Showing papers on "Unitary state published in 1983"

A Classification of Unitary Highest Weight Modules

Abstract: Let G be a simply connected, connected simple Lie group with center Z. Let K be a closed maximal subgroup of G with K/Z compact and let g be the Lie algebra of G. A unitary representation (π,H) of G such that the underlying (ℊK) — module is an irreducible quotient of a Verma module for ℊℂ is called a unitary highest weight module. Harish-Chandra ([4],[5]) has shown that G admits nontrivial unitary highest weight modules precisely when (G,K) is a Hermitian symmetric pair. In this paper we give a complete classification of the unitary highest weight modules.

Unitary representations of non-compact supergroups

Abstract: We give a general theory for the construction of oscillator-like unitary irreducible representations (UIRs) of non-compact supergroups in a super Fock space. This construction applies to all non-compact supergroupsG whose coset spaceG/K with respect to their maximal compact subsupergroupK is “Hermitean supersymmetric”. We illustrate our method with the example of SU(m, p/n+q) by giving its oscillator-like UIRs in a “particle state” basis as well as “supercoherent state basis”. The same class of UIRs can also be realized over the “super Hilbert spaces” of holomorphic functions of aZ variable labelling the coherent states.

Oscillator-like unitary representations of non-compact groups and supergroups and extended supergravity theories

Abstract: A general theory of a unified construction of the oscillator-like unitary irreducible representations (UIR) of non-compact groups and supergroups is presented. Particle state as well as coherent state bases for these UIRs are given and the case of SU(m,p/n+q) is treated in detail. Applications of this theory to the construction of unitary representations of non-compact groups and supergroups of extended supergravity theories, with particular emphasis on E7(7) and OSp(8/4,IR) are also discussed.

The unitary spectrum for real rank one groups

Abstract: Let G be a connected real semi-simple Lie group with finite center. One of the main problems in harmonic analysis is to determine the unitary spectrum of G. In this paper we treat this question in the case when real rank of G is I. Although the answer was known for G of classical type previously ([2], [5], [7], [15]), we have redone this work sometimes giving simpler arguments. With the arbitrary rank case in mind we have tried to deal with the problem of classifying unitary representations in as systematic a way as possible pro- ceeding by induction on the dimension of G. We have concentrated on the case when G is linear and has a compact Cartan subgroup, the other cases being known already. As an application we also give a list of the unitary representations that contribute to the L2-index formula for the Dirac operator with coefficients. As is apparent from the calculations in [19], this is intimately connected with one of our main techniques for determining the unitary spectrum, the Dirac in- equality. We will deal with some related problems in a future paper.

Marginal distribution of the S-matrix elements for Dyson's measure and some applications

Abstract: In recent attempts to construct a statistical theory of nuclear reactions by doing statistics directly on the S-matrix elements, Dyson's measure, which remains invariant under an automorphism that maps the space of unitary and symmetric matrices into itself, is of fundamental importance. The authors study some of the marginal distributions of the individual S-matrix elements, or of groups of them, that arise from Dyson's measure. To understand the problem better, a similar discussion is first carried out for Haar's measure of unitary matrices which do not have the restriction of symmetry, and some of the effects of this restriction are thus exhibited. Some applications of these mathematical results to reaction theory are discussed.

Lie Isotopic Lifting of Unitary Symmetries and of Wigner's Theorem for Extended Deformable Particles

Abstract: As is well known, the notions of symmetries and Wigner's theorem constitute some of the ultimate foundations of quantum mechanics Nevertheless, the theory is crucially dependent on the simplest possible realization of Lie's theory, that via unitary linear or antilinear operators, which is characterized by enveloping associative algebras ℰ of operatorsA, B … with trivial associative productAB A series of recent, mathematical and physical studies have established the existence of the Lie-isotopic reformulation of Lie's theory, which is based on enveloping algebrasE that are still associative, yet are realized via the less trivial associative-isotopic productA*B=AgB, whereg is a suitable, fixed, operator Furthermore, it has been proved that the Lieisotopic theory can be consistently formulated on a Hilbert space, by providing realistic possibilities of achieving a generalization of quantum mechanics known under the name of «hadronic mechanics» In this paper, we present the notion of Lie-isotopic lifting of unitary linear and antilinear symmetries and of Wigner's theorem within the context of (the closed-exterior branch of) hadronic mechanics The results are applied to the isotopic lifting of the operator formulation of the rotational symmetry It is shown that the generalized symmetry can provide the invariance of all possible ellipsoidical deformations of spherical particles This confirms the general lines of hadronic mechanics conjectured earlier, that space-time (and other) symmetries can be exact for extended particles, provided that they are expressed in a structurally more general way (isotopic-unitary) while the same symmetries can be violated when expressed via the simplest possible (unitary) realizations for pointlike approximations

