interested in the features of the bi-partite entanglement entropy for this model and on building blocks thereof, namely twist field form factors. Non-unitarity selects out a new type of twist field as the operator whose two-point function (appropriately normalized yields the entanglement entropy. We compute this two-point function both from a form factor expansion and by means of perturbed conformal field theory. We find good agreement with CFT predictions put forward in a recent work involving the present authors. In particular, our results are consistent with a scaling of the entanglement entropy given by ceff3logℓ where ceff is the effective central charge of the theory (a positive number related to the central charge and ℓ is the size of the region. Furthermore the form factor expansion of twist fields allows us to explore the large region limit of the entanglement entropy and find the next-to-leading order correction to saturation. We find that this correction is very different from its counterpart in unitary models. Whereas in the latter case, it had a form depending only on few parameters of the model (the particle spectrum, it appears to be much more model-dependent for non-unitary models.
Higher dimensional unitary braid matrices: Construction, associated structures and entanglements
International Nuclear Information System (INIS)
Abdesselam, B.; Chakrabarti, A.; Dobrev, V.K.; Mihov, S.G.
2007-03-01
We construct (2n) 2 x (2n) 2 unitary braid matrices R-circumflex for n ≥ 2 generalizing the class known for n = 1. A set of (2n) x (2n) matrices (I, J,K,L) are defined. R-circumflex is expressed in terms of their tensor products (such as K x J), leading to a canonical formulation for all n. Complex projectors P ± provide a basis for our real, unitary R-circumflex. Baxterization is obtained. Diagonalizations and block- diagonalizations are presented. The loss of braid property when R-circumflex (n > 1) is block-diagonalized in terms of R-circumflex (n = 1) is pointed out and explained. For odd dimension (2n + 1) 2 x (2n + 1) 2 , a previously constructed braid matrix is complexified to obtain unitarity. R-circumflexLL- and R-circumflexTT- algebras, chain Hamiltonians, potentials for factorizable S-matrices, complex non-commutative spaces are all studied briefly in the context of our unitary braid matrices. Turaev construction of link invariants is formulated for our case. We conclude with comments concerning entanglements. (author)
IJzendoorn, van M.H.; Bakermans-Kranenburg, M.J.
1996-01-01
This meta-analysis on 33 studies, including more than 2,000 Adult Attachment Interview (AAI) classifications, presents distributions of AAI classifications in samples of nonclinical fathers and mothers, in adolescents, in samples from different cultures, and in clinical groups. Fathers, adolescents,
Sakuraba, Takao
The approach to quantum physics via current algebra and unitary representations of the diffeomorphism group is established. This thesis studies possible infinite Bose gas systems using this approach. Systems of locally finite configurations and systems of configurations with accumulation points are considered, with the main emphasis on the latter. In Chapter 2, canonical quantization, quantization via current algebra and unitary representations of the diffeomorphism group are reviewed. In Chapter 3, a new definition of the space of configurations is proposed and an axiom for general configuration spaces is abstracted. Various subsets of the configuration space, including those specifying the number of points in a Borel set and those specifying the number of accumulation points in a Borel set are proved to be measurable using this axiom. In Chapter 4, known results on the space of locally finite configurations and Poisson measure are reviewed in the light of the approach developed in Chapter 3, including the approach to current algebra in the Poisson space by Albeverio, Kondratiev, and Rockner. Goldin and Moschella considered unitary representations of the group of diffeomorphisms of the line based on self-similar random processes, which may describe infinite quantum gas systems with clusters. In Chapter 5, the Goldin-Moschella theory is developed further. Their construction of measures quasi-invariant under diffeomorphisms is reviewed, and a rigorous proof of their conjectures is given. It is proved that their measures with distinct correlation parameters are mutually singular. A quasi-invariant measure constructed by Ismagilov on the space of configurations with accumulation points on the circle is proved to be singular with respect to the Goldin-Moschella measures. Finally a generalization of the Goldin-Moschella measures to the higher-dimensional case is studied, where the notion of covariance matrix and the notion of condition number play important roles. A
International Nuclear Information System (INIS)
Berkovich, Alexander
1994-01-01
The Hilbert space of an RSOS model, introduced by Andrews, Baxter, and Forrester, can be viewed as a space of sequences (paths) {a 0 ,a 1 ,.s, a L }, with a j -integers restricted by 1≤qslanta j ≤qslantν,vertical stroke a j -a j+1 vertical stroke =1,a 0 ≡s, a L ≡r. In this paper we introduce different basis which, as shown here, has the same dimension as that of an RSOS model. This basis appears naturally in the Bethe ansatz calculations of the spin (ν-1)/2 XXZ model. Following McCoy et al., we call this basis fermionic (FB).Our first theorem Dim(FB)=Dim(RSOS-basis) can be succinctly expressed in terms of some identities for binomial coefficients. Remarkably, these binomial identities can be q-deformed. Here, we give a simple proof of these q-binomial identities in the spirit of Schur's proof of the Rogers-Ramanujan identities. Notably, the proof involves only the elementary recurrences for the q-binomial coefficients and a few creative observations.Finally, taking the limit L→∞ in these q-identities, we derive an expression for the character formulas of the unitary minimal series M(ν,ν+1) ''Bosonic Sum ≡ Fermionic Sum''. Here, Bosonic Sum denotes Rocha-Caridi representation (χ r,s=1 ν,ν+1 (q)) and Fermionic Sum stands for the companion representation recently conjectured by the McCoy group. ((orig.))
A unitary ESPRIT scheme of joint angle estimation for MOTS MIMO radar.
Wen, Chao; Shi, Guangming
2014-08-07
The transmit array of multi-overlapped-transmit-subarray configured bistatic multiple-input multiple-output (MOTS MIMO) radar is partitioned into a number of overlapped subarrays, which is different from the traditional bistatic MIMO radar. In this paper, a new unitary ESPRIT scheme for joint estimation of the direction of departure (DOD) and the direction of arrival (DOA) for MOTS MIMO radar is proposed. In our method, each overlapped-transmit-subarray (OTS) with the identical effective aperture is regarded as a transmit element and the characteristics that the phase delays between the two OTSs is utilized. First, the measurements corresponding to all the OTSs are partitioned into two groups which have a rotational invariance relationship with each other. Then, the properties of centro-Hermitian matrices and real-valued rotational invariance factors are exploited to double the measurement samples and reduce computational complexity. Finally, the close-formed solution of automatically paired DOAs and DODs of targets is derived in a new manner. The proposed scheme provides increased estimation accuracy with the combination of inherent advantages of MOTS MIMO radar with unitary ESPRIT. Simulation results are presented to demonstrate the effectiveness and advantage of the proposed scheme.
Quantization and harmonic analysis on nilpotent Lie groups
International Nuclear Information System (INIS)
Wildberger, N.J.
1983-01-01
Weyl Quantization is a procedure for associating a function on which the canonical commutation relations are realized. If G is a simply-connected, connected nilpotent Lie group with Lie algebra g and dual g/sup */, it is shown how to inductively construct symplectic isomorphisms between every co-adjoint orbit O and the bundle in Hilbert Space for some m. Weyl Quantization can then be used to associate to each orbit O a unitary representation rho 0 of G, recovering the classification of the unitary dual by Kirillov. It is used to define a geometric Fourier transform, F : L 1 (G) → functions on g/sup */, and it is shown that the usual operator-valued Fourier transform can be recovered from F, characters are inverse Fourier transforms of invariant measures on orbits, and matrix coefficients are inverse Fourier transforms of non-invariant measures supported on orbits. Realizations of the representations rho 0 in subspaces of L 2 (O) are obtained.. Finally, the kernel function is computed for the upper triangular unipotent group and one other example
International Nuclear Information System (INIS)
Yao, Yao
2015-01-01
The deep sub-Ohmic spin–boson model shows a longstanding non-Markovian coherence at low temperature. Motivating to quench this robust coherence, the thermal effect is unitarily incorporated into the time evolution of the model, which is calculated by the adaptive time-dependent density matrix renormalization group algorithm combined with the orthogonal polynomials theory. Via introducing a unitary heating operator to the bosonic bath, the bath is heated up so that a majority portion of the bosonic excited states is occupied. It is found in this situation the coherence of the spin is quickly quenched even in the coherent regime, in which the non-Markovian feature dominates. With this finding we come up with a novel way to implement the unitary equilibration, the essential term of the eigenstate-thermalization hypothesis, through a short-time evolution of the model
8x8 and 10x10 Hyperspace Representations of SU(3) and 10-fold Point-Symmetry Group of Quasicrystals
Animalu, Alexander
2012-02-01
In order to further elucidate the unexpected 10-fold point-symmetry group structure of quasi-crystals for which the 2011 Nobel Prize in chemistry was awarded to Daniel Shechtman, we explore a correspondence principle between the number of (projective) geometric elements (points[vertices] + lines[edges] + planes[faces]) of primitive cells of periodic or quasi-periodic arrangement of hard or deformable spheres in 3-dimensional space of crystallography and elements of quantum field theory of particle physics [points ( particles, lines ( particles, planes ( currents] and hence construct 8x8 =64 = 28+36 = 26 + 38, and 10x10 =100= 64 + 36 = 74 + 26 hyperspace representations of the SU(3) symmetry of elementary particle physics and quasicrystals of condensed matter (solid state) physics respectively, As a result, we predict the Cabibbo-like angles in leptonic decay of hadrons in elementary-particle physics and the observed 10-fold symmetric diffraction pattern of quasi-crystals.
Directory of Open Access Journals (Sweden)
J. Buitrago
Full Text Available A new classical 2-spinor approach to U(1 gauge theory is presented in which the usual four-potential vector field is replaced by a symmetric second rank spinor. Following a lagrangian formulation, it is shown that the four-rank spinor representing the Maxwell field tensor has a U(1 local gauge invariance in terms of the electric and magnetic field strengths. When applied to the magnetic field of a monopole, this formulation, via the irreducible representation condition for the gauge group, leads to a quantization condition differing by a factor 2 of the one predicted by Dirac without relying on any kind of singular vector potentials. Finally, the U(1 invariant spinor equations, are applied to electron magnetic resonance which has many applications in the study of materials. Keywords: Weyl 2-spinor lenguage, Dirac equation, Gauge theories, Charge quantization
Energy Technology Data Exchange (ETDEWEB)
Fadin, V.S. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Budker Nuclear Physics Institute, Novosibirsk (Russian Federation); Novosibirskij Gosudarstvennyj Univ., Novosibirsk (Russian Federation); Lipatov, L.N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Petersburg Nuclear Physics Institute, Gatchina (Russian Federation); St. Petersburg State Univ., Gatchina (Russian Federation)
2011-12-15
We calculate the eigenvalues of the next-to-leading kernel for the BFKL equation in the adjoint representation of the gauge group SU(N{sub c}) in the N=4 supersymmetric Yang-Mills model. These eigenvalues are used to obtain the high energy behavior of the remainder function for the 6-point scattering amplitude with the maximal helicity violation in the kinematical regions containing the Mandelstam cut contribution. The leading and next-to-leading singularities of the corresponding collinear anomalous dimension are calculated in all orders of perturbation theory. We compare our result with the known collinear limit and with the recently suggested ansatz for the remainder function in three loops and obtain the full agreement providing that the numerical parameters in this anzatz are chosen in an appropriate way.
Lindemann, Elizabeth A; Chen, Elizabeth S; Wang, Yan; Skube, Steven J; Melton, Genevieve B
2017-01-01
As individuals age, there is potential for dramatic changes in the social and behavioral determinants that affect health status and outcomes. The importance of these determinants has been increasingly recognized in clinical decision-making. We sought to characterize how social and behavioral health determinants vary in different demographic groups using a previously established schema of 28 social history types through both manual analysis and automated topic analysis of social documentation in the electronic health record across the population of an entire integrated healthcare system. Our manual analysis generated 8,335 annotations over 1,400 documents, representing 24 (86%) social history types. In contrast, automated topic analysis generated 22 (79%) social history types. A comparative evaluation demonstrated both similarities and differences in coverage between the manual and topic analyses. Our findings validate the widespread nature of social and behavioral determinants that affect health status over populations of individuals over their lifespan.
Homogeneous operators and projective representations of the ...
Indian Academy of Sciences (India)
Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45
group of all unitary operators in B(H) will be denoted by U(H). .... with the characteristic function of the compression of multiplication by z to the subspace ...... [32] Varadarajan V S, Geometry of quantum theory (New York: Springer Verlag) 1985.
Multiscale differential phase contrast analysis with a unitary detector
Lopatin, Sergei; Ivanov, Yurii P.; Kosel, Jü rgen; Chuvilin, Andrey
2015-01-01
A new approach to generate differential phase contrast (DPC) images for the visualization and quantification of local magnetic fields in a wide range of modern nano materials is reported. In contrast to conventional DPC methods our technique utilizes the idea of a unitary detector under bright field conditions, making it immediately usable by a majority of modern transmission electron microscopes. The approach is put on test to characterize the local magnetization of cylindrical nanowires and their 3D ordered arrays, revealing high sensitivity of our method in a combination with nanometer-scale spatial resolution.
Configurable unitary transformations and linear logic gates using quantum memories.
Campbell, G T; Pinel, O; Hosseini, M; Ralph, T C; Buchler, B C; Lam, P K
2014-08-08
We show that a set of optical memories can act as a configurable linear optical network operating on frequency-multiplexed optical states. Our protocol is applicable to any quantum memories that employ off-resonant Raman transitions to store optical information in atomic spins. In addition to the configurability, the protocol also offers favorable scaling with an increasing number of modes where N memories can be configured to implement arbitrary N-mode unitary operations during storage and readout. We demonstrate the versatility of this protocol by showing an example where cascaded memories are used to implement a conditional cz gate.
Implementing controlled-unitary operations over the butterfly network
Energy Technology Data Exchange (ETDEWEB)
Soeda, Akihito; Kinjo, Yoshiyuki; Turner, Peter S. [Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo (Japan); Murao, Mio [Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo, Japan and NanoQuine, The University of Tokyo, Tokyo (Japan)
2014-12-04
We introduce a multiparty quantum computation task over a network in a situation where the capacities of both the quantum and classical communication channels of the network are limited and a bottleneck occurs. Using a resource setting introduced by Hayashi [1], we present an efficient protocol for performing controlled-unitary operations between two input nodes and two output nodes over the butterfly network, one of the most fundamental networks exhibiting the bottleneck problem. This result opens the possibility of developing a theory of quantum network coding for multiparty quantum computation, whereas the conventional network coding only treats multiparty quantum communication.
A model of diffraction scattering with unitary corrections
International Nuclear Information System (INIS)
Etim, E.; Malecki, A.; Satta, L.
1989-01-01
The inability of the multiple scattering model of Glauber and similar geometrical picture models to fit data at Collider energies, to fit low energy data at large momentum transfers and to explain the absence of multiple diffraction dips in the data is noted. It is argued and shown that a unitary correction to the multiple scattering amplitude gives rise to a better model and allows to fit all available data on nucleon-nucleon and nucleus-nucleus collisions at all energies and all momentum transfers. There are no multiple diffraction dips
Non-unitary neutrino propagation from neutrino decay
Energy Technology Data Exchange (ETDEWEB)
Berryman, Jeffrey M., E-mail: jeffreyberryman2012@u.northwestern.edu [Northwestern University, Department of Physics & Astronomy, 2145 Sheridan Road, Evanston, IL 60208 (United States); Gouvêa, André de; Hernández, Daniel [Northwestern University, Department of Physics & Astronomy, 2145 Sheridan Road, Evanston, IL 60208 (United States); Oliveira, Roberto L.N. [Northwestern University, Department of Physics & Astronomy, 2145 Sheridan Road, Evanston, IL 60208 (United States); Instituto de Física Gleb Wataghin Universidade Estadual de Campinas, UNICAMP 13083-970, Campinas, São Paulo (Brazil)
2015-03-06
Neutrino propagation in space-time is not constrained to be unitary if very light states – lighter than the active neutrinos – exist into which neutrinos may decay. If this is the case, neutrino flavor-change is governed by a handful of extra mixing and “oscillation” parameters, including new sources of CP-invariance violation. We compute the transition probabilities in the two- and three-flavor scenarios and discuss the different phenomenological consequences of the new physics. These are qualitatively different from other sources of unitarity violation discussed in the literature.
Non-unitary neutrino propagation from neutrino decay
International Nuclear Information System (INIS)
Berryman, Jeffrey M.; Gouvêa, André de; Hernández, Daniel; Oliveira, Roberto L.N.
2015-01-01
Neutrino propagation in space-time is not constrained to be unitary if very light states – lighter than the active neutrinos – exist into which neutrinos may decay. If this is the case, neutrino flavor-change is governed by a handful of extra mixing and “oscillation” parameters, including new sources of CP-invariance violation. We compute the transition probabilities in the two- and three-flavor scenarios and discuss the different phenomenological consequences of the new physics. These are qualitatively different from other sources of unitarity violation discussed in the literature
Experiments with Highly-Ionized Atoms in Unitary Penning Traps
Directory of Open Access Journals (Sweden)
Shannon Fogwell Hoogerheide
2015-08-01
Full Text Available Highly-ionized atoms with special properties have been proposed for interesting applications, including potential candidates for a new generation of optical atomic clocks at the one part in 1019 level of precision, quantum information processing and tests of fundamental theory. The proposed atomic systems are largely unexplored. Recent developments at NIST are described, including the isolation of highly-ionized atoms at low energy in unitary Penning traps and the use of these traps for the precise measurement of radiative decay lifetimes (demonstrated with a forbidden transition in Kr17+, as well as for studying electron capture processes.
A Unitary-Transformative Nursing Science: From Angst to Appreciation.
Cowling, W Richard
2017-10-01
The discord within nursing regarding the definition of nursing science has created great angst, particularly for those who view nursing science as a body of knowledge derived from theories specific to its unique concerns. The purpose of this brief article is to suggest a perspective and process grounded in appreciation of wholeness that may offer a way forward for proponents of a unitary-transformative nursing science that transcends the discord. This way forward is guided by principles of fostering dissent without contempt, generating a well-imagined future, and garnering appreciatively inspired action for change.
Multiscale differential phase contrast analysis with a unitary detector
Lopatin, Sergei
2015-12-30
A new approach to generate differential phase contrast (DPC) images for the visualization and quantification of local magnetic fields in a wide range of modern nano materials is reported. In contrast to conventional DPC methods our technique utilizes the idea of a unitary detector under bright field conditions, making it immediately usable by a majority of modern transmission electron microscopes. The approach is put on test to characterize the local magnetization of cylindrical nanowires and their 3D ordered arrays, revealing high sensitivity of our method in a combination with nanometer-scale spatial resolution.
Directory of Open Access Journals (Sweden)
Ryan Rebecca
2010-03-01
Full Text Available Abstract Background Communicating risk is part of primary prevention of coronary heart disease and stroke, collectively referred to as cardiovascular disease (CVD. In Australia, health organisations have promoted an absolute risk approach, thereby raising the question of suitable standardised formats for risk communication. Methods Sixteen formats of risk representation were prepared including statements, icons, graphical formats, alone or in combination, and with variable use of colours. All presented the same risk, i.e., the absolute risk for a 55 year old woman, 16% risk of CVD in five years. Preferences for a five or ten-year timeframe were explored. Australian GPs and consumers were recruited for participation in focus groups, with the data analysed thematically and preferred formats tallied. Results Three focus groups with health consumers and three with GPs were held, involving 19 consumers and 18 GPs. Consumers and GPs had similar views on which formats were more easily comprehended and which conveyed 16% risk as a high risk. A simple summation of preferences resulted in three graphical formats (thermometers, vertical bar chart and one statement format as the top choices. The use of colour to distinguish risk (red, yellow, green and comparative information (age, sex, smoking status were important ingredients. Consumers found formats which combined information helpful, such as colour, effect of changing behaviour on risk, or comparison with a healthy older person. GPs preferred formats that helped them relate the information about risk of CVD to their patients, and could be used to motivate patients to change behaviour. Several formats were reported as confusing, such as a percentage risk with no contextual information, line graphs, and icons, particularly those with larger numbers. Whilst consumers and GPs shared preferences, the use of one format for all situations was not recommended. Overall, people across groups felt that risk
Zhou, Junhe; Wu, Jianjie; Hu, Qinsong
2018-02-05
In this paper, we propose a novel tunable unitary transformer, which can achieve arbitrary discrete unitary transforms. The unitary transformer is composed of multiple sections of multi-core fibers with closely aligned coupled cores. Phase shifters are inserted before and after the sections to control the phases of the waves in the cores. A simple algorithm is proposed to find the optimal phase setup for the phase shifters to realize the desired unitary transforms. The proposed device is fiber based and is particularly suitable for the mode division multiplexing systems. A tunable mode MUX/DEMUX for a three-mode fiber is designed based on the proposed structure.
On the equivalence of massive qed with renormalizable and in unitary gauge
International Nuclear Information System (INIS)
Abdalla, E.
1978-03-01
In the framework of BPHZ renormalization procedure, we discuss the equivalence between 4-dimensional renormalizable massive quantum electrodynamics (Stueckelberg lagrangian), and massive QED in the unitary gauge
The universal sound velocity formula for the strongly interacting unitary Fermi gas
International Nuclear Information System (INIS)
Liu Ke; Chen Ji-Sheng
2011-01-01
Due to the scale invariance, the thermodynamic laws of strongly interacting limit unitary Fermi gas can be similar to those of non-interacting ideal gas. For example, the virial theorem between pressure and energy density of the ideal gas P = 2E/3V is still satisfied by the unitary Fermi gas. This paper analyses the sound velocity of unitary Fermi gases with the quasi-linear approximation. For comparison, the sound velocities for the ideal Boltzmann, Bose and Fermi gas are also given. Quite interestingly, the sound velocity formula for the ideal non-interacting gas is found to be satisfied by the unitary Fermi gas in different temperature regions. (general)
First unitary, then divided: the temporal dynamics of dividing attention.
Jefferies, Lisa N; Witt, Joseph B
2018-04-24
Whether focused visual attention can be divided has been the topic of much investigation, and there is a compelling body of evidence showing that, at least under certain conditions, attention can be divided and deployed as two independent foci. Three experiments were conducted to examine whether attention can be deployed in divided form from the outset, or whether it is first deployed as a unitary focus before being divided. To test this, we adapted the methodology of Jefferies, Enns, and Di Lollo (Journal of Experimental Psychology: Human Perception and Performance 40: 465, 2014), who used a dual-stream Attentional Blink paradigm and two letter-pair targets. One aspect of the AB, Lag-1 sparing, has been shown to occur only if the second target pair appears within the focus of attention. By presenting the second target pair at various spatial locations and assessing the magnitude of Lag-1 sparing, we probed the spatial distribution of attention. By systematically manipulating the stimulus-onset-asynchrony between the targets, we also tracked changes to the spatial distribution of attention over time. The results showed that even under conditions which encourage the division of attention, the attentional focus is first deployed in unitary form before being divided. It is then maintained in divided form only briefly before settling on a single location.
Introduction to representation theory
Etingof, Pavel; Hensel, Sebastian; Liu, Tiankai; Schwendner, Alex
2011-01-01
Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a "holistic" introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic k...
DEFF Research Database (Denmark)
Wulf-Andersen, Trine Østergaard
2012-01-01
, and dialogue, of situated participants. The article includes a lengthy example of a poetic representation of one participant’s story, and the author comments on the potentials of ‘doing’ poetic representations as an example of writing in ways that challenges what sometimes goes unasked in participative social...
International Nuclear Information System (INIS)
Akemann, G.; Bender, M.
2010-01-01
We consider a family of chiral non-Hermitian Gaussian random matrices in the unitarily invariant symmetry class. The eigenvalue distribution in this model is expressed in terms of Laguerre polynomials in the complex plane. These are orthogonal with respect to a non-Gaussian weight including a modified Bessel function of the second kind, and we give an elementary proof for this. In the large n limit, the eigenvalue statistics at the spectral edge close to the real axis are described by the same family of kernels interpolating between Airy and Poisson that was recently found by one of the authors for the elliptic Ginibre ensemble. We conclude that this scaling limit is universal, appearing for two different non-Hermitian random matrix ensembles with unitary symmetry. As a second result we give an equivalent form for the interpolating Airy kernel in terms of a single real integral, similar to representations for the asymptotic kernel in the bulk and at the hard edge of the spectrum. This makes its structure as a one-parameter deformation of the Airy kernel more transparent.
The Schur algorithm for generalized Schur functions III : J-unitary matrix polynomials on the circle
Alpay, Daniel; Azizov, Tomas; Dijksma, Aad; Langer, Heinz
2003-01-01
The main result is that for J = ((1)(0) (0)(-1)) every J-unitary 2 x 2-matrix polynomial on the unit circle is an essentially unique product of elementary J-unitary 2 x 2-matrix polynomials which are either of degree 1 or 2k. This is shown by means of the generalized Schur transformation introduced
Construction of unitary matrices from observable transition probabilities
International Nuclear Information System (INIS)
Peres, A.
1989-01-01
An ideal measuring apparatus defines an orthonormal basis vertical strokeu m ) in Hilbert space. Another apparatus defines another basis vertical strokeυ μ ). Both apparatuses together allow to measure the transition probabilities P mμ =vertical stroke(u m vertical strokeυ μ )vertical stroke 2 . The problem is: Given all the elements of a doubly stochastic matrix P mμ , find a unitary matrix U mμ such that P mμ =vertical strokeU mμ vertical stroke 2 . The number of unknown nontrivial phases is equal to the number of independent equations to satisfy. The problem can therefore be solved provided that the values of the P mμ satisfy some inequalities. (orig.)
The Science of Unitary Human Beings in a Creative Perspective.
Caratao-Mojica, Rhea
2015-10-01
In moving into a new kind of world, nurses are encouraged to look ahead and be innovative by transcending to new ways of using nursing knowledge while embracing a new worldview. "We need to recognize that we're going to have to use our imagination more and more" (Rogers, 1994). On that note, the author in this paper explicates Rogers' science of unitary human beings in a creative way relating it to painting. In addition, the author also explores works derived from Rogers' science such as Butcher's (1993) and Cowling's (1997), which are here discussed in light of an artwork. A painting is presented with the unpredictability, creativity, and the "dance of color and light" (Butcher, 1993) is appreciated through comprehending essence, pandimensionality, and wholeness. © The Author(s) 2015.
Qubit transport model for unitary black hole evaporation without firewalls*
Osuga, Kento; Page, Don N.
2018-03-01
We give an explicit toy qubit transport model for transferring information from the gravitational field of a black hole to the Hawking radiation by a continuous unitary transformation of the outgoing radiation and the black hole gravitational field. The model has no firewalls or other drama at the event horizon, and it avoids a counterargument that has been raised for subsystem transfer models as resolutions of the firewall paradox. Furthermore, it fits the set of six physical constraints that Giddings has proposed for models of black hole evaporation. It does utilize nonlocal qubits for the gravitational field but assumes that the radiation interacts locally with these nonlocal qubits, so in some sense the nonlocality is confined to the gravitational sector. Although the qubit model is too crude to be quantitatively correct for the detailed spectrum of Hawking radiation, it fits qualitatively with what is expected.
Mesoscopic Fluctuations for the Thinned Circular Unitary Ensemble
Berggren, Tomas; Duits, Maurice
2017-09-01
In this paper we study the asymptotic behavior of mesoscopic fluctuations for the thinned Circular Unitary Ensemble. The effect of thinning is that the eigenvalues start to decorrelate. The decorrelation is stronger on the larger scales than on the smaller scales. We investigate this behavior by studying mesoscopic linear statistics. There are two regimes depending on the scale parameter and the thinning parameter. In one regime we obtain a CLT of a classical type and in the other regime we retrieve the CLT for CUE. The two regimes are separated by a critical line. On the critical line the limiting fluctuations are no longer Gaussian, but described by infinitely divisible laws. We argue that this transition phenomenon is universal by showing that the same transition and their laws appear for fluctuations of the thinned sine process in a growing box. The proofs are based on a Riemann-Hilbert problem for integrable operators.
Unitary pole approximations and expansions in few-body systems
International Nuclear Information System (INIS)
Casel, A.; Haberzettl, H.; Sandhas, W.
1982-01-01
The unitary pole approximations or expansions of the two-body subsystem operators are well known, and particularly efficient and practical, methods to reduce the three-body problem to an effective two-body theory. In the present investigation we develop generalizations of these approximation techniques to the subsystem amplitudes of problems with higher particle numbers. They are based on the expansion of effective potentials which, in contrast to the genuine two-body interactions, are now energy dependent. Despite this feature our generalizations require only energy independent form factors, thus preserving one of the essential advantages of the genuine two-body approach. The application of these techniques to the four-body case is discussed in detail
Nonclassicality by Local Gaussian Unitary Operations for Gaussian States
Directory of Open Access Journals (Sweden)
Yangyang Wang
2018-04-01
Full Text Available A measure of nonclassicality N in terms of local Gaussian unitary operations for bipartite Gaussian states is introduced. N is a faithful quantum correlation measure for Gaussian states as product states have no such correlation and every non product Gaussian state contains it. For any bipartite Gaussian state ρ A B , we always have 0 ≤ N ( ρ A B < 1 , where the upper bound 1 is sharp. An explicit formula of N for ( 1 + 1 -mode Gaussian states and an estimate of N for ( n + m -mode Gaussian states are presented. A criterion of entanglement is established in terms of this correlation. The quantum correlation N is also compared with entanglement, Gaussian discord and Gaussian geometric discord.
Nataf, Pierre; Mila, Frédéric
2018-04-01
We develop an efficient method to perform density matrix renormalization group simulations of the SU(N ) Heisenberg chain with open boundary conditions taking full advantage of the SU(N ) symmetry of the problem. This method is an extension of the method previously developed for exact diagonalizations and relies on a systematic use of the basis of standard Young tableaux. Concentrating on the model with the fundamental representation at each site (i.e., one particle per site in the fermionic formulation), we have benchmarked our results for the ground-state energy up to N =8 and up to 420 sites by comparing them with Bethe ansatz results on open chains, for which we have derived and solved the Bethe ansatz equations. The agreement for the ground-state energy is excellent for SU(3) (12 digits). It decreases with N , but it is still satisfactory for N =8 (six digits). Central charges c are also extracted from the entanglement entropy using the Calabrese-Cardy formula and agree with the theoretical values expected from the SU (N) 1 Wess-Zumino-Witten conformal field theories.
International Nuclear Information System (INIS)
Gottschalk, Hanno; Hack, Thomas-Paul
2009-12-01
Using *-calculus on the dual of the Borchers-Uhlmann algebra endowed with a combinatorial co-product, we develop a method to calculate a unitary transformation relating the GNS representations of a non-quasifree and a quasifree state of the free hermitian scalar field. The motivation for such an analysis and a further result is the fact that a unitary transformation of this kind arises naturally in scattering theory on non-stationary backgrounds. Indeed, employing the perturbation theory of the Yang-Feldman equations with a free CCR field in a quasifree state as an initial condition and making use of extended Feynman graphs, we are able to calculate the Wightman functions of the interacting and outgoing fields in a φ p -theory on arbitrary curved spacetimes. A further examination then reveals two major features of the aforementioned theory: firstly, the interacting Wightman functions fulfil the basic axioms of hermiticity, invariance, spectrality (on stationary spacetimes), perturbative positivity, and locality. Secondly, the outgoing field is free and fulfils the CCR, but is in general not in a quasifree state in the case of a non-stationary spacetime. In order to obtain a sensible particle picture for the outgoing field and, hence, a description of the scattering process in terms of particles (in asymptotically flat spacetimes), it is thus necessary to compute a unitary transformation of the abovementioned type. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Gottschalk, Hanno [Bonn Univ. (Germany). Inst. fuer Angewandte Mathematik; Hack, Thomas-Paul [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2009-12-15
Using *-calculus on the dual of the Borchers-Uhlmann algebra endowed with a combinatorial co-product, we develop a method to calculate a unitary transformation relating the GNS representations of a non-quasifree and a quasifree state of the free hermitian scalar field. The motivation for such an analysis and a further result is the fact that a unitary transformation of this kind arises naturally in scattering theory on non-stationary backgrounds. Indeed, employing the perturbation theory of the Yang-Feldman equations with a free CCR field in a quasifree state as an initial condition and making use of extended Feynman graphs, we are able to calculate the Wightman functions of the interacting and outgoing fields in a {phi}{sup p}-theory on arbitrary curved spacetimes. A further examination then reveals two major features of the aforementioned theory: firstly, the interacting Wightman functions fulfil the basic axioms of hermiticity, invariance, spectrality (on stationary spacetimes), perturbative positivity, and locality. Secondly, the outgoing field is free and fulfils the CCR, but is in general not in a quasifree state in the case of a non-stationary spacetime. In order to obtain a sensible particle picture for the outgoing field and, hence, a description of the scattering process in terms of particles (in asymptotically flat spacetimes), it is thus necessary to compute a unitary transformation of the abovementioned type. (orig.)
International Nuclear Information System (INIS)
Dumitrescu, T.S.
1977-01-01
A new method is applied in order to obtain the irreducible single row representations of the groups under study. For the case U(3) contained in SO(3) also an explicit realization is constructed. The method has the advantage of being simpler than the previously used ones. (author)
Polynomial representations of GLn
Green, James A; Erdmann, Karin
2007-01-01
The first half of this book contains the text of the first edition of LNM volume 830, Polynomial Representations of GLn. This classic account of matrix representations, the Schur algebra, the modular representations of GLn, and connections with symmetric groups, has been the basis of much research in representation theory. The second half is an Appendix, and can be read independently of the first. It is an account of the Littelmann path model for the case gln. In this case, Littelmann's 'paths' become 'words', and so the Appendix works with the combinatorics on words. This leads to the repesentation theory of the 'Littelmann algebra', which is a close analogue of the Schur algebra. The treatment is self- contained; in particular complete proofs are given of classical theorems of Schensted and Knuth.
Polynomial representations of GLN
Green, James A
1980-01-01
The first half of this book contains the text of the first edition of LNM volume 830, Polynomial Representations of GLn. This classic account of matrix representations, the Schur algebra, the modular representations of GLn, and connections with symmetric groups, has been the basis of much research in representation theory. The second half is an Appendix, and can be read independently of the first. It is an account of the Littelmann path model for the case gln. In this case, Littelmann's 'paths' become 'words', and so the Appendix works with the combinatorics on words. This leads to the repesentation theory of the 'Littelmann algebra', which is a close analogue of the Schur algebra. The treatment is self- contained; in particular complete proofs are given of classical theorems of Schensted and Knuth.
Alpay, D.; Dijksma, A.; Langer, H.
2004-01-01
We prove that a 2 × 2 matrix polynomial which is J-unitary on the real line can be written as a product of normalized elementary J-unitary factors and a J-unitary constant. In the second part we give an algorithm for this factorization using an analog of the Schur transformation.
Congruence properties of induced representations
DEFF Research Database (Denmark)
Mayer, Dieter; Momeni, Arash; Venkov, Alexei
In this paper we study representations of the projective modular group induced from the Hecke congruence group of level 4 with Selberg's character. We show that the well known congruence properties of Selberg's character are equivalent to the congruence properties of the induced representations...
Directory of Open Access Journals (Sweden)
Maria das Dores Campos Machado
2005-08-01
Full Text Available O objetivo deste artigo é realizar um balanço das principais transformações ocorridas nos últimos 15 anos no sistema de gênero hegemônico no pentecostalismo. Inicialmente, procuro apresentar o perfil demográfico e socioeconômico dos pentecostais. Em seguida, discuto as conseqüências da opção religiosa dos homens e das mulheres e chamo atenção para os limites do processo de reconfiguração das subjetividades femininas e masculinas no interior das comunidades. O exame das tendências de crescimento do sacerdócio feminino e da participação política das mulheres pentecostais complementa esta análise e ajuda no entendimento das ambivalências na revisão das representações e relações de gênero nesses grupos religiosos.The objective of this article is to conduct an evaluation of the main changes produced throughout the last fifteen years in the hegemonic gender system of pentecostalism. After presenting the demographic and socio-economic profile of Pentecostals, I discuss the consequences of religious choice for men and women , and the limits of the rearrangement process of female and male subjectivities inside the communities. The growth trends of female priesthood and the political participation of pentecostal women are also analysed, to help us understand the ambivalences in reviewing the representations and gender relations in these religious groups.
Schiffler, Ralf
2014-01-01
This book is intended to serve as a textbook for a course in Representation Theory of Algebras at the beginning graduate level. The text has two parts. In Part I, the theory is studied in an elementary way using quivers and their representations. This is a very hands-on approach and requires only basic knowledge of linear algebra. The main tool for describing the representation theory of a finite-dimensional algebra is its Auslander-Reiten quiver, and the text introduces these quivers as early as possible. Part II then uses the language of algebras and modules to build on the material developed before. The equivalence of the two approaches is proved in the text. The last chapter gives a proof of Gabriel’s Theorem. The language of category theory is developed along the way as needed.
DEFF Research Database (Denmark)
Photography not only represents space. Space is produced photographically. Since its inception in the 19th century, photography has brought to light a vast array of represented subjects. Always situated in some spatial order, photographic representations have been operatively underpinned by social...... to the enterprises of the medium. This is the subject of Representational Machines: How photography enlists the workings of institutional technologies in search of establishing new iconic and social spaces. Together, the contributions to this edited volume span historical epochs, social environments, technological...... possibilities, and genre distinctions. Presenting several distinct ways of producing space photographically, this book opens a new and important field of inquiry for photography research....
DEFF Research Database (Denmark)
Rasmussen, Majken Kirkegaard; Petersen, Marianne Graves
2011-01-01
Stereotypic presumptions about gender affect the design process, both in relation to how users are understood and how products are designed. As a way to decrease the influence of stereotypic presumptions in design process, we propose not to disregard the aspect of gender in the design process......, as the perspective brings valuable insights on different approaches to technology, but instead to view gender through a value lens. Contributing to this perspective, we have developed Value Representations as a design-oriented instrument for staging a reflective dialogue with users. Value Representations...
Social representations about cancer
Directory of Open Access Journals (Sweden)
Andreja Cirila Škufca
2003-09-01
Full Text Available In this article we are presenting the results of the comparison study on social representations and causal attributions about cancer. We compared a breast cancer survivors group and control group without own experience of cancer of their own. Although social representations about cancer differ in each group, they are closely related to the concept of suffering, dying and death. We found differences in causal attribution of cancer. In both groups we found a category of risky behavior, which attributes a responsibility for a disease to an individual. Besides these factors we found predominate stress and psychological influences in cancer survivors group. On the other hand control group indicated factors outside the ones control e.g. heredity and environmental factors. Representations about a disease inside person's social space are important in co-shaping the individual process of coping with own disease. Since these representations are not always coherent with the knowledge of modern medicine their knowledge and appreciation in the course of treatment is of great value. We find the findingss of applied social psychology important as starting points in the therapeutic work with patients.
Koithan, Mary S; Kreitzer, Mary Jo; Watson, Jean
2017-07-01
The principles of integrative nursing and caring science align with the unitary paradigm in a way that can inform and shape nursing knowledge, patient care delivery across populations and settings, and new healthcare policy. The proposed policies may transform the healthcare system in a way that supports nursing praxis and honors the discipline's unitary paradigm. This call to action provides a distinct and hopeful vision of a healthcare system that is accessible, equitable, safe, patient-centered, and affordable. In these challenging times, it is the unitary paradigm and nursing wisdom that offer a clear path forward.
A unitary model of the black hole evaporation
Feng, Yu-Lei; Chen, Yi-Xin
2014-12-01
A unitary effective field model of the black hole evaporation is proposed to satisfy almost the four postulates of the black hole complementarity (BHC). In this model, we enlarge a black hole-scalar field system by adding an extra radiation detector that couples with the scalar field. After performing a partial trace over the scalar field space, we obtain an effective entanglement between the black hole and the detector (or radiation in it). As the whole system evolves, the S-matrix formula can be constructed formally step by step. Without local quantum measurements, the paradoxes of the information loss and AMPS's firewall can be resolved. However, the information can be lost due to quantum decoherence, as long as some local measurement has been performed on the detector to acquire the information of the radiation in it. But unlike Hawking's completely thermal spectrum, some residual correlations can be found in the radiations. All these considerations can be simplified in a qubit model that provides a modified quantum teleportation to transfer the information via an EPR pairs.
The unitary conformal field theory behind 2D Asymptotic Safety
Energy Technology Data Exchange (ETDEWEB)
Nink, Andreas; Reuter, Martin [Institute of Physics, PRISMA & MITP, Johannes Gutenberg University Mainz,Staudingerweg 7, D-55099 Mainz (Germany)
2016-02-25
Being interested in the compatibility of Asymptotic Safety with Hilbert space positivity (unitarity), we consider a local truncation of the functional RG flow which describes quantum gravity in d>2 dimensions and construct its limit of exactly two dimensions. We find that in this limit the flow displays a nontrivial fixed point whose effective average action is a non-local functional of the metric. Its pure gravity sector is shown to correspond to a unitary conformal field theory with positive central charge c=25. Representing the fixed point CFT by a Liouville theory in the conformal gauge, we investigate its general properties and their implications for the Asymptotic Safety program. In particular, we discuss its field parametrization dependence and argue that there might exist more than one universality class of metric gravity theories in two dimensions. Furthermore, studying the gravitational dressing in 2D asymptotically safe gravity coupled to conformal matter we uncover a mechanism which leads to a complete quenching of the a priori expected Knizhnik-Polyakov-Zamolodchikov (KPZ) scaling. A possible connection of this prediction to Monte Carlo results obtained in the discrete approach to 2D quantum gravity based upon causal dynamical triangulations is mentioned. Similarities of the fixed point theory to, and differences from, non-critical string theory are also described. On the technical side, we provide a detailed analysis of an intriguing connection between the Einstein-Hilbert action in d>2 dimensions and Polyakov’s induced gravity action in two dimensions.
Conditional mutual information of bipartite unitaries and scrambling
Energy Technology Data Exchange (ETDEWEB)
Ding, Dawei; Hayden, Patrick; Walter, Michael [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,382 Via Pueblo, Stanford, CA 94305 (United States)
2016-12-28
One way to diagnose chaos in bipartite unitary channels is via the tripartite information of the corresponding Choi state, which for certain choices of the subsystems reduces to the negative conditional mutual information (CMI). We study this quantity from a quantum information-theoretic perspective to clarify its role in diagnosing scrambling. When the CMI is zero, we find that the channel has a special normal form consisting of local channels between individual inputs and outputs. However, we find that arbitrarily low CMI does not imply arbitrary proximity to a channel of this form, although it does imply a type of approximate recoverability of one of the inputs. When the CMI is maximal, we find that the residual channel from an individual input to an individual output is completely depolarizing when the other input is maximally mixed. However, we again find that this result is not robust. We also extend some of these results to the multipartite case and to the case of Haar-random pure input states. Finally, we look at the relationship between tripartite information and its Rényi-2 version which is directly related to out-of-time-order correlation functions. In particular, we demonstrate an arbitrarily large gap between the two quantities.
Correlation functions in unitary minimal Liouville gravity and Frobenius manifolds
Energy Technology Data Exchange (ETDEWEB)
Belavin, V. [I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute,Leninsky prospect 53, 119991 Moscow (Russian Federation); Department of Quantum Physics, Institute for Information Transmission Problems,Bolshoy Karetny per. 19, 127994 Moscow (Russian Federation); Department of Theoretical Physics, National Research Nuclear University MEPhI,Kashirskoe shosse 31, 115409 Moscow (Russian Federation)
2015-02-10
We continue to study minimal Liouville gravity (MLG) using a dual approach based on the idea that the MLG partition function is related to the tau function of the A{sub q} integrable hierarchy via the resonance transformations, which are in turn fixed by conformal selection rules. One of the main problems in this approach is to choose the solution of the Douglas string equation that is relevant for MLG. The appropriate solution was recently found using connection with the Frobenius manifolds. We use this solution to investigate three- and four-point correlators in the unitary MLG models. We find an agreement with the results of the original approach in the region of the parameters where both methods are applicable. In addition, we find that only part of the selection rules can be satisfied using the resonance transformations. The physical meaning of the nonzero correlators, which before coupling to Liouville gravity are forbidden by the selection rules, and also the modification of the dual formulation that takes this effect into account remains to be found.
Energy Technology Data Exchange (ETDEWEB)
Akibue, Seiseki [Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo (Japan); Murao, Mio [Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo, Japan and NanoQuine, The University of Tokyo, Tokyo (Japan)
2014-12-04
We investigate distributed implementation of two-qubit unitary operations over two primitive networks, the butterfly network and the ladder network, as a first step to apply network coding for quantum computation. By classifying two-qubit unitary operations in terms of the Kraus-Cirac number, the number of non-zero parameters describing the global part of two-qubit unitary operations, we analyze which class of two-qubit unitary operations is implementable over these networks with free classical communication. For the butterfly network, we show that two classes of two-qubit unitary operations, which contain all Clifford, controlled-unitary and matchgate operations, are implementable over the network. For the ladder network, we show that two-qubit unitary operations are implementable over the network if and only if their Kraus-Cirac number do not exceed the number of the bridges of the ladder.
International Nuclear Information System (INIS)
Akibue, Seiseki; Murao, Mio
2014-01-01
We investigate distributed implementation of two-qubit unitary operations over two primitive networks, the butterfly network and the ladder network, as a first step to apply network coding for quantum computation. By classifying two-qubit unitary operations in terms of the Kraus-Cirac number, the number of non-zero parameters describing the global part of two-qubit unitary operations, we analyze which class of two-qubit unitary operations is implementable over these networks with free classical communication. For the butterfly network, we show that two classes of two-qubit unitary operations, which contain all Clifford, controlled-unitary and matchgate operations, are implementable over the network. For the ladder network, we show that two-qubit unitary operations are implementable over the network if and only if their Kraus-Cirac number do not exceed the number of the bridges of the ladder
Grms or graphical representation of model spaces. Vol. I Basics
International Nuclear Information System (INIS)
Duch, W.
1986-01-01
This book presents a novel approach to the many-body problem in quantum chemistry, nuclear shell-theory and solid-state theory. Many-particle model spaces are visualized using graphs, each path of a graph labeling a single basis function or a subspace of functions. Spaces of a very high dimension are represented by small graphs. Model spaces have structure that is reflected in the architecture of the corresponding graphs, that in turn is reflected in the structure of the matrices corresponding to operators acting in these spaces. Insight into this structure leads to formulation of very efficient computer algorithms. Calculation of matrix elements is reduced to comparison of paths in a graph, without ever looking at the functions themselves. Using only very rudimentary mathematical tools graphical rules of matrix element calculation in abelian cases are derived, in particular segmentation rules obtained in the unitary group approached are rederived. The graphs are solutions of Diophantine equations of the type appearing in different branches of applied mathematics. Graphical representation of model spaces should find as many applications as has been found for diagramatical methods in perturbation theory
DEFF Research Database (Denmark)
Mullins, Michael
Contemporary communicational and informational processes contribute to the shaping of our physical environment by having a powerful influence on the process of design. Applications of virtual reality (VR) are transforming the way architecture is conceived and produced by introducing dynamic...... elements into the process of design. Through its immersive properties, virtual reality allows access to a spatial experience of a computer model very different to both screen based simulations as well as traditional forms of architectural representation. The dissertation focuses on processes of the current...... representation? How is virtual reality used in public participation and how do virtual environments affect participatory decision making? How does VR thus affect the physical world of built environment? Given the practical collaborative possibilities of immersive technology, how can they best be implemented...
Unitary three-body calculation of nucleon-nucleon scattering
International Nuclear Information System (INIS)
Tanabe, H.; Ohta, K.
1986-07-01
We calculate nucleon-nucleon elastic scattering phase parameters based on a unitary, relativistic, pion-exchange model. The results are highly dependent on the off-shell amplitudes of πN scattering. The isobar-dominated model for the P 33 interaction leads to too small pion production rates owing to its strong suppression of off-shell pions. We propose to expand the idea of the Δ-isobar model in such a manner as to incorporate a background (non-pole) interaction. The two-potential model, which was first applied to the P 11 partial wave by Mizutani and Koltun, is applied also to the P 33 wave. Our phenomenological model for πN interaction in the P 33 partial wave differs from the conventional model only in its off-shell extrapolation, and has two different variants for the πN → Δ vertex. The three-body approach of Kloet and Silbar is extended such that the background interactions can be included straightfowardly. We make detailed comparisons of the new model with the conventional one and find that our model adequately reproduces the 1 D 2 phase parameters as well as those of peripheral partial waves. We also find that the longitudinal total cross section difference Δσ L (pp → NNπ) comes closer to the data compared to Kloet and Silbar. We discuss about the backward pion propagation in the three-body calculation, and the Pauli-principle violating states for the background P 11 interaction. (author)
Energy Technology Data Exchange (ETDEWEB)
Hoff da Silva, J.M.; Rogerio, R.J.B. [Universidade Estadual Paulista, Departamento de Fisica e Quimica, Guaratingueta, SP (Brazil); Villalobos, C.H.C. [Universidade Estadual Paulista, Departamento de Fisica e Quimica, Guaratingueta, SP (Brazil); Universidade Federal Fluminense, Instituto de Fisica, Niteroi, RJ (Brazil); Rocha, Roldao da [Universidade Federal do ABC-UFABC, Centro de Matematica, Computacao e Cognicao, Santo Andre (Brazil)
2017-07-15
A systematic study of the spinor representation by means of the fermionic physical space is accomplished and implemented. The spinor representation space is shown to be constrained by the Fierz-Pauli-Kofink identities among the spinor bilinear covariants. A robust geometric and topological structure can be manifested from the spinor space, wherein the first and second homotopy groups play prominent roles on the underlying physical properties, associated to fermionic fields. The mapping that changes spinor fields classes is then exemplified, in an Einstein-Dirac system that provides the spacetime generated by a fermion. (orig.)
Diagram Techniques in Group Theory
Stedman, Geoffrey E.
2009-09-01
Preface; 1. Elementary examples; 2. Angular momentum coupling diagram techniques; 3. Extension to compact simple phase groups; 4. Symmetric and unitary groups; 5. Lie groups and Lie algebras; 6. Polarisation dependence of multiphoton processes; 7. Quantum field theoretic diagram techniques for atomic systems; 8. Applications; Appendix; References; Indexes.
Surveying the quantum group symmetries of integrable open spin chains
Nepomechie, Rafael I.; Retore, Ana L.
2018-05-01
Using anisotropic R-matrices associated with affine Lie algebras g ˆ (specifically, A2n(2), A2n-1 (2) , Bn(1), Cn(1), Dn(1)) and suitable corresponding K-matrices, we construct families of integrable open quantum spin chains of finite length, whose transfer matrices are invariant under the quantum group corresponding to removing one node from the Dynkin diagram of g ˆ . We show that these transfer matrices also have a duality symmetry (for the cases Cn(1) and Dn(1)) and additional Z2 symmetries that map complex representations to their conjugates (for the cases A2n-1 (2) , Bn(1) and Dn(1)). A key simplification is achieved by working in a certain "unitary" gauge, in which only the unbroken symmetry generators appear. The proofs of these symmetries rely on some new properties of the R-matrices. We use these symmetries to explain the degeneracies of the transfer matrices.
Neural activity reveals perceptual grouping in working memory.
Rabbitt, Laura R; Roberts, Daniel M; McDonald, Craig G; Peterson, Matthew S
2017-03-01
There is extensive evidence that the contralateral delay activity (CDA), a scalp recorded event-related brain potential, provides a reliable index of the number of objects held in visual working memory. Here we present evidence that the CDA not only indexes visual object working memory, but also the number of locations held in spatial working memory. In addition, we demonstrate that the CDA can be predictably modulated by the type of encoding strategy employed. When individual locations were held in working memory, the pattern of CDA modulation mimicked previous findings for visual object working memory. Specifically, CDA amplitude increased monotonically until working memory capacity was reached. However, when participants were instructed to group individual locations to form a constellation, the CDA was prolonged and reached an asymptote at two locations. This result provides neural evidence for the formation of a unitary representation of multiple spatial locations. Published by Elsevier B.V.
International Nuclear Information System (INIS)
Burdík, C; Reshetnyak, A
2012-01-01
We derive non-linear commutator HS symmetry algebra, which encode unitary irreducible representations of AdS group subject to Young tableaux Y(s 1 ,..., s k ) with κ ≥ 2 rows on d-dimensional anti-de-Sitter space. Auxiliary representations for specially deformed non-linear HS symmetry algebra in terms of generalized Verma module in order to additively convert a subsystem of second-class constraints in the HS symmetry algebra into one with first-class constraints are found explicitly for the case of HS fields for κ = 2 Young tableaux. The oscillator realization over Heisenberg algebra for obtained Verma module is constructed. The results generalize the method of auxiliary representations construction for symplectic sp(2κ) algebra used for mixed-symmetry HS fields on a flat spaces and can be extended on a case of arbitrary HS fields in AdS-space. Gauge-invariant unconstrained reducible Lagrangian formulation for free bosonic HS fields with generalized spin (s 1 , s 2 ) is derived.
Analytical and unitary approach in mesons electromagnetic form factor applications
International Nuclear Information System (INIS)
Liptaj, A.
2010-07-01
In the dissertation thesis we address several topics related to the domain of particle physics. All of them represent interesting open problems that can be connected to the elastic or transition electromagnetic form factors of mesons, the form factors being the main objects of our interest. Our ambition is to contribute to the solution of these problems and use for that purpose known analytic properties of the form factors and the unitarity condition. These two tools are very powerful in the low energy domain (such as bound states of partons), where the perturbative QCD looses its validity. This is the motivation for construction of the unitary and analytic (U and A) models of studied form factors, that enable us to get the majority of our results. We use the U and A model to evaluate the contribution of the processes e"+e"- → Pγ, P = π"0, η, η to the muon magnetic anomaly a_μ in the lowest order of the hadronic vacuum polarization. For the contribution a_μ"h"a"d","L"O (π"+π"-) we demonstrate, that the use of the model leads to a dramatic error reduction with respect to the results of other authors. We also get a shift in the central value in the 'correct' direction, that brings the theoretical value closer to the experimental one. This results encourages us to use the model also for the evaluation of a_μ"h"a"d","L"O (P_γ). These contributions are smaller, however the precision of the experiment makes their evaluation necessary. We further use the U and A model of the transition form factors of π"0, η and η"' mesons to predict the partial decay widths of these particles Γ_π_"0_→_γ_γ and Γ_η_→_γ_γ and Γ_η_"'_→_γ_γ. In this way we make an independent cross check of the PDG table values. We find an agreement in the case of Γ_η_→_γ_γ and Γ_η_"'_→_γ_γ, even a smaller uncertainty for Γ_η_"'_→_γ_γ. In the case of Γ_π_"0_→_γ_γ we find a disagreement that points to an interesting problem. We wonder whether it could be
Solitons and theory of representations
International Nuclear Information System (INIS)
Kulish, P.P.
1985-01-01
Problems on the theory of group representations finding application in constructing the quantum variant of the inverse scattering problem are discussed. The multicomponent nonlinear Shroedinger equation is considered as a main example of nonlinear evolution equations (NEE)
Valla, Jeffrey M; Williams, Wendy M
2012-01-01
The under-representation of women and ethnic minorities in Science, Technology, Engineering, and Mathematics (STEM) education and professions has resulted in a loss of human capital for the US scientific workforce and spurred the development of myriad STEM educational intervention programs. Increased allocation of resources to such programs begs for a critical, prescriptive, evidence-based review that will enable researchers to develop optimal interventions and administrators to maximize investments. We begin by providing a theoretical backdrop for K-12 STEM programs by reviewing current data on under-representation and developmental research describing individual-level social factors undergirding these data. Next, we review prototypical designs of these programs, highlighting specific programs in the literature as examples of program structures and components currently in use. We then evaluate these interventions in terms of overall effectiveness, as a function of how well they address age-, ethnicity-, or gender-specific factors, suggesting improvements in program design based on these critiques. Finally, program evaluation methods are briefly reviewed and discussed in terms of how their empirical soundness can either enable or limit our ability to delineate effective program components. "Now more than ever, the nation's changing demographics demand that we include all of our citizens in science and engineering education and careers. For the U.S. to benefit from the diverse talents of all its citizens, we must grow the pipeline of qualified, underrepresented minority engineers and scientists to fill positions in industry and academia."-Irving P. McPhail..
Probing non-unitary CP violation effects in neutrino oscillation experiments
Verma, Surender; Bhardwaj, Shankita
2018-05-01
In the present work, we have considered minimal unitarity violation scheme to obtain the general expression for ν _{μ }→ ν _{τ } oscillation probability in vacuum and matter. For this channel, we have investigated the sensitivities of short baseline experiments to non-unitary parameters |ρ _{μ τ }| and ω _{μ τ } for normal as well as inverted hierarchical neutrino masses and θ _{23} being above or below maximality. We find that for normal hierarchy, the 3σ sensitivity of |ρ _{μ τ }| is maximum for non-unitary phase ω _{μ τ }=0 whereas it is minimum for ω _{μ τ }=± π . For inverted hierarchy, the sensitivity is minimum at ω _{μ τ }=0 and maximum for ω _{μ τ }=± π . We observe that the sensitivity to measure non-unitarity remains unaffected for unitary CP phase δ =0 or δ =π /2 . We have, also, explored wide spectrum of L/E ratio to investigate the possibilities to observe CP-violation due to unitary (δ ) and non-unitary (ω _{μ τ } ) phases. We find that the both phases can be disentangled, in principle, from each other for L/E<200 km/GeV.
Pioneers of representation theory
Curtis, Charles W
1999-01-01
The year 1897 was marked by two important mathematical events: the publication of the first paper on representations of finite groups by Ferdinand Georg Frobenius (1849-1917) and the appearance of the first treatise in English on the theory of finite groups by William Burnside (1852-1927). Burnside soon developed his own approach to representations of finite groups. In the next few years, working independently, Frobenius and Burnside explored the new subject and its applications to finite group theory. They were soon joined in this enterprise by Issai Schur (1875-1941) and some years later, by Richard Brauer (1901-1977). These mathematicians' pioneering research is the subject of this book. It presents an account of the early history of representation theory through an analysis of the published work of the principals and others with whom the principals' work was interwoven. Also included are biographical sketches and enough mathematics to enable readers to follow the development of the subject. An introductor...
International Nuclear Information System (INIS)
Vyas, Manan; Kota, V.K.B.
2010-01-01
For m fermions in Ω number of single particle orbitals, each fourfold degenerate, we introduce and analyze in detail embedded Gaussian unitary ensemble of random matrices generated by random two-body interactions that are SU(4) scalar [EGUE(2)-SU(4)]. Here the SU(4) algebra corresponds to the Wigner's supermultiplet SU(4) symmetry in nuclei. Embedding algebra for the EGUE(2)-SU(4) ensemble is U(4Ω) contains U(Ω) x SU(4). Exploiting the Wigner-Racah algebra of the embedding algebra, analytical expression for the ensemble average of the product of any two m particle Hamiltonian matrix elements is derived. Using this, formulas for a special class of U(Ω) irreducible representations (irreps) {4 r , p}, p = 0, 1, 2, 3 are derived for the ensemble averaged spectral variances and also for the covariances in energy centroids and spectral variances. On the other hand, simplifying the tabulations of Hecht for SU(Ω) Racah coefficients, numerical calculations are carried out for general U(Ω) irreps. Spectral variances clearly show, by applying Jacquod and Stone prescription, that the EGUE(2)-SU(4) ensemble generates ground state structure just as the quadratic Casimir invariant (C 2 ) of SU(4). This is further corroborated by the calculation of the expectation values of C 2 [SU(4)] and the four periodicity in the ground state energies. Secondly, it is found that the covariances in energy centroids and spectral variances increase in magnitude considerably as we go from EGUE(2) for spinless fermions to EGUE(2) for fermions with spin to EGUE(2)-SU(4) implying that the differences in ensemble and spectral averages grow with increasing symmetry. Also for EGUE(2)-SU(4) there are, unlike for GUE, non-zero cross-correlations in energy centroids and spectral variances defined over spaces with different particle numbers and/or U(Ω) [equivalently SU(4)] irreps. In the dilute limit defined by Ω → ∞, r >> 1 and r/Ω → 0, for the {4 r , p} irreps, we have derived analytical
Women and political representation.
Rathod, P B
1999-01-01
A remarkable progress in women's participation in politics throughout the world was witnessed in the final decade of the 20th century. According to the Inter-Parliamentary Union report, there were only eight countries with no women in their legislatures in 1998. The number of women ministers at the cabinet level worldwide doubled in a decade, and the number of countries without any women ministers dropped from 93 to 48 during 1987-96. However, this progress is far from satisfactory. Political representation of women, minorities, and other social groups is still inadequate. This may be due to a complex combination of socioeconomic, cultural, and institutional factors. The view that women's political participation increases with social and economic development is supported by data from the Nordic countries, where there are higher proportions of women legislators than in less developed countries. While better levels of socioeconomic development, having a women-friendly political culture, and higher literacy are considered favorable factors for women's increased political representation, adopting one of the proportional representation systems (such as a party-list system, a single transferable vote system, or a mixed proportional system with multi-member constituencies) is the single factor most responsible for the higher representation of women.
Treating experimental data of inverse kinetic method by unitary linear regression analysis
International Nuclear Information System (INIS)
Zhao Yusen; Chen Xiaoliang
2009-01-01
The theory of treating experimental data of inverse kinetic method by unitary linear regression analysis was described. Not only the reactivity, but also the effective neutron source intensity could be calculated by this method. Computer code was compiled base on the inverse kinetic method and unitary linear regression analysis. The data of zero power facility BFS-1 in Russia were processed and the results were compared. The results show that the reactivity and the effective neutron source intensity can be obtained correctly by treating experimental data of inverse kinetic method using unitary linear regression analysis and the precision of reactivity measurement is improved. The central element efficiency can be calculated by using the reactivity. The result also shows that the effect to reactivity measurement caused by external neutron source should be considered when the reactor power is low and the intensity of external neutron source is strong. (authors)
International Nuclear Information System (INIS)
Qin Fang; Chen Jisheng
2010-01-01
We utilize the fractional exclusion statistics of the Haldane and Wu hypothesis to study the thermodynamics of a unitary Fermi gas trapped in a harmonic oscillator potential at ultra-low finite temperature. The entropy per particle as a function of the energy per particle and energy per particle versus rescaled temperature are numerically compared with the experimental data. The study shows that, except the chemical potential behaviour, there exists a reasonable consistency between the experimental measurement and theoretical attempt for the entropy and energy per particle. In the fractional exclusion statistics formalism, the behaviour of the isochore heat capacity for a trapped unitary Fermi gas is also analysed.
Comparison of the unitary pole and Adhikari-Sloan expansions in the three nucleon system
International Nuclear Information System (INIS)
Afnan, I.R.; Birrell, N.D.
1977-01-01
The binding energy of 3 H, percentage S-, S'- and D-state probability, and charge form factor of 3 He are calculated using the unitary pole and Adhikari-Sloan separable expansions to the Reid soft core potential. Comparison of the results for the two separable expansions show that the expansion of Adhikari and Sloan has the better convergence property, and the lowest rank expansion considered (equivalent to the unitary pole approximation) gives a good approximation to the binding energy of 3 H and the charge form factor of 3 He, even at large momentum transfer (K 2 -2 ). (Author)
How many invariant polynomials are needed to decide local unitary equivalence of qubit states?
International Nuclear Information System (INIS)
Maciążek, Tomasz; Oszmaniec, Michał; Sawicki, Adam
2013-01-01
Given L-qubit states with the fixed spectra of reduced one-qubit density matrices, we find a formula for the minimal number of invariant polynomials needed for solving local unitary (LU) equivalence problem, that is, problem of deciding if two states can be connected by local unitary operations. Interestingly, this number is not the same for every collection of the spectra. Some spectra require less polynomials to solve LU equivalence problem than others. The result is obtained using geometric methods, i.e., by calculating the dimensions of reduced spaces, stemming from the symplectic reduction procedure
Attention and Representational Momentum
Hayes, Amy; Freyd, Jennifer J
1995-01-01
Representational momentum, the tendency for memory to be distorted in the direction of an implied transformation, suggests that dynamics are an intrinsic part of perceptual representations. We examined the effect of attention on dynamic representation by testing for representational momentum under conditions of distraction. Forward memory shifts increase when attention is divided. Attention may be involved in halting but not in maintaining dynamic representations.
Unitary embedding for data hiding with the SVD
Bergman, Clifford; Davidson, Jennifer
2005-03-01
Steganography is the study of data hiding for the purpose of covert communication. A secret message is inserted into a cover file so that the very existence of the message is not apparent. Most current steganography algorithms insert data in the spatial or transform domains; common transforms include the discrete cosine transform, the discrete Fourier transform, and discrete wavelet transform. In this paper, we present a data-hiding algorithm that exploits a decomposition representation of the data instead of a frequency-based transformation of the data. The decomposition transform used is the singular value decomposition (SVD). The SVD of a matrix A is a decomposition A= USV' in which S is a nonnegative diagonal matrix and U and V are orthogonal matrices. We show how to use the orthogonal matrices in the SVD as a vessel in which to embed information. Several challenges were presented in order to accomplish this, and we give effective information-hiding using the SVD can be just as effective as using transform-based techniques. Furthermore, different problems arise when using the SVD than using a transform-based technique. We have applied the SVD to image data, but the technique can be formulated for other data types such as audio and video.
Symmetries and groups in particle physics
International Nuclear Information System (INIS)
Scherer, Stefan
2016-01-01
The aim of this book consists of a didactic introduction to the group-theoretical considerations and methods, which have led to an ever deeper understanding of the interactions of the elementary particles. The first three chapters deal primarily with the foundations of the representation theory of primarily finite groups, whereby many results are also transferable to compact Lie groups. In the third chapter we discuss the concept of Lie groups and their connection with Lie algebras. In the remaining chapter it is mainly about the application of group theory in physics. Chapter 4 deals with the groups SO(3) and SU(2), which occur in connection with the description of the angular momentum in quantum mechanics. We discuss the Wigner-Eckar theorem together with some applications. In chapter 5 we are employed to the composition properties of strongly interacting systems, so called hadrons, and discuss extensively the transformation properties of quarks with relation to the special unitary groups. The Noether theorem is generally treated in connection to the conservation laws belonging to the Galilei group and the Poincare group. We confine us in chapter 6 to internal symmetries, but explain for that extensively the application to quantum field theory. Especially an outlook on the effect of symmetries in form of so called Ward identities is granted. In chapter 7 we turn towards the gauge principle and discuss first the construction of quantum electrodynamics. In the following we generalize the gauge principle to non-Abelian groups (Yang-Mills theories) and formulate the quantum chromodynamics (QCD). Especially we take a view of ''random'' global symmetries of QCD, especially the chiral symmetry. In chapter 8 we illuminate the phenomenon of spontaneous symmetry breaking both for global and for local symmetries. In the final chapter we work out the group-theoretical structure of the Standard Model. Finally by means of the group SU(5) we take a view to
Matrix elements and few-body calculations within the unitary correlation operator method
International Nuclear Information System (INIS)
Roth, R.; Hergert, H.; Papakonstantinou, P.
2005-01-01
We employ the unitary correlation operator method (UCOM) to construct correlated, low-momentum matrix elements of realistic nucleon-nucleon interactions. The dominant short-range central and tensor correlations induced by the interaction are included explicitly by an unitary transformation. Using correlated momentum-space matrix elements of the Argonne V18 potential, we show that the unitary transformation eliminates the strong off-diagonal contributions caused by the short-range repulsion and the tensor interaction and leaves a correlated interaction dominated by low-momentum contributions. We use correlated harmonic oscillator matrix elements as input for no-core shell model calculations for few-nucleon systems. Compared to the bare interaction, the convergence properties are dramatically improved. The bulk of the binding energy can already be obtained in very small model spaces or even with a single Slater determinant. Residual long-range correlations, not treated explicitly by the unitary transformation, can easily be described in model spaces of moderate size allowing for fast convergence. By varying the range of the tensor correlator we are able to map out the Tjon line and can in turn constrain the optimal correlator ranges. (orig.)
Matrix elements and few-body calculations within the unitary correlation operator method
International Nuclear Information System (INIS)
Roth, R.; Hergert, H.; Papakonstantinou, P.; Neff, T.; Feldmeier, H.
2005-01-01
We employ the unitary correlation operator method (UCOM) to construct correlated, low-momentum matrix elements of realistic nucleon-nucleon interactions. The dominant short-range central and tensor correlations induced by the interaction are included explicitly by an unitary transformation. Using correlated momentum-space matrix elements of the Argonne V18 potential, we show that the unitary transformation eliminates the strong off-diagonal contributions caused by the short-range repulsion and the tensor interaction and leaves a correlated interaction dominated by low-momentum contributions. We use correlated harmonic oscillator matrix elements as input for no-core shell model calculations for few-nucleon systems. Compared to the bare interaction, the convergence properties are dramatically improved. The bulk of the binding energy can already be obtained in very small model spaces or even with a single Slater determinant. Residual long-range correlations, not treated explicitly by the unitary transformation, can easily be described in model spaces of moderate size allowing for fast convergence. By varying the range of the tensor correlator we are able to map out the Tjon line and can in turn constrain the optimal correlator ranges
Experimental implementation of optimal linear-optical controlled-unitary gates
Czech Academy of Sciences Publication Activity Database
Lemr, K.; Bartkiewicz, K.; Černoch, Antonín; Dušek, M.; Soubusta, Jan
2015-01-01
Roč. 114, č. 15 (2015), "153602-1"-"153602-5" ISSN 0031-9007 R&D Projects: GA ČR GAP205/12/0382 Institutional support: RVO:68378271 Keywords : two-qubit gates * optimal linear-optical controlled-unitary gates * quantum computing Subject RIV: BH - Optics, Masers, Lasers Impact factor: 7.645, year: 2015
Unitary eikonal formalism for multiproduction of isovector mesons at high energy
Redei, L B
1973-01-01
Unitary eikonal models for multiproduction of isovector mesons are discussed in general terms. A closed analytic expression is derived for the partial production cross sections and for the meson multiplicity moments. A simple class of models is discussed in more detail. (11 refs).
Point transformations and renormalization in the unitary gauge. III. Renormalization effects
International Nuclear Information System (INIS)
Sherry, T.N.
1976-06-01
An analysis of two simple gauge theory models is continued using point transformations rather than gauge transformations. The renormalization constants are examined directly in two gauges, the renormalization (Landau) and unitary gauges. The result is that the individual coupling constant renormalizations are identical when calculated in each of the above two gauges, although the wave-function and proper vertex renormalizations differ
Beyond the Tipping Point: Issues of Racial Diversity in Magnet Schools Following Unitary Status
Smrekar, Claire
2009-01-01
This article uses qualitative case study methodology to examine why the racial composition of magnet schools in Nashville, Tennessee, has shifted to predominantly African American in the aftermath of unitary status. The article compares the policy contexts and parents' reasons for choosing magnet schools at two points in time--under court order…
J(l)-unitary factorization and the Schur algorithm for Nevanlinna functions in an indefinite setting
Alpay, D.; Dijksma, A.; Langer, H.
2006-01-01
We introduce a Schur transformation for generalized Nevanlinna functions and show that it can be used in obtaining the unique minimal factorization of a class of rational J(l)-unitary 2 x 2 matrix functions into elementary factors from the same class. (c) 2006 Elsevier Inc. All rights reserved.
Unitary-model-operator approach to Λ17O and lambda-nucleon effective interaction
International Nuclear Information System (INIS)
Fujii, Shinichiro; Okamoto, Ryoji; Suzuki, Kenji
1998-01-01
The unitary-model-operator approach (UMOA) is applied to Λ 17 O. A lambda-nucleon effective interaction is derived, taking the coupling of the sigma-nucleon channel into account. The lambda single-particle energies are calculated for the Os 1/2 , Op 3/2 and Op 1/2 states employing the Nijmegen soft-core potential. (author)
The Bogolubov Representation of the Polaron Model and Its Completely Integrable RPA-Approximation
International Nuclear Information System (INIS)
Bogolubov, Nikolai N. Jr.; Prykarpatsky, Yarema A.; Ghazaryan, Anna A.
2009-12-01
The polaron model in ionic crystal is studied in the N. Bogolubov representation using a special RPA-approximation. A new exactly solvable approximated polaron model is derived and described in detail. Its free energy at finite temperature is calculated analytically. The polaron free energy in the constant magnetic field at finite temperature is also discussed. Based on the structure of the N. Bogolubov unitary transformed polaron Hamiltonian a very important new result is stated: the full polaron model is exactly solvable. (author)
Intuition & reason: re-assessing dual-process theories with representational sub-activation
Trafford, James; Tillas, Alexandros
2015-01-01
There is a prevalent distinction in the literature on reasoning, between Type-1 processes, (fast, automatic, associative, heuristic and intuitive); and Type-2 processes (rule-based, analytical and reflective). In this paper, we follow up recent empirical evidence [De Neys (2006b); Osman (2013)] in favour of a unitary cognitive system. More specifically, we suggest that intuitions (T1-processes) are sub-activated representations, which are in turn influenced by the weightings of the connection...
Path integral for coherent states of the dynamical U2 group and U2/1 supergroup
International Nuclear Information System (INIS)
Kochetov, E.A.
1992-01-01
A part-integral formulation in the representation of coherent states for the unitary U 2 group and U 2/1 supergroup is introduced. U 2 and U 2/1 path integrals are shown to be defined on the coset spaces U 2 /U 1 xU 1 and U 2/1 /U 1/1 xU 1 , respectively. These coset appears as curved classical phase spaces. Partition functions are expressed as path integrals over these spaces. In the case when U 2 and U 2/1 are the dynamical groups, the corresponding path integrals are evaluated with the help of linear fractional transformations that appear as the group (supergroup) action in the coset space (superspace). Possible applications for quantum models are discussed. 9 refs
Directory of Open Access Journals (Sweden)
Allan Victor Ribeiro
2013-07-01
Full Text Available One tool that has been in evidence, especially among young people, is Facebook. It can be classified as a synchronous communication tool that allows communities of people with similar interests to discuss and exchange experiences in real time, promoting the sharing of information and the creation of collective knowledge, even if they being in different parts of the globe. In this paper we show that Facebook can be used as an educational tool to aid the work done in the classroom and the impact of creating closed groups in online social networking for educational purposes. The survey was conducted with a group of students at a private school in Bauru/SP. We investigated the interaction profile of students with a closed group created on Facebook and through a questionnaire analyzed whether students use virtual environments for personal or educational. The survey reveals students perceptions about relevant aspects and the potential use of this tool as teaching-learning strategy.
Cohen-Macaulay representations
Leuschke, Graham J
2012-01-01
This book is a comprehensive treatment of the representation theory of maximal Cohen-Macaulay (MCM) modules over local rings. This topic is at the intersection of commutative algebra, singularity theory, and representations of groups and algebras. Two introductory chapters treat the Krull-Remak-Schmidt Theorem on uniqueness of direct-sum decompositions and its failure for modules over local rings. Chapters 3-10 study the central problem of classifying the rings with only finitely many indecomposable MCM modules up to isomorphism, i.e., rings of finite CM type. The fundamental material--ADE/simple singularities, the double branched cover, Auslander-Reiten theory, and the Brauer-Thrall conjectures--is covered clearly and completely. Much of the content has never before appeared in book form. Examples include the representation theory of Artinian pairs and Burban-Drozd's related construction in dimension two, an introduction to the McKay correspondence from the point of view of maximal Cohen-Macaulay modules, Au...
Directory of Open Access Journals (Sweden)
Alexsandro Medeiros do Nascimento
2007-01-01
Full Text Available O estudo objetivou acessar a estrutura da representação social da morte em equipes multiprofissionais de saúde na interface com a religiosidade, no que esta interfere nas significações atribuídas à morte por esta população em específico. Utilizou-se um instrumento com questões abertas e fechadas sobre a morte e o morrer, bem como sobre a vivência religiosa singular dos participantes. Protocolos escritos foram capturados em uma amostra de 80 profissionais (49 médicos, 13 psicólogas, 18 enfermeiras pertencentes a 10 equipes multiprofissionais de saúde. Estes foram analisados através de Análise de Conteúdo e de Análise de Estrutura de Similaridade (SSA e interpretados pela Teoria das Representações Sociais. Os dados revelaram uma interferência expressiva das crenças religiosas na estruturação da representação da Morte.The study aims to investigate the structure of social representation of death in a Healthcare professional group establishing an interface with religiosity and how the latter interferes in the meaning attributed to death by this specific population. Open and closed questions on death or the act of dying, and on the singular religious experience of the participants were applied. Written protocols were collected from a sample of 80 professionals (49 physicians, 13 psychologists, and 18 nurses, which were analyzed according to content analysis and non-metric multidimensional analysis, SSA (Similarity Structure Analysis, and interpreted according to the theory of Social Representations, revealing a significant interference of religious believes in the structure of death representation.
LGBT Representations on Facebook : Representations of the Self and the Content
Chu, Yawen
2017-01-01
The topic of LGBT rights has been increasingly discussed and debated over recent years. More and more scholars show their interests in the field of LGBT representations in media. However, not many studies involved LGBT representations in social media. This paper explores LGBT representations on Facebook by analysing posts on an open page and in a private group, including both representations of the self as the identity of sexual minorities, content that is displayed on Facebook and the simila...
Factorizations and physical representations
International Nuclear Information System (INIS)
Revzen, M; Khanna, F C; Mann, A; Zak, J
2006-01-01
A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the decomposition of M into prime numbers. Representations that exhibit the factorization of M into two relatively prime numbers: the kq representation (Zak J 1970 Phys. Today 23 51), and related representations termed q 1 q 2 representations (together with their conjugates) are analysed, as well as a representation that exhibits the complete factorization of M. In this latter representation each quantum number varies in a subspace that is associated with one of the prime numbers that make up M
International Nuclear Information System (INIS)
Olmos, C.
1990-05-01
The restricted holonomy group of a Riemannian manifold is a compact Lie group and its representation on the tangent space is a product of irreducible representations and a trivial one. Each one of the non-trivial factors is either an orthogonal representation of a connected compact Lie group which acts transitively on the unit sphere or it is the isotropy representation of a single Riemannian symmetric space of rank ≥ 2. We prove that, all these properties are also true for the representation on the normal space of the restricted normal holonomy group of any submanifold of a space of constant curvature. 4 refs
Thinking together with material representations
DEFF Research Database (Denmark)
Stege Bjørndahl, Johanne; Fusaroli, Riccardo; Østergaard, Svend
2014-01-01
of an experiment. Qualitative micro-analyses of the group interactions motivate a taxonomy of different roles that the material representations play in the joint epistemic processes: illustration, elaboration and exploration. Firstly, the LEGO blocks were used to illustrate already well-formed ideas in support......-down and bottom-up cognitive processes and division of cognitive labor.......How do material representations such as models, diagrams and drawings come to shape and aid collective, epistemic processes? This study investigated how groups of participants spontaneously recruited material objects (in this case LEGO blocks) to support collective creative processes in the context...
DEFF Research Database (Denmark)
Churchill, Nathan William; Madsen, Kristoffer Hougaard; Mørup, Morten
2016-01-01
flexibility: they only estimate segregated structure and do not model interregional functional connectivity, nor do they account for network variability across voxels or between subjects. To address these issues, this letter develops the functional segregation and integration model (FSIM). This extension......The brain consists of specialized cortical regions that exchange information between each other, reflecting a combination of segregated (local) and integrated (distributed) processes that define brain function. Functional magnetic resonance imaging (fMRI) is widely used to characterize...... brain regions where network expression predicts subject age in the experimental data. Thus, the FSIM is effective at summarizing functional connectivity structure in group-level fMRI, with applications in modeling the relationships between network variability and behavioral/demographic variables....
Extended higher-spin superalgebras and their massless representations
Energy Technology Data Exchange (ETDEWEB)
Konstein, S E; Vasiliev, M A [AN SSSR, Moscow (USSR). Fizicheskij Inst.
1990-02-12
Three two-parameter sequences of infinite-dimensional extended higher-spin superalgebras are constructed, which give rise to consistent equations of motion of interacting gauge fields of all spins in four dimensions. In the Yang-Mills sector of spin-1 gauge fields, these higher-spin superalgebras reduce to u(n) + u(m), o(n) + o(m) and usp(n) + usp(m) with arbitrary integer parameters n {ge} 0 and m {ge} 0 (n and m are assumed to be even for symplectic algebras). Massless unitary representations of the proposed higher-spin superalgebras are analyzed. It is shown that all these superalgebras obey the admissibility condition which requires them to possess massless unitary representations with just the same spectra of spins as follows from the structure of the related higher-spin gauge fields. We argue that the infinite-dimensional (super)algebras listed in this article classify all possible higher-spin rigid (super)symmetries in four dimensions. (orig.).
Non-binary unitary error bases and quantum codes
Energy Technology Data Exchange (ETDEWEB)
Knill, E.
1996-06-01
Error operator bases for systems of any dimension are defined and natural generalizations of the bit-flip/ sign-change error basis for qubits are given. These bases allow generalizing the construction of quantum codes based on eigenspaces of Abelian groups. As a consequence, quantum codes can be constructed form linear codes over {ital Z}{sub {ital n}} for any {ital n}. The generalization of the punctured code construction leads to many codes which permit transversal (i.e. fault tolerant) implementations of certain operations compatible with the error basis.
Continuous unitary transformation approach to pairing interactions in statistical physics
Directory of Open Access Journals (Sweden)
T.Domański
2008-06-01
Full Text Available We apply the flow equation method to the study of the fermion systems with pairing interactions which lead to the BCS instability signalled by the appearance of the off-diagonal order parameter. For this purpose we rederive the continuous Bogoliubov transformation in a fashion of renormalization group procedure where the low and high energy sectors are treated subsequently. We further generalize this procedure to the case of fermions interacting with the discrete boson mode. Andreev-type interactions are responsible for developing a gap in the excitation spectrum. However, the long-range coherence is destroyed due to strong quantum fluctuations.
Adesso, Gerardo; Giampaolo, Salvatore M.; Illuminati, Fabrizio
2007-10-01
We present a geometric approach to the characterization of separability and entanglement in pure Gaussian states of an arbitrary number of modes. The analysis is performed adapting to continuous variables a formalism based on single subsystem unitary transformations that has been recently introduced to characterize separability and entanglement in pure states of qubits and qutrits [S. M. Giampaolo and F. Illuminati, Phys. Rev. A 76, 042301 (2007)]. In analogy with the finite-dimensional case, we demonstrate that the 1×M bipartite entanglement of a multimode pure Gaussian state can be quantified by the minimum squared Euclidean distance between the state itself and the set of states obtained by transforming it via suitable local symplectic (unitary) operations. This minimum distance, corresponding to a , uniquely determined, extremal local operation, defines an entanglement monotone equivalent to the entropy of entanglement, and amenable to direct experimental measurement with linear optical schemes.
Dynamics of Three-Body Correlations in Quenched Unitary Bose Gases
Colussi, V. E.; Corson, J. P.; D'Incao, J. P.
2018-03-01
We investigate dynamical three-body correlations in the Bose gas during the earliest stages of evolution after a quench to the unitary regime. The development of few-body correlations is theoretically observed by determining the two- and three-body contacts. We find that the growth of three-body correlations is gradual compared to two-body correlations. The three-body contact oscillates coherently, and we identify this as a signature of Efimov trimers. We show that the growth of three-body correlations depends nontrivially on parameters derived from both the density and Efimov physics. These results demonstrate the violation of scaling invariance of unitary bosonic systems via the appearance of log-periodic modulation of three-body correlations.
International Nuclear Information System (INIS)
Adesso, Gerardo; Giampaolo, Salvatore M.; Illuminati, Fabrizio
2007-01-01
We present a geometric approach to the characterization of separability and entanglement in pure Gaussian states of an arbitrary number of modes. The analysis is performed adapting to continuous variables a formalism based on single subsystem unitary transformations that has been recently introduced to characterize separability and entanglement in pure states of qubits and qutrits [S. M. Giampaolo and F. Illuminati, Phys. Rev. A 76, 042301 (2007)]. In analogy with the finite-dimensional case, we demonstrate that the 1xM bipartite entanglement of a multimode pure Gaussian state can be quantified by the minimum squared Euclidean distance between the state itself and the set of states obtained by transforming it via suitable local symplectic (unitary) operations. This minimum distance, corresponding to a, uniquely determined, extremal local operation, defines an entanglement monotone equivalent to the entropy of entanglement, and amenable to direct experimental measurement with linear optical schemes
The solution space of the unitary matrix model string equation and the Sato Grassmannian
International Nuclear Information System (INIS)
Anagnostopoulos, K.N.; Bowick, M.J.; Schwarz, A.
1992-01-01
The space of all solutions to the string equation of the symmetric unitary one-matrix model is determined. It is shown that the string equations is equivalent to simple conditions on points V 1 and V 2 in the big cell Gr (0) of the Sato Grassmannian Gr. This is a consequence of a well-defined continuum limit in which the string equation has the simple form [P, 2 - ]=1, with P and 2 - 2x2 matrices of differential operators. These conditions on V 1 and V 2 yield a simple system of first order differential equations whose analysis determines the space of all solutions to the string equation. This geometric formulation leads directly to the Virasoro constraints L n (n≥0), where L n annihilate the two modified-KdV τ-functions whose product gives the partition function of the Unitary Matrix Model. (orig.)
Non-unitary neutrino mixing and CP violation in the minimal inverse seesaw model
International Nuclear Information System (INIS)
Malinsky, Michal; Ohlsson, Tommy; Xing, Zhi-zhong; Zhang He
2009-01-01
We propose a simplified version of the inverse seesaw model, in which only two pairs of the gauge-singlet neutrinos are introduced, to interpret the observed neutrino mass hierarchy and lepton flavor mixing at or below the TeV scale. This 'minimal' inverse seesaw scenario (MISS) is technically natural and experimentally testable. In particular, we show that the effective parameters describing the non-unitary neutrino mixing matrix are strongly correlated in the MISS, and thus, their upper bounds can be constrained by current experimental data in a more restrictive way. The Jarlskog invariants of non-unitary CP violation are calculated, and the discovery potential of such new CP-violating effects in the near detector of a neutrino factory is discussed.
International Nuclear Information System (INIS)
Namgung, W.
1991-01-01
The well known requirement that physical theories should be gauge independent is not so apparent in the actual calculation of gauge theories, especially in the perturbative approach. In this paper the authors show that the Weyl, Coulomb, and unitary gauges of the scalar QED are manifestly equivalent in the context of the functional Schrodinger picture. Further, the three gauge conditions are shown equivalent to the covariant gauge in the way that they correspond to some specific cases of the latter
Prats, J. M.; Lopez-Aguilar, F.
1996-01-01
Using unitary transformations, we express the Kondo lattice Hamiltonian in terms of fermionic operators that annihilate the ground state of the interacting system and that represent the best possible approximations to the actual charged excitations. In this way, we obtain an effective Hamiltonian which, for small couplings, consists in a kinetic term for conduction electrons and holes, an RKKY-like term, and a renormalized Kondo interaction. The physical picture of the system implied by this ...
High-energy properties of a class of unitary eikonal models for multiproduction
Redei, L B
1974-01-01
The high-energy properties of a simple class of unitary, crossing- symmetric eikonal models of multiproduction are discussed on the basis of the general closed expression given for the S-matrix elements in a previous publication. In particular, the high-energy behaviour of the multiplicity moments is discussed and it is shown that the KNO scaling relation emerges in a very natural fashion in this class of models. (8 refs).
On the reconstruction of a unitary matrix from its moduli. Existence of continuous ambiguities
International Nuclear Information System (INIS)
Auberson, G.
1989-01-01
It is shown that, for an n x n unitary matrix with n ≥ 4, the knowledge of the moduli of its elements is not always sufficient to determine this matrix up to 'trivial' or 'discrete' ambiguities. Using a parametrization a la Kobayashi-Maskawa in the case n=4, we exhibit various configurations of the moduli for which a continuous ambiguity appears (i.e., some non-trivial phase remains free). (orig.)
Entanglement Capacity of Two-Qubit Unitary Operator with the Help of Auxiliary System
International Nuclear Information System (INIS)
Hu Baolin; Di Yaomin
2007-01-01
The entanglement capacity of general two-qubit unitary operators is studied when auxiliary systems are allowed, and the analytical results based on linear entropy when input states are disentangled are given. From the results the condition for perfect entangler, α 1 = α 2 = π/4, is obtained. Contrary to the case without auxiliary system, the parameter α 3 may play active role to the entanglement capacity when auxiliary systems are allowed.
Massless scalar field in de Sitter spacetime: unitary quantum time evolution
International Nuclear Information System (INIS)
Cortez, Jerónimo; Blas, Daniel Martín-de; Marugán, Guillermo A Mena; Velhinho, José M
2013-01-01
We prove that, under the standard conformal scaling, a free scalar field in de Sitter spacetime admits an O(4)-invariant Fock quantization such that time evolution is unitarily implemented. Since this applies in particular to the massless case, this result disproves previous claims in the literature. We discuss the relationship between this quantization with unitary dynamics and the family of O(4)-invariant Hadamard states given by Allen and Folacci, as well as with the Bunch–Davies vacuum. (paper)
Optimal control landscape for the generation of unitary transformations with constrained dynamics
International Nuclear Information System (INIS)
Hsieh, Michael; Wu, Rebing; Rabitz, Herschel; Lidar, Daniel
2010-01-01
The reliable and precise generation of quantum unitary transformations is essential for the realization of a number of fundamental objectives, such as quantum control and quantum information processing. Prior work has explored the optimal control problem of generating such unitary transformations as a surface-optimization problem over the quantum control landscape, defined as a metric for realizing a desired unitary transformation as a function of the control variables. It was found that under the assumption of nondissipative and controllable dynamics, the landscape topology is trap free, which implies that any reasonable optimization heuristic should be able to identify globally optimal solutions. The present work is a control landscape analysis, which incorporates specific constraints in the Hamiltonian that correspond to certain dynamical symmetries in the underlying physical system. It is found that the presence of such symmetries does not destroy the trap-free topology. These findings expand the class of quantum dynamical systems on which control problems are intrinsically amenable to a solution by optimal control.
Unitary W-algebras and three-dimensional higher spin gravities with spin one symmetry
International Nuclear Information System (INIS)
Afshar, Hamid; Creutzig, Thomas; Grumiller, Daniel; Hikida, Yasuaki; Rønne, Peter B.
2014-01-01
We investigate whether there are unitary families of W-algebras with spin one fields in the natural example of the Feigin-Semikhatov W_n"("2")-algebra. This algebra is conjecturally a quantum Hamiltonian reduction corresponding to a non-principal nilpotent element. We conjecture that this algebra admits a unitary real form for even n. Our main result is that this conjecture is consistent with the known part of the operator product algebra, and especially it is true for n=2 and n=4. Moreover, we find certain ranges of allowed levels where a positive definite inner product is possible. We also find a unitary conformal field theory for every even n at the special level k+n=(n+1)/(n−1). At these points, the W_n"("2")-algebra is nothing but a compactified free boson. This family of W-algebras admits an ’t Hooft limit. Further, in the case of n=4, we reproduce the algebra from the higher spin gravity point of view. In general, gravity computations allow us to reproduce some leading coefficients of the operator product.
On the complete classification of unitary N=2 minimal superconformal field theories
Energy Technology Data Exchange (ETDEWEB)
Gray, Oliver
2009-08-03
Aiming at a complete classification of unitary N=2 minimal models (where the assumption of space-time supersymmetry has been dropped), it is shown that each candidate for a modular invariant partition function of such a theory is indeed the partition function of a minimal model. A family of models constructed via orbifoldings of either the diagonal model or of the space-time supersymmetric exceptional models demonstrates that there exists a unitary N=2 minimal model for every one of the allowed partition functions in the list obtained from Gannon's work. Kreuzer and Schellekens' conjecture that all simple current invariants can be obtained as orbifolds of the diagonal model, even when the extra assumption of higher-genus modular invariance is dropped, is confirmed in the case of the unitary N=2 minimal models by simple counting arguments. We nd a nice characterisation of the projection from the Hilbert space of a minimal model with k odd to its modular invariant subspace, and we present a new simple proof of the superconformal version of the Verlinde formula for the minimal models using simple currents. Finally we demonstrate a curious relation between the generating function of simple current invariants and the Riemann zeta function. (orig.)
International Nuclear Information System (INIS)
Luca, Gheorghe
2004-01-01
In our country, within the studies, on which the development strategies of power output are based on, the assessment of the economical efficiency of the use of two main energetic resources, the fuel used in cogeneration thermal power plants and the water used in hydropower plants respectively, was made in compliance with non-unitary specific norms. In contradiction with the degree of utilization of hydroelectric resources, realized all over the world in the developed countries (80-90%) resulted that in our country, where the degree of utilization is only 40%, the use of hydroelectric potential is not yet justified from technical-economical point of view. This anomaly was determined by the cause of non-unitary assessment of the economic efficiency for the cogeneration thermo-power plants and hydropower plants. This paper presents comparatively the elements, which were to the basis of the assessment of the economic efficiency for two types of electrical power plants, and one presents a proposal in the aim to perform a unitary assessment of the economical efficiency by applying efficiently the laws in force. (author)
On the complete classification of unitary N=2 minimal superconformal field theories
Energy Technology Data Exchange (ETDEWEB)
Gray, Oliver
2009-08-03
Aiming at a complete classification of unitary N=2 minimal models (where the assumption of space-time supersymmetry has been dropped), it is shown that each candidate for a modular invariant partition function of such a theory is indeed the partition function of a minimal model. A family of models constructed via orbifoldings of either the diagonal model or of the space-time supersymmetric exceptional models demonstrates that there exists a unitary N=2 minimal model for every one of the allowed partition functions in the list obtained from Gannon's work. Kreuzer and Schellekens' conjecture that all simple current invariants can be obtained as orbifolds of the diagonal model, even when the extra assumption of higher-genus modular invariance is dropped, is confirmed in the case of the unitary N=2 minimal models by simple counting arguments. We nd a nice characterisation of the projection from the Hilbert space of a minimal model with k odd to its modular invariant subspace, and we present a new simple proof of the superconformal version of the Verlinde formula for the minimal models using simple currents. Finally we demonstrate a curious relation between the generating function of simple current invariants and the Riemann zeta function. (orig.)
On the complete classification of unitary N=2 minimal superconformal field theories
International Nuclear Information System (INIS)
Gray, Oliver
2009-01-01
Aiming at a complete classi cation of unitary N=2 minimal models (where the assumption of space-time supersymmetry has been dropped), it is shown that each candidate for a modular invariant partition function of such a theory is indeed the partition function of a minimal model. A family of models constructed via orbifoldings of either the diagonal model or of the space-time supersymmetric exceptional models demonstrates that there exists a unitary N=2 minimal model for every one of the allowed partition functions in the list obtained from Gannon's work. Kreuzer and Schellekens' conjecture that all simple current invariants can be obtained as orbifolds of the diagonal model, even when the extra assumption of higher-genus modular invariance is dropped, is confirmed in the case of the unitary N=2 minimal models by simple counting arguments. We nd a nice characterisation of the projection from the Hilbert space of a minimal model with k odd to its modular invariant subspace, and we present a new simple proof of the superconformal version of the Verlinde formula for the minimal models using simple currents. Finally we demonstrate a curious relation between the generating function of simple current invariants and the Riemann zeta function. (orig.)
International Nuclear Information System (INIS)
Lindesay, James V
2002-01-01
Starting from a unitary, Lorentz invariant two-particle scattering amplitude, we show how to use an identification and replacement process to construct a unique, unitary particle-antiparticle amplitude. This process differs from conventional on-shell Mandelstam s,t,u crossing in that the input and constructed amplitudes can be off-diagonal and off-energy shell. Further, amplitudes are constructed using the invariant parameters which are appropriate to use as driving terms in the multi-particle, multichannel nonperturbative, cluster decomposable, relativistic scattering equations of the Faddeev-type integral equations recently presented by Alfred, Kwizera, Lindesay and Noyes. It is therefore anticipated that when so employed, the resulting multi-channel solutions will also be unitary. The process preserves the usual particle-antiparticle symmetries. To illustrate this process, we construct a J=0 scattering length model chosen for simplicity. We also exhibit a class of physical models which contain a finite quantum mass parameter and are Lorentz invariant. These are constructed to reduce in the appropriate limits, and with the proper choice of value and sign of the interaction parameter, to the asymptotic solution of the nonrelativistic Coulomb problem, including the forward scattering singularity , the essential singularity in the phase, and the Bohr bound-state spectrum
The Weyl group of the Cuntz algebra
DEFF Research Database (Denmark)
Conti, Roberto; Hong, Jeong Hee; Szymanski, Wojciech
2012-01-01
The Weyl group of the Cuntz algebra O_n is investigated. This is (isomorphic to) the group of polynomial automorphisms lambda_u of O_n, namely those induced by unitaries u that can be written as finite sums of words in the canonical generating isometries S_i and their adjoints. A necessary...
Multi-representation based on scientific investigation for enhancing students’ representation skills
Siswanto, J.; Susantini, E.; Jatmiko, B.
2018-03-01
This research aims to implementation learning physics with multi-representation based on the scientific investigation for enhancing students’ representation skills, especially on the magnetic field subject. The research design is one group pretest-posttest. This research was conducted in the department of mathematics education, Universitas PGRI Semarang, with the sample is students of class 2F who take basic physics courses. The data were obtained by representation skills test and documentation of multi-representation worksheet. The Results show gain analysis value of .64 which means some medium improvements. The result of t-test (α = .05) is shows p-value = .001. This learning significantly improves students representation skills.
Non-unitary boson mapping and its application to nuclear collective motions
International Nuclear Information System (INIS)
Takada, Kenjiro
2001-01-01
First, the general theory of boson mapping for even-number many-fermion systems is surveyed. In order to overcome the confusion concerning the so-called unphysical or spurious states in the boson mapping, the correct concept of the unphysical states is precisely given in a clear-cut way. Next, a method to apply the boson mapping to a truncated many-fermion Hilbert space consisting of collective phonons is proposed, by putting special emphasis on the Dyson-type non-unitary boson mapping. On the basis of this method, it becomes possible for the first time to apply the Dyson-type boson mapping to analyses of collective motions in realistic nuclei. This method is also extended to be applicable to odd-number-fermion systems. As known well, the Dyson-type boson mapping is a non-unitary transformation and it gives a non-Hermitian boson Hamiltonian. It is not easy (but not impossible) to solve the eigenstates of the non-Hermitian Hamiltonian. A Hermitian treatment of this non-Hermitian eigenvalue problem is discussed and it is shown that this treatment is a very good approximation. using this Hermitian treatment, we can obtain the normal-ordered Holstein-Primakoff-type boson expansion in the multi-collective-phonon subspace. Thereby the convergence of the boson expansion can be tested. Some examples of application of the Dyson-type non-unitary boson mapping to simplified models and realistic nuclei are also shown, and we can see that it is quite useful for analysis of the collective motions in realistic nuclei. In contrast to the above-mentioned ordinary type of boson mapping, which may be called a a 'static' boson mapping, the Dyson-type non-unitary self-consistent-collective-coordinate method is discussed. The latter is, so to speak, a 'dynamical' boson mapping, which is a dynamical extension of the ordinary boson mapping to be capable to include the coupling effects from the non-collective degrees of freedom self-consistently.Thus all of the Dyson-type non-unitary boson
Chevalley, Claude
2018-01-01
The standard text on the subject for many years, this introductory treatment covers classical linear groups, topological groups, manifolds, analytic groups, differential calculus of Cartan, and compact Lie groups and their representations. 1946 edition.
Directory of Open Access Journals (Sweden)
Patrícia Déa Braga
2010-01-01
Full Text Available Diante da grande preocupação com a estética corporal demonstrada por um grupo de adolescentes de classes populares, o presente estudo teve como objetivo conhecer e analisar as suas representações sociais de corpo. Tratou-se de investigação de abordagem qualitativa realizada com adolescentes trabalhadores vinculados ao Centro Salesiano do Menor, em Vitória (ES. Uma amostra aleatória foi selecionada de um grupo de 334 sujeitos. Oito meninas e sete meninos foram abordados por meio de entrevista não-estruturada. A partir da análise de suas falas, foi realizada uma categorização e utilizada a teoria das representações sociais para sua discussão. Os resultados apontaram que a percepção de corpo, tanto para meninos quanto para as meninas, está voltada para as idéias de proporcionalidade, normalidade e perfeição. Quanto às consequências de não ter o corpo ideal, ambos apontaram situações como exclusão, doenças, infelicidade e até morte. Aprofundar o conhecimento sobre a percepção, os pensamentos e sentimentos dos adolescentes relativos ao corpo pode contribuir para subsidiar intervenções nesse grupo, ampliando significativamente o âmbito de atuação dos profissionais na área da saúde.In view of the great body aesthetic concern demonstrated by a group of adolescents from popular classes, this study had the purpose of getting to know and analyze the social representations of the body. It investigated the qualitative approach carried out with adolescent workers from the Centro Salesiano do Menor, in Vitória, Espírito Santo State. A random sample was selected from a group of 334 individuals. Eight girls and seven boys were approached by means of non-structured interview. From the analysis of their speeches, a categorization was performed and the theory of the Social Representations was used for discussion. The results pointed out that body perception, for boys as well as for girls, are focused on the ideas of
Directory of Open Access Journals (Sweden)
Seabra Daniel
2017-03-01
Full Text Available The following text relates to a more recent approach to the problem of hooliganism and the Ultra Movement. It does not focus on a broad theory aimed to explain these two phenomena, but rather concentrates on the use of concepts that are relevant for a multifaceted understanding of them. Therefore, this text is the result of an investigation carried out on the four Ultra groups who support clubs in Oporto.
Rumelhart, David E.; Norman, Donald A.
This paper reviews work on the representation of knowledge from within psychology and artificial intelligence. The work covers the nature of representation, the distinction between the represented world and the representing world, and significant issues concerned with propositional, analogical, and superpositional representations. Specific topics…
Preon representations and composite models
International Nuclear Information System (INIS)
Kang, Kyungsik
1982-01-01
This is a brief report on the preon models which are investigated by In-Gyu Koh, A. N. Schellekens and myself and based on complex, anomaly-free and asymptotically free representations of SU(3) to SU(8), SO(4N+2) and E 6 with no more than two different preons. Complete list of the representations that are complex anomaly-free and asymptotically free has been given by E. Eichten, I.-G. Koh and myself. The assumptions made about the ground state composites and the role of Fermi statistics to determine the metaflavor wave functions are discussed in some detail. We explain the method of decompositions of tensor products with definite permutation properties which has been developed for this purpose by I.-G. Koh, A.N. Schellekens and myself. An example based on an anomaly-free representation of the confining metacolor group SU(5) is discussed
Representational constraints on children's suggestibility.
Ceci, Stephen J; Papierno, Paul B; Kulkofsky, Sarah
2007-06-01
In a multistage experiment, twelve 4- and 9-year-old children participated in a triad rating task. Their ratings were mapped with multidimensional scaling, from which euclidean distances were computed to operationalize semantic distance between items in target pairs. These children and age-mates then participated in an experiment that employed these target pairs in a story, which was followed by a misinformation manipulation. Analyses linked individual and developmental differences in suggestibility to children's representations of the target items. Semantic proximity was a strong predictor of differences in suggestibility: The closer a suggested distractor was to the original item's representation, the greater was the distractor's suggestive influence. The triad participants' semantic proximity subsequently served as the basis for correctly predicting memory performance in the larger group. Semantic proximity enabled a priori counterintuitive predictions of reverse age-related trends to be confirmed whenever the distance between representations of items in a target pair was greater for younger than for older children.
Directory of Open Access Journals (Sweden)
Silvana Inés Weller
1997-09-01
Full Text Available El objetivo de este trabajo fue indagar la existencia de diferentes "grupos" de jóvenes en función de sus representaciones alrededor de la salud y la enfermedad. En la construcción de estos "grupos" se busca incorporar conceptos tradicionalmente relegados al estudio de la subjetividad. Se trabajó con una encuesta cerrada que se aplicó sobre 400 jóvenes escolarizados. El procesamiento de los datos se realizó con el análisis de correspondencias múltiples, una técnica de análisis multivariado especialmente diseñada para trabajar con un alto número de variables cualitativas. El estudio permitió despejar ocho "tipos" de jóvenes los asustados, los que cierran los ojos, los hipocondríacos, los sensuales, los felices, los amargados, los que miran al mundo y los que miran su ombligo. Estos resultados indicarían la necesidad de diversificar las estrategias de indagación e intervención en terreno dirigidas a esta población.This study explores the presence of different "groups" of adolescents based on their representations of health and disease. Concepts traditionally linked to the study of subjectivity were incorporated into the building of these "groups". Four hundred students participated in the survey. Data were analyzed through multiple correspondence analysis, a multivariate approach especially designed to work with large numbers of qualitative variables. Eight groups of adolescents were detected, described as follows: frightened; tends to close eyes; hypochondriac; sensual; happy; embittered; outgoing (looks out on the world; and introspective (contemplates own navel. The results highlight the importance of diversifying research and interventions focusing on this age bracket.
Helsy, I.; Maryamah; Farida, I.; Ramdhani, M. A.
2017-09-01
This study aimed to describe the application of teaching materials, analyze the increase in the ability of students to connect the three levels of representation and student responses after application of multiple representations based teaching materials chemistry. The method used quasi one-group pretest-posttest design to 71 students. The results showed the application of teaching materials carried 88% with very good category. A significant increase ability to connect the three levels of representation of students after the application of multiple representations based teaching materials chemistry with t-value > t-crit (11.402 > 1.991). Recapitulation N-gain pretest and posttest showed relatively similar for all groups is 0.6 criterion being achievement. Students gave a positive response to the application of multiple representations based teaching materials chemistry. Students agree teaching materials used in teaching chemistry (88%), and agrees teaching materials to provide convenience in connecting the three levels of representation (95%).
Analysis of SPECTROX method of multigroup spectra calculation in unitary reactor cells
International Nuclear Information System (INIS)
Leite, Sergio de Q. Bogado
2005-01-01
The thermal neutron spectrum in a lattice cell is strongly space-dependent. In addition, in many situations, as for example in core design calculations, a more precise energetic and spatial representation of the flux is needed, which cannot be provided by few group diffusion theory. In such cases, the well-known SPECTROX method, employing diffusion theory in the moderator, where it is supposed sufficiently accurate, and collision probability theory in the fuel, together with appropriate interface current relations for assuring neutron conservation, has been widely used by WIMS as well as other codes. In this work, the approximations leading to the SPECTROX equations are reviewed and the calculated average fluxes in the fuel are compared with accurate values obtained from the solution of the transport equation by the FN method. (author)
Realization of a unique time evolution unitary operator in Klein Gordon theory
International Nuclear Information System (INIS)
Balasubramanian, T.S.; Bhatia, S.Kr.
1986-01-01
The scattering theory for the Klein Gordon equation, with time-dependent potential and in a non-static space-time, is considered. Using the Klein Gordon equation formulated in the Hilbert space L 2 (R 3 ) and the Einstein's relativistic equation in the space L 2 (R 3 ,dx) and establishing the equivalence of the vacuum states of their linearized forms in the Hilbert space L 2 (R 3 ) with the help of unique symmetric symplectic operator, the time evolution unitary operator U(t) has been fixed for the Klein Gordon eqution, incorporating either the positive or negative frequencies, in the infinite dimensional Hilbert space L 2 (R 3 ). (author)
A gauge-invariant chiral unitary framework for kaon photo- and electroproduction on the proton
International Nuclear Information System (INIS)
Borasoy, B.; Bruns, P.C.; Nissler, R.; Meissner, U.G.
2007-01-01
We present a gauge-invariant approach to photoproduction of mesons on nucleons within a chiral unitary framework. The interaction kernel for meson-baryon scattering is derived from the chiral effective Lagrangian and iterated in a Bethe-Salpeter equation. Within the leading-order approximation to the interaction kernel, data on kaon photoproduction from SAPHIR, CLAS and CBELSA/TAPS are analyzed in the threshold region. The importance of gauge invariance and the precision of various approximations in the interaction kernel utilized in earlier works are discussed. (orig.)
On Parseval Wavelet Frames with Two or Three Generators via the Unitary Extension Principle
DEFF Research Database (Denmark)
Christensen, Ole; Kim, Hong Oh; Kim, Rae Young
2014-01-01
The unitary extension principle (UEP) by A. Ron and Z. Shen yields a sufficient condition for the construction of Parseval wavelet frames with multiple generators. In this paper we characterize the UEP-type wavelet systems that can be extended to a Parseval wavelet frame by adding just one UEP......-type wavelet system. We derive a condition that is necessary for the extension of a UEP-type wavelet system to any Parseval wavelet frame with any number of generators and prove that this condition is also sufficient to ensure that an extension with just two generators is possible....
Pore dimensions and the role of occupancy in unitary conductance of Shaker K channels
Díaz-Franulic, Ignacio; Sepúlveda, Romina V.; Navarro-Quezada, Nieves; González-Nilo, Fernando
2015-01-01
K channels mediate the selective passage of K+ across the plasma membrane by means of intimate interactions with ions at the pore selectivity filter located near the external face. Despite high conservation of the selectivity filter, the K+ transport properties of different K channels vary widely, with the unitary conductance spanning a range of over two orders of magnitude. Mutation of Pro475, a residue located at the cytoplasmic entrance of the pore of the small-intermediate conductance K channel Shaker (Pro475Asp (P475D) or Pro475Gln (P475Q)), increases Shaker’s reported ∼20-pS conductance by approximately six- and approximately threefold, respectively, without any detectable effect on its selectivity. These findings suggest that the structural determinants underlying the diversity of K channel conductance are distinct from the selectivity filter, making P475D and P475Q excellent probes to identify key determinants of the K channel unitary conductance. By measuring diffusion-limited unitary outward currents after unilateral addition of 2 M sucrose to the internal solution to increase its viscosity, we estimated a pore internal radius of capture of ∼0.82 Å for all three Shaker variants (wild type, P475D, and P475Q). This estimate is consistent with the internal entrance of the Kv1.2/2.1 structure if the effective radius of hydrated K+ is set to ∼4 Å. Unilateral exposure to sucrose allowed us to estimate the internal and external access resistances together with that of the inner pore. We determined that Shaker resistance resides mainly in the inner cavity, whereas only ∼8% resides in the selectivity filter. To reduce the inner resistance, we introduced additional aspartate residues into the internal vestibule to favor ion occupancy. No aspartate addition raised the maximum unitary conductance, measured at saturating [K+], beyond that of P475D, suggesting an ∼200-pS conductance ceiling for Shaker. This value is approximately one third of the maximum
Quantum entanglement: the unitary 8-vertex braid matrix with imaginary rapidity
International Nuclear Information System (INIS)
Chakrabarti, Amitabha; Chakraborti, Anirban; Jedidi, Aymen
2010-01-01
We study quantum entanglements induced on product states by the action of 8-vertex braid matrices, rendered unitary with purely imaginary spectral parameters (rapidity). The unitarity is displayed via the 'canonical factorization' of the coefficients of the projectors spanning the basis. This adds one more new facet to the famous and fascinating features of the 8-vertex model. The double periodicity and the analytic properties of the elliptic functions involved lead to a rich structure of the 3-tangle quantifying the entanglement. We thus explore the complex relationship between topological and quantum entanglement. (fast track communication)
Scalar ΛN and ΛΛ interaction in a chiral unitary approach
International Nuclear Information System (INIS)
Sasaki, K.; Oset, E.; Vacas, M. J. Vicente
2006-01-01
We study the central part of the ΛN and ΛΛ potential by considering the correlated and uncorrelated two-meson exchange in addition to the ω exchange contribution. The correlated two-meson exchange is evaluated within a chiral unitary approach. We find that a short-range repulsion is generated by the correlated two-meson potential, which also produces an attraction in the intermediate-distance region. The uncorrelated two-meson exchange produces a sizable attraction in all cases that is counterbalanced by the ω exchange contribution
Cold dilute neutron matter on the lattice. II. Results in the unitary limit
International Nuclear Information System (INIS)
Lee, Dean; Schaefer, Thomas
2006-01-01
This is the second of two articles that investigate cold dilute neutron matter on the lattice using pionless effective field theory. In the unitary limit, where the effective range is zero and scattering length is infinite, simple scaling relations relate thermodynamic functions at different temperatures. When the second virial coefficient is properly tuned, we find that the lattice results obey these scaling relations. We compute the energy per particle, pressure, spin susceptibility, dineutron correlation function, and an upper bound for the superfluid critical temperature
Fortran code for generating random probability vectors, unitaries, and quantum states
Directory of Open Access Journals (Sweden)
Jonas eMaziero
2016-03-01
Full Text Available The usefulness of generating random configurations is recognized in many areas of knowledge. Fortran was born for scientific computing and has been one of the main programming languages in this area since then. And several ongoing projects targeting towards its betterment indicate that it will keep this status in the decades to come. In this article, we describe Fortran codes produced, or organized, for the generation of the following random objects: numbers, probability vectors, unitary matrices, and quantum state vectors and density matrices. Some matrix functions are also included and may be of independent interest.
Evolved Representation and Computational Creativity
Directory of Open Access Journals (Sweden)
Ashraf Fouad Hafez Ismail
2001-01-01
Full Text Available Advances in science and technology have influenced designing activity in architecture throughout its history. Observing the fundamental changes to architectural designing due to the substantial influences of the advent of the computing era, we now witness our design environment gradually changing from conventional pencil and paper to digital multi-media. Although designing is considered to be a unique human activity, there has always been a great dependency on design aid tools. One of the greatest aids to architectural design, amongst the many conventional and widely accepted computational tools, is the computer-aided object modeling and rendering tool, commonly known as a CAD package. But even though conventional modeling tools have provided designers with fast and precise object handling capabilities that were not available in the pencil-and-paper age, they normally show weaknesses and limitations in covering the whole design process.In any kind of design activity, the design worked on has to be represented in some way. For a human designer, designs are for example represented using models, drawings, or verbal descriptions. If a computer is used for design work, designs are usually represented by groups of pixels (paintbrush programs, lines and shapes (general-purpose CAD programs or higher-level objects like ‘walls’ and ‘rooms’ (purpose-specific CAD programs.A human designer usually has a large number of representations available, and can use the representation most suitable for what he or she is working on. Humans can also introduce new representations and thereby represent objects that are not part of the world they experience with their sensory organs, for example vector representations of four and five dimensional objects. In design computing on the other hand, the representation or representations used have to be explicitly defined. Many different representations have been suggested, often optimized for specific design domains
Energy Technology Data Exchange (ETDEWEB)
Bang, Jeongho [Seoul National University, Seoul (Korea, Republic of); Hanyang University, Seoul (Korea, Republic of); Yoo, Seokwon [Hanyang University, Seoul (Korea, Republic of)
2014-12-15
We propose a genetic-algorithm-based method to find the unitary transformations for any desired quantum computation. We formulate a simple genetic algorithm by introducing the 'genetic parameter vector' of the unitary transformations to be found. In the genetic algorithm process, all components of the genetic parameter vectors are supposed to evolve to the solution parameters of the unitary transformations. We apply our method to find the optimal unitary transformations and to generalize the corresponding quantum algorithms for a realistic problem, the one-bit oracle decision problem, or the often-called Deutsch problem. By numerical simulations, we can faithfully find the appropriate unitary transformations to solve the problem by using our method. We analyze the quantum algorithms identified by the found unitary transformations and generalize the variant models of the original Deutsch's algorithm.
Understanding representations in design
DEFF Research Database (Denmark)
Bødker, Susanne
1998-01-01
Representing computer applications and their use is an important aspect of design. In various ways, designers need to externalize design proposals and present them to other designers, users, or managers. This article deals with understanding design representations and the work they do in design....... The article is based on a series of theoretical concepts coming out of studies of scientific and other work practices and on practical experiences from design of computer applications. The article presents alternatives to the ideas that design representations are mappings of present or future work situations...... and computer applications. It suggests that representations are primarily containers of ideas and that representation is situated at the same time as representations are crossing boundaries between various design and use activities. As such, representations should be carriers of their own contexts regarding...
Ren, Shiwei; Ma, Xiaochuan; Yan, Shefeng; Hao, Chengpeng
2013-03-28
A unitary transformation-based algorithm is proposed for two-dimensional (2-D) direction-of-arrival (DOA) estimation of coherent signals. The problem is solved by reorganizing the covariance matrix into a block Hankel one for decorrelation first and then reconstructing a new matrix to facilitate the unitary transformation. By multiplying unitary matrices, eigenvalue decomposition and singular value decomposition are both transformed into real-valued, so that the computational complexity can be reduced significantly. In addition, a fast and computationally attractive realization of the 2-D unitary transformation is given by making a Kronecker product of the 1-D matrices. Compared with the existing 2-D algorithms, our scheme is more efficient in computation and less restrictive on the array geometry. The processing of the received data matrix before unitary transformation combines the estimation of signal parameters via rotational invariance techniques (ESPRIT)-Like method and the forward-backward averaging, which can decorrelate the impinging signalsmore thoroughly. Simulation results and computational order analysis are presented to verify the validity and effectiveness of the proposed algorithm.
Efficient Nonlocal M-Control and N-Target Controlled Unitary Gate Using Non-symmetric GHZ States
Chen, Li-Bing; Lu, Hong
2018-03-01
Efficient local implementation of a nonlocal M-control and N-target controlled unitary gate is considered. We first show that with the assistance of two non-symmetric qubit(1)-qutrit(N) Greenberger-Horne-Zeilinger (GHZ) states, a nonlocal 2-control and N-target controlled unitary gate can be constructed from 2 local two-qubit CNOT gates, 2 N local two-qutrit conditional SWAP gates, N local qutrit-qubit controlled unitary gates, and 2 N single-qutrit gates. At each target node, the two third levels of the two GHZ target qutrits are used to expose one and only one initial computational state to the local qutrit-qubit controlled unitary gate, instead of being used to hide certain states from the conditional dynamics. This scheme can be generalized straightforwardly to implement a higher-order nonlocal M-control and N-target controlled unitary gate by using M non-symmetric qubit(1)-qutrit(N) GHZ states as quantum channels. Neither the number of the additional levels of each GHZ target particle nor that of single-qutrit gates needs to increase with M. For certain realistic physical systems, the total gate time may be reduced compared with that required in previous schemes.
A self-consistency check for unitary propagation of Hawking quanta
Baker, Daniel; Kodwani, Darsh; Pen, Ue-Li; Yang, I.-Sheng
2017-11-01
The black hole information paradox presumes that quantum field theory in curved space-time can provide unitary propagation from a near-horizon mode to an asymptotic Hawking quantum. Instead of invoking conjectural quantum-gravity effects to modify such an assumption, we propose a self-consistency check. We establish an analogy to Feynman’s analysis of a double-slit experiment. Feynman showed that unitary propagation of the interfering particles, namely ignoring the entanglement with the double-slit, becomes an arbitrarily reliable assumption when the screen upon which the interference pattern is projected is infinitely far away. We argue for an analogous self-consistency check for quantum field theory in curved space-time. We apply it to the propagation of Hawking quanta and test whether ignoring the entanglement with the geometry also becomes arbitrarily reliable in the limit of a large black hole. We present curious results to suggest a negative answer, and we discuss how this loss of naive unitarity in QFT might be related to a solution of the paradox based on the soft-hair-memory effect.
Regarding the unitary theory of agonist and antagonist action at presynaptic adrenoceptors.
Kalsner, S; Abdali, S A
2001-06-01
1. The linkage between potentiation of field stimulation-induced noradrenaline release and blockade of the presynaptic inhibitory effect of exogenous noradrenaline by a presynaptic antagonist was examined in superfused rabbit aorta preparations. 2. Rauwolscine clearly potentiated the release of noradrenaline in response to 100 pulses at 2 Hz but reduced the capacity of noradrenaline to inhibit transmitter release to a questionable extent, and then only when comparisons were made with untreated, rather then to rauwolscine-treated, controls. 3. Aortic preparations exposed for 60 min to rauwolscine followed by superfusion with antagonist-free Krebs for 60 min retained the potentiation of stimulation-induced transmitter release but no antagonism of the noradrenaline-induced inhibition could be detected at either of two noradrenaline concentrations when comparisons were made with rauwolscine treated controls. 4. Comparisons of the inhibitory effect of exogenous noradrenaline (1.8 x 10-6 M) on transmitter efflux in the presence and absence of rauwolscine pretreatment revealed that the antagonist enhanced rather than antagonized the presynaptic inhibition by noradrenaline. 5 It is concluded that the unitary hypothesis that asserts that antagonist enhancement of transmitter release and its blockade of noradrenaline induced inhibition are manifestations of a unitary event are not supportable.
Radio-Frequency-Controlled Cold Collisions and Universal Properties of Unitary Bose Gases
Ding, Yijue
This thesis investigates two topics: ultracold atomic collisions in a radio-frequency field and universal properties of a degenerate unitary Bose gas. One interesting point of the unitary Bose gas is that the system has only one length scale, that is, the average interparticle distance. This single parameter determines all properties of the gas, which is called the universality of the system. We first introduce a renormalized contact interaction to extend the validity of the zero-range interaction to large scattering lengths. Then this renormalized interaction is applied to many-body theories to determined those universal relations of the system. From the few-body perspective, we discuss the scattering between atoms in a single-color radio-frequency field. Our motivation is proposing the radio-frequency field as an effective tool to control interactions between cold atoms. Such a technique may be useful in future experiments such as creating phase transitions in spinor condensates. We also discuss the formation of ultracold molecules using radio-freqency fields from a time-dependent approach.
The virial equation of state for unitary fermion thermodynamics with non-Gaussian correlations
International Nuclear Information System (INIS)
Chen Jisheng; Li Jiarong; Wang Yanping; Xia Xiangjun
2008-01-01
We study the roles of the dynamical high order perturbation and statistically non-linear infrared fluctuation/correlation in the virial equation of state for the Fermi gas in the unitary limit. Incorporating the quantum level crossing rearrangement effects, the spontaneously generated entropy departing from the mean-field theory formalism leads to concise thermodynamical expressions. The dimensionless virial coefficients with complex non-local correlations are calculated up to the fourth order for the first time. The virial coefficients of unitary Fermi gas are found to be proportional to those of the ideal quantum gas with integer ratios through a general term formula. Counterintuitively, contrary to those of the ideal bosons (a (0) 2 =-(1/4√2)) or fermions (a (0) 2 =(1/4√2)), the second virial coefficient a 2 of Fermi gas at unitarity is found to be equal to zero. With the vanishing leading order quantum correction, the BCS–BEC crossover thermodynamics manifests the famous pure classical Boyle's law in the Boltzmann regime. The non-Gaussian correlation phenomena can be validated by studying the Joule–Thomson effect
Three-body unitary transformations, three-body forces, and trinucleon bound state properties
International Nuclear Information System (INIS)
Haftel, M.I.
1976-01-01
A three-body unitary transformation method for the study of three-body forces is presented. Starting with a three-body Hamiltonian with two-body forces, unitary transformations are introduced to generate Hamiltonians that have both two- and three-body forces. For cases of physical interest, the two-body forces of the altered Hamiltonians are phase equivalent (for two-body scattering) to the original and the three-body force vanishes when any interparticle distance is large. Specific examples are presented. Applications for studying the possible role of three-body forces in accounting for trinucleon bound state properties are examined. Calculations of the 3 He and 3 H charge form factors and Coulomb energy difference with hyperspherical radial transformations and with conventional N-N potentials are performed. The form factor calculations demonstrate how the proposed method can help obtain improved agreement with experiment by the introduction of appropriate three-body forces. Calculations of the Coulomb energy difference confirm previous estimates concerning charge symmetry breaking in the N-N interaction
Reconstitutable nuclear reactor fuel assembly with unitary removable top nozzle subassembly
International Nuclear Information System (INIS)
Shallenberger, J.M.
1987-01-01
A reconstitutable fuel assembly is described having at least one control rod guide thimble and a top nozzle, the guide thimble including an upper extension, the top nozzle including at least one hold-down spring, an upper hold-down plate and a lower adapter plate, an improved attaching structure removably mounting the top nozzle as a unitary subassembly on the guide thimble. The attaching structure comprises: (a) a coupling member interfitting the lower adapter plate, the upper hold-down plate and the hold-down spring disposed between the plates so as to capture and retain the plates and spring together as a unitary subassembly in which the upper plate is slidably moveable along the coupling member relative to the lower plate with the spring biasing the upper plate away from the lower plate. The coupling member has spaced apart upper and lower portions with a central passageway extending for slidably receiving the upper extension of the guide thimble in a nonattached relationship in which the coupling member is slidably movable relative to the guide thimble extension for respectively inserting and removing the coupling member on and from the guide thimble extension
Democracy and Representation in Paraguay
Directory of Open Access Journals (Sweden)
Liliana Rocío Duarte-Recalde
2017-05-01
Full Text Available This article reviews the electoral accountability dimension as a constitutive mechanism of Paraguayan democracy since 1989, analyzing the factors that limit the representation contained in the administration of the Paraguayan government as a result of the electoral process. We provide an analytic contrast between the democratic principles that guide the Paraguayan electoral institutions and the way their designs are enforced, identifying the gap between formal and informal rules as determinants of political representation. We also describe the barriers that prevent effective access of the population to political participation and competition, the advantages possessed by traditional political parties and interest groups, as well as their implications for democracy. We also review the degree to which elected officials are representative of historically excluded social groups as a result, emphasizing the way women, indigenous and peasant communities have potentially limited power to exercise political influence due to limitations to participation by structural and institutional factors.
Discrimination and the aim of proportional representation
DEFF Research Database (Denmark)
Lippert-Rasmussen, Kasper
2008-01-01
Many organizations, companies, and so on are committed to certain representational aims as regards the composition of their workforce. One motivation for such aims is the assumption that numerical underrepresentation of groups manifests discrimination against them. In this article, I articulate...... representational aims in a way that best captures this rationale. My main claim is that the achievement of such representational aims is reducible to the elimination of the effects of wrongful discrimination on individuals and that this very important concern is, in principle, compatible with the representation...... of discrimination against numerically overrepresented groups, or overlook the innocently different ambitions of some numerically underrepresented groups. In relation to the latter point, I appeal to the fact that many luck egalitarians think justice should be ambition sensitive (but endowment insensitive). Also...
Sequent Calculus Representations for Quantum Circuits
Directory of Open Access Journals (Sweden)
Cameron Beebe
2016-06-01
Full Text Available When considering a sequent-style proof system for quantum programs, there are certain elements of quantum mechanics that we may wish to capture, such as phase, dynamics of unitary transformations, and measurement probabilities. Traditional quantum logics which focus primarily on the abstract orthomodular lattice theory and structures of Hilbert spaces have not satisfactorily captured some of these elements. We can start from 'scratch' in an attempt to conceptually characterize the types of proof rules which should be in a system that represents elements necessary for quantum algorithms. This present work attempts to do this from the perspective of the quantum circuit model of quantum computation. A sequent calculus based on single quantum circuits is suggested, and its ability to incorporate important conceptual and dynamic aspects of quantum computing is discussed. In particular, preserving the representation of phase helps illustrate the role of interference as a resource in quantum computation. Interference also provides an intuitive basis for a non-monotonic calculus.
Exploration of solids based on representation systems
Directory of Open Access Journals (Sweden)
Publio Suárez Sotomonte
2011-01-01
Full Text Available This article refers to some of the findings of a research project implemented as a teaching strategy to generate environments for the learning of platonic and archimedean solids, with a group of eighth grade students. This strategy was based on the meaningful learning approach and on the use of representation systems using the ontosemiotic approach in mathematical education, as a framework for the construction of mathematical concepts. This geometry teaching strategy adopts the stages of exploration, representation-modeling, formal construction and study of applications. It uses concrete, physical and tangible materials for origami, die making, and structures for the construction of threedimensional solids considered external tangible solid representation systems, as well as computer based educational tools to design dynamic geometry environments as intangible external representation systems.These strategies support both the imagination and internal systems of representation, fundamental to the comprehension of geometry concepts.
Operator representation for effective realistic interactions
Energy Technology Data Exchange (ETDEWEB)
Weber, Dennis; Feldmeier, Hans; Neff, Thomas [GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Darmstadt (Germany)
2013-07-01
We present a method to derive an operator representation from the partial wave matrix elements of effective realistic nucleon-nucleon potentials. This method allows to employ modern effective interactions, which are mostly given in matrix element representation, also in nuclear many-body methods requiring explicitly the operator representation, for example ''Fermionic Molecular Dynamics'' (FMD). We present results for the operator representation of effective interactions obtained from the Argonne V18 potential with the Uenitary Correlation Operator Method'' (UCOM) and the ''Similarity Renormalization Group'' (SRG). Moreover, the operator representation allows a better insight in the nonlocal structure of the potential: While the UCOM transformed potential only shows a quadratic momentum dependence, the momentum dependence of SRG transformed potentials is beyond such a simple polynomial form.
Representations of Nets of C*-Algebras over S 1
Ruzzi, Giuseppe; Vasselli, Ezio
2012-11-01
In recent times a new kind of representations has been used to describe superselection sectors of the observable net over a curved spacetime, taking into account the effects of the fundamental group of the spacetime. Using this notion of representation, we prove that any net of C*-algebras over S 1 admits faithful representations, and when the net is covariant under Diff( S 1), it admits representations covariant under any amenable subgroup of Diff( S 1).
Features of common representations of suiciders in young people
Directory of Open Access Journals (Sweden)
I. B. Bovina
2013-04-01
Full Text Available We discuss the first phase results of a research project dedicated to study of suicide representations in youth. In the framework of structural approach to social representations, we study features of structure and content of social representations of suiciders in two groups of young people (the criterion for group allocation was their acquaintance with people who has suicide attempts. Our sample (N = 106 consisted of representatives of several youth groups (students and working youths with specialized secondary, higher or incomplete higher education, aged 18 to 35 years (M = 23,48 years, SD = 4,36 years: 67 women and 39 men. The 1st group includes respondents personally acquainted with suicide attempters (44 respondents, the 2nd group – respondents without such experience. The subject of research were common representations of suiciders. We tested assumptions about the specificity of protective functions of social representations, as well as consistency of representations in the two groups of respondents.
Factorizable sheaves and quantum groups
Bezrukavnikov, Roman; Schechtman, Vadim
1998-01-01
The book is devoted to the geometrical construction of the representations of Lusztig's small quantum groups at roots of unity. These representations are realized as some spaces of vanishing cycles of perverse sheaves over configuration spaces. As an application, the bundles of conformal blocks over the moduli spaces of curves are studied. The book is intended for specialists in group representations and algebraic geometry.
DEFF Research Database (Denmark)
Willett, Wesley; Jansen, Yvonne; Dragicevic, Pierre
2017-01-01
We introduce embedded data representations, the use of visual and physical representations of data that are deeply integrated with the physical spaces, objects, and entities to which the data refers. Technologies like lightweight wireless displays, mixed reality hardware, and autonomous vehicles...
International Nuclear Information System (INIS)
Santos, Marcelo Franca
2005-01-01
We present a simple quantum circuit that allows for the universal and deterministic manipulation of the quantum state of confined harmonic oscillators. The scheme is based on the selective interactions of the referred oscillator with an auxiliary three-level system and a classical external driving source, and enables any unitary operations on Fock states, two by two. One circuit is equivalent to a single qubit unitary logical gate on Fock states qubits. Sequences of similar protocols allow for complete, deterministic, and state-independent manipulation of the harmonic oscillator quantum state
International Nuclear Information System (INIS)
Collins, David
2010-01-01
A general framework for regarding oracle-assisted quantum algorithms as tools for discriminating among unitary transformations is described. This framework is applied to the Deutsch-Jozsa problem and all possible quantum algorithms which solve the problem with certainty using oracle unitaries in a particular form are derived. It is also used to show that any quantum algorithm that solves the Deutsch-Jozsa problem starting with a quantum system in a particular class of initial, thermal equilibrium-based states of the type encountered in solution-state NMR can only succeed with greater probability than a classical algorithm when the problem size n exceeds ∼10 5 .
International Nuclear Information System (INIS)
Doering, A.; Isham, C. J.
2008-01-01
This paper is the third in a series whose goal is to develop a fundamentally new way of viewing theories of physics. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. In Paper II, we studied the topos representations of the propositional language PL(S) for the case of quantum theory, and in the present paper we do the same thing for the, more extensive, local language L(S). One of the main achievements is to find a topos representation for self-adjoint operators. This involves showing that, for any physical quantity A, there is an arrow δ o (A):Σ lowbar →R sccue lowbar , where R sccue lowbar is the quantity-value object for this theory. The construction of δ o (A) is an extension of the daseinisation of projection operators that was discussed in Paper II. The object R sccue lowbar is a monoid object only in the topos, τ φ =Sets V(H) op , of the theory, and to enhance the applicability of the formalism, we apply to R sccue lowbar a topos analog of the Grothendieck extension of a monoid to a group. The resulting object, k(R sccue lowbar ), is an abelian group object in τ φ . We also discuss another candidate, R ↔ lowbar , for the quantity-value object. In this presheaf, both inner and outer daseinisations are used in a symmetric way. Finally, there is a brief discussion of the role of unitary operators in the quantum topos scheme
Passman, Donald S
2012-01-01
This volume by a prominent authority on permutation groups consists of lecture notes that provide a self-contained account of distinct classification theorems. A ready source of frequently quoted but usually inaccessible theorems, it is ideally suited for professional group theorists as well as students with a solid background in modern algebra.The three-part treatment begins with an introductory chapter and advances to an economical development of the tools of basic group theory, including group extensions, transfer theorems, and group representations and characters. The final chapter feature
Covariant representations of nuclear *-algebras
International Nuclear Information System (INIS)
Moore, S.M.
1978-01-01
Extensions of the Csup(*)-algebra theory for covariant representations to nuclear *-algebra are considered. Irreducible covariant representations are essentially unique, an invariant state produces a covariant representation with stable vacuum, and the usual relation between ergodic states and covariant representations holds. There exist construction and decomposition theorems and a possible relation between derivations and covariant representations
Unitary vs Multiple Semantics: PET Studies of Word and Picture Processing
Bright, P.; Moss, H.; Tyler, L. K.
2004-01-01
In this paper we examine a central issue in cognitive neuroscience: are there separate conceptual representations associated with different input modalities (e.g., Paivio, 1971, 1986; Warrington & Shallice, 1984) or do inputs from different modalities converge on to the same set of representations (e.g., Caramazza, Hillis, Rapp, & Romani, 1990;…
Cognitive Representation in Ethnophaulisms and Illusory Correlation in Stereotyping.
Mullen, Brian; Johnson, Craig
1995-01-01
Extends previous research by examining developing stereotypes for novel ethnic groups as indicators of cognitive representations. Results from three studies confirmed that in the absence of any preconceived cognitive representations of, or valuative responses toward, these novel groups, more salient groups are subject to greater prototype…
Knot invariants and higher representation theory
Webster, Ben
2018-01-01
The author constructs knot invariants categorifying the quantum knot variants for all representations of quantum groups. He shows that these invariants coincide with previous invariants defined by Khovanov for \\mathfrak{sl}_2 and \\mathfrak{sl}_3 and by Mazorchuk-Stroppel and Sussan for \\mathfrak{sl}_n. The author's technique is to study 2-representations of 2-quantum groups (in the sense of Rouquier and Khovanov-Lauda) categorifying tensor products of irreducible representations. These are the representation categories of certain finite dimensional algebras with an explicit diagrammatic presentation, generalizing the cyclotomic quotient of the KLR algebra. When the Lie algebra under consideration is \\mathfrak{sl}_n, the author shows that these categories agree with certain subcategories of parabolic category \\mathcal{O} for \\mathfrak{gl}_k.
International Nuclear Information System (INIS)
Kiritsis, E.B.
1987-01-01
N = 2 superconformal-invariant theories are studied and their general structure is analyzed. The geometry of N = 2 complex superspace is developed as a tool to study the correlation functions of the theories above. The Ward identities of the global N = 2 superconformal symmetry are solved, to restrict the form of correlation functions. Advantage is taken of the existence of the degenerate operators to derive the ''fusion'' rules for the unitary minimal systems with c<1. In particular, the closure of the operator algebra for such systems is shown. The c = (1/3 minimal system is analyzed and its two-, three-, and four-point functions as well as its operator algebra are calculated explicitly
Gap probabilities for edge intervals in finite Gaussian and Jacobi unitary matrix ensembles
International Nuclear Information System (INIS)
Witte, N.S.; Forrester, P.J.
1999-01-01
The probabilities for gaps in the eigenvalue spectrum of the finite dimension N x N random matrix Hermite and Jacobi unitary ensembles on some single and disconnected double intervals are found. These are cases where a reflection symmetry exists and the probability factors into two other related probabilities, defined on single intervals. Our investigation uses the system of partial differential equations arising from the Fredholm determinant expression for the gap probability and the differential-recurrence equations satisfied by Hermite and Jacobi orthogonal polynomials. In our study we find second and third order nonlinear ordinary differential equations defining the probabilities in the general N case, specific explicit solutions for N = 1 and N = 2, asymptotic expansions, scaling at the edge of the Hermite spectrum as N →∞ and the Jacobi to Hermite limit both of which make correspondence to other cases reported here or known previously. (authors)
Some new aspects of the unitary and analytic VMD model for electromagnetic structure of hadrons
International Nuclear Information System (INIS)
Dubnickova, A.Z.; Dubnicka, S.
1991-01-01
Recent J/φ→π + π - data analyzed along with all existing pion form factor data by means of the unitary and analytic vector dominance model manifest a strong evidence of the third excited state of the ρ(770) meson with resonance parameters m ρ ''' =2169±46 MeV and Γ ρ ''' =319±136 MeV. A simultaneous analysis of all reliable proton and neutron form factor data in the space-like region along with data on the total cross section of electron-positron annihilation into a proton-antiproton pair by the same model predicts an unexpected inequality σ tot (e e- +→nn-bar)>>σ tot (e + e - →pp-bar) just above the nucleon-antinucleon threshold and also surprisingly large one-photon electromagnetic corrections to the strong J/φ→pp-bar and J/φ→nn-bar decay amplitudes. 21 refs.; 5 figs.; 1 tab
First and second sound of a unitary Fermi gas in highly oblate harmonic traps
International Nuclear Information System (INIS)
Hu, Hui; Dyke, Paul; Vale, Chris J; Liu, Xia-Ji
2014-01-01
We theoretically investigate first and second sound modes of a unitary Fermi gas trapped in a highly oblate harmonic trap at finite temperatures. Following the idea by Stringari and co-workers (2010 Phys. Rev. Lett. 105 150402), we argue that these modes can be described by the simplified two-dimensional two-fluid hydrodynamic equations. Two possible schemes—sound wave propagation and breathing mode excitation—are considered. We calculate the sound wave velocities and discretized sound mode frequencies, as a function of temperature. We find that in both schemes, the coupling between first and second sound modes is large enough to induce significant density fluctuations, suggesting that second sound can be directly observed by measuring in situ density profiles. The frequency of the second sound breathing mode is found to be highly sensitive to the superfluid density. (paper)
Stability of the Zagreb realization of the Carnegie-Mellon-Berkeley coupled-channels unitary model
Osmanović, H.; Ceci, S.; Švarc, A.; Hadžimehmedović, M.; Stahov, J.
2011-09-01
In Hadžimehmedović [Phys. Rev. CPRVCAN0556-281310.1103/PhysRevC.84.035204 84, 035204 (2011)] we have used the Zagreb realization of Carnegie-Melon-Berkeley coupled-channel, unitary model as a tool for extracting pole positions from the world collection of partial-wave data, with the aim of eliminating model dependence in pole-search procedures. In order that the method is sensible, we in this paper discuss the stability of the method with respect to the strong variation of different model ingredients. We show that the Zagreb CMB procedure is very stable with strong variation of the model assumptions and that it can reliably predict the pole positions of the fitted partial-wave amplitudes.
Stability of the Zagreb realization of the Carnegie-Mellon-Berkeley coupled-channels unitary model
International Nuclear Information System (INIS)
Osmanovic, H.; Hadzimehmedovic, M.; Stahov, J.; Ceci, S.; Svarc, A.
2011-01-01
In Hadzimehmedovicet al.[Phys. Rev. C 84, 035204 (2011)] we have used the Zagreb realization of Carnegie-Melon-Berkeley coupled-channel, unitary model as a tool for extracting pole positions from the world collection of partial-wave data, with the aim of eliminating model dependence in pole-search procedures. In order that the method is sensible, we in this paper discuss the stability of the method with respect to the strong variation of different model ingredients. We show that the Zagreb CMB procedure is very stable with strong variation of the model assumptions and that it can reliably predict the pole positions of the fitted partial-wave amplitudes.
11 Foot Unitary Plan Tunnel Facility Optical Improvement Large Window Analysis
Hawke, Veronica M.
2015-01-01
The test section of the 11 by 11-foot Unitary Plan Transonic Wind Tunnel (11-foot UPWT) may receive an upgrade of larger optical windows on both the North and South sides. These new larger windows will provide better access for optical imaging of test article flow phenomena including surface and off body flow characteristics. The installation of these new larger windows will likely produce a change to the aerodynamic characteristics of the flow in the Test Section. In an effort understand the effect of this change, a computational model was employed to predict the flows through the slotted walls, in the test section and around the model before and after the tunnel modification. This report documents the solid CAD model that was created and the inviscid computational analysis that was completed as a preliminary estimate of the effect of the changes.
Life-cycle cost and payback period analysis for commercial unitary air conditioners
Energy Technology Data Exchange (ETDEWEB)
Rosenquist, Greg; Coughlin, Katie; Dale, Larry; McMahon, James; Meyers, Steve
2004-03-31
This report describes an analysis of the economic impacts of possible energy efficiency standards for commercial unitary air conditioners and heat pumps on individual customers in terms of two metrics: life-cycle cost (LCC) and payback period (PBP). For each of the two equipment classes considered, the 11.5 EER provides the largest mean LCC savings. The results show how the savings vary among customers facing different electricity prices and other conditions. At 11.5 EER, at least 80% of the users achieve a positive LCC savings. At 12.0 EER, the maximum efficiency analyzed, mean LCC savings are lower but still positive. For the {ge} $65,000 Btu/h to <135,000 Btu/h equipment class, 59% of users achieve a positive LCC savings. For the $135,000 Btu/h to <240,000 Btu/h equipment class, 91% of users achieve a positive LCC savings.
Multiply-ionized atoms isolated at low energy in a unitary Penning trap
International Nuclear Information System (INIS)
Tan, Joseph N.; Hoogerheide, Shannon Fogwell; Guise, Nicholas D.; Brewer, Samuel M.
2015-01-01
Ions extracted from the EBIT at NIST are slowed and captured in a Penning trap that is made very compact (< 150 cm 3 ) by a unitary architecture [1]. Measurements after 1 ms of ion storage indicate that the isolated ions are distributed with 5.5(5) eV of energy spread, which is roughly 2 orders of magnitude lower than expected in the ion source, without implementing any active cooling [2]. Some experiments are discussed. One goal is to produce one-electron ions in high angular momentum states for studying optical transitions between Rydberg states that could potentially enable new tests of quantum electrodynamics (QED) and determinations of fundamental constants [3
Penning traps with unitary architecture for storage of highly charged ions
International Nuclear Information System (INIS)
Tan, Joseph N.; Guise, Nicholas D.; Brewer, Samuel M.
2012-01-01
Penning traps are made extremely compact by embedding rare-earth permanent magnets in the electrode structure. Axially-oriented NdFeB magnets are used in unitary architectures that couple the electric and magnetic components into an integrated structure. We have constructed a two-magnet Penning trap with radial access to enable the use of laser or atomic beams, as well as the collection of light. An experimental apparatus equipped with ion optics is installed at the NIST electron beam ion trap (EBIT) facility, constrained to fit within 1 meter at the end of a horizontal beamline for transporting highly charged ions. Highly charged ions of neon and argon, extracted with initial energies up to 4000 eV per unit charge, are captured and stored to study the confinement properties of a one-magnet trap and a two-magnet trap. Design considerations and some test results are discussed.
Penning traps with unitary architecture for storage of highly charged ions.
Tan, Joseph N; Brewer, Samuel M; Guise, Nicholas D
2012-02-01
Penning traps are made extremely compact by embedding rare-earth permanent magnets in the electrode structure. Axially-oriented NdFeB magnets are used in unitary architectures that couple the electric and magnetic components into an integrated structure. We have constructed a two-magnet Penning trap with radial access to enable the use of laser or atomic beams, as well as the collection of light. An experimental apparatus equipped with ion optics is installed at the NIST electron beam ion trap (EBIT) facility, constrained to fit within 1 meter at the end of a horizontal beamline for transporting highly charged ions. Highly charged ions of neon and argon, extracted with initial energies up to 4000 eV per unit charge, are captured and stored to study the confinement properties of a one-magnet trap and a two-magnet trap. Design considerations and some test results are discussed.
On the ratio probability of the smallest eigenvalues in the Laguerre unitary ensemble
Atkin, Max R.; Charlier, Christophe; Zohren, Stefan
2018-04-01
We study the probability distribution of the ratio between the second smallest and smallest eigenvalue in the Laguerre unitary ensemble. The probability that this ratio is greater than r > 1 is expressed in terms of an Hankel determinant with a perturbed Laguerre weight. The limiting probability distribution for the ratio as is found as an integral over containing two functions q 1(x) and q 2(x). These functions satisfy a system of two coupled Painlevé V equations, which are derived from a Lax pair of a Riemann-Hilbert problem. We compute asymptotic behaviours of these functions as and , as well as large n asymptotics for the associated Hankel determinants in several regimes of r and x.
Unitary input DEA model to identify beef cattle production systems typologies
Directory of Open Access Journals (Sweden)
Eliane Gonçalves Gomes
2012-08-01
Full Text Available The cow-calf beef production sector in Brazil has a wide variety of operating systems. This suggests the identification and the characterization of homogeneous regions of production, with consequent implementation of actions to achieve its sustainability. In this paper we attempted to measure the performance of 21 livestock modal production systems, in their cow-calf phase. We measured the performance of these systems, considering husbandry and production variables. The proposed approach is based on data envelopment analysis (DEA. We used unitary input DEA model, with apparent input orientation, together with the efficiency measurements generated by the inverted DEA frontier. We identified five modal production systems typologies, using the isoefficiency layers approach. The results showed that the knowledge and the processes management are the most important factors for improving the efficiency of beef cattle production systems.
The Coulomb gas representation of critical RSOS models on the sphere and the torus
International Nuclear Information System (INIS)
Foda, O.; Nienhuis, B.
1989-01-01
We derive the Coulomb gas formulation of the c<1 discrete unitary series, on the sphere and the torus, starting from the corresponding regime-III RSOS models on a square lattice with appropriate topology. We clarify the origin of the background charge, the screening charges, and the choice of operator representations in a correlation function. In the scaling limit, we obtain a bosonic action coupled to the background curvature in addition to topological terms that vanish on the Riemann sphere. Its Virasoro algebra has the central charge expected on the basis of comparing conformal dimensions. As an application, we derive general expressions for the correlation functions on the torus. (orig.)
The Coulomb gas representation of critical RSOS models on the sphere and the torus
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Foda, O. (Rijksuniversiteit Utrecht (Netherlands). Inst. voor Theoretische Fysica); Nienhuis, B. (Rijksuniversiteit Leiden (Netherlands). Inst. Lorentz voor Theoretische Natuurkunde)
1989-10-02
We derive the Coulomb gas formulation of the c<1 discrete unitary series, on the sphere and the torus, starting from the corresponding regime-III RSOS models on a square lattice with appropriate topology. We clarify the origin of the background charge, the screening charges, and the choice of operator representations in a correlation function. In the scaling limit, we obtain a bosonic action coupled to the background curvature in addition to topological terms that vanish on the Riemann sphere. Its Virasoro algebra has the central charge expected on the basis of comparing conformal dimensions. As an application, we derive general expressions for the correlation functions on the torus. (orig.).
Representation theory of finite monoids
Steinberg, Benjamin
2016-01-01
This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully worked examples and exercises provide the bells and whistles for graduate accessibility, bringing a broad range of advanced readers to the forefront of research in the area. Highlights of the text include applications to probability theory, symbolic dynamics, and automata theory. Comfort with module theory, a familiarity with ordinary group representation theory, and the basics of Wedderburn theory, are prerequisites for advanced graduate level study. Researchers in algebra, algebraic combinatorics, automata theory, and probability theory, will find this text enriching with its thorough presentation of applications of the theory to these fields. Prior knowledge of semigroup theory is not expected for the diverse readership that may benefit from this exposition. The approach taken in this book is highly module-theoretic and follows the modern flavor of the theory of finite dimensional ...
Representation theory a first course
Fulton, William
1991-01-01
The primary goal of these lectures is to introduce a beginner to the finite dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book. Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians. This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways. It is for ...
Nilsen, Sven
2010-01-01
The purpose of the article is to study the development of educational policy in Norway in the field of the unitary school system and to analyse whether the development can be seen as a move towards increasing inclusion. The educational policy, when seen over a long time span, has progressively aimed towards the development of a common compulsory…