Defining a Unitary Business: An Economist's View

Abstract: The definition of a unitary business has figured prominently in several recent decisions of the U.S. Supreme Court on the constitutionality of state corporate income taxes. This paper employs economic analysis to frame a three part test of whether a unitary business exists. Underlying the tests is the notion that a unitary business exists when separate accounting can not satisfactorily isolate the profits of individual firms. The first test is common control. The second is whether transfer prices on transactions within the group could be manipulated or are diificult to verify or substantial vertical integration, shared costs,economies of scale or scope, or other forms of economic interdependence make isolation of profits of affiliated firms impossible.The third test is one of substantiality.

Unitary bordism of circle actions

Abstract: The purpose of this paper is to describe , the bordism module of unitary T -manifolds, where T denotes the circle group S 1 . We give both an algebraic and a geometric description. The algebraic result is where I = ( i (1), i (2),… i (2 n )) runs through all finite ordered 2 n -tuples ( n ≧0) of non-negative integers which satisfy the conditions ( a ) i (l) + i (2 n )≠0 and ( b ) if i (2 n )≠0 then i (2 n )=≠. The isomorphism is also described geometrically and this leads to geometric generators of .

Energy variation and elementary Jacobi rotations

Abstract: A general exploration of elementary Jacobi unitary transformations is carried out in order to acomplish, within the LCAO-MO scheme, the minimum search of the electronic energy expression for any system and to construct an optimal wavefunction. It has been found that when comparing the Jacobi procedure with the classical SCF schemes, based on coupling operators, some facts arise allowing to consider the unitary transformation technique as an excellent candidate to compute energy and an alternative way to take into account in front SCF procedures.

Usage de l'Algèbre de Lie su (n) dans l'Etude des Systèmes Quantiques à n Etats. II. Transformation de l'Espace des Observables, Problèmes d'Evolution

Abstract: In the previous paper we examined, for a quantum system, the relation between its n-dimensional state space and the su (n) Lie algebra. The present paper is devoted to relations between unitary transformations in the state space and orthogonal transformations in Lie's algebra. Two cases can happen. First, the transformations are independently chosen in the two spaces; this amounts to changing the former relation. On the other hand, the relation is maintained and the unitary operators are then related to some of the orthogonal operators. This second case is used to study the evolution operators.

On unitary interpolants and Fredholm infinite block Toeplitz matrices

Abstract: Conditions for the existence and uniqueness of unitary n × n matrix valued functions f on the unit circle with prescribed Fourier coefficients fj for j ⩾ 0 are given (in terms of infinite block Hankel matrices based on the prescribed coefficients f0,f1,⋯ ) for a natural class of functions. A unitary function belongs to this class if and only if it admits a generalized factorization (in a sense which will be made precise in the paper) or equivalently if and only if any one (and hence both) of the two Toeplitz operators defined by the function are Fredholm. In particular this class includes all continuous unitary n × n matrix valued functions. It is shown that the nonnegative factorization indices of every such unitary f are uniquely determined by f0,f1,⋯ and formulas for them are given.

Defining a Unitary Business: An Economist's View

Abstract: The definition of a unitary business has figured prominently in several recent decisions of the US Supreme Court on the constitutionality of state corporate income taxes This paper employs economic analysis to frame a three part test of whether a unitary business exists Underlying the tests is the notion that a unitary business exists when separate accounting can not satisfactorily isolate the profits of individual firms The first test is common control The second is whether transfer prices on transactions within the group could be manipulated or are diificult to verify or substantial vertical integration, shared costs,economies of scale or scope, or other forms of economic interdependence make isolation of profits of affiliated firms impossibleThe third test is one of substantiality

A description of E -unitary inverse semigroups

Abstract: On considere un semigroupe inverse E unitaire. On cherche a decrire S en termes de E: son treillis d'idempotents et G son image morphique du groupe maximal

Phase conventions consistent with duality between SUn and SL

Abstract: The Schur–Weyl construction of irreducible tensors by symmetrized Lth rank exterior products of a defining n‐dimensional vector space establishes a duality between the coupling algebra of the unitary group Un and the symmetric group SL . The coupling coefficients shared by these two groups are real and possess symmetries due to complex conjugation in Un and association in SL . The unitary group is factored by its unitary unimodular subgroup SUn≂Un/U1 so it is usual to identify the coupling algebras of Un and SUn by choosing the trivial (phaseless) coupling for U1. This establishes a set of equivalence relations since all pseudoscalar irreducible representations (irreps) of Un subduce onto the scalar irrep of SUn. The question remains can this trivial identification with the coupling algebra of SUn be made consistent with the symmetries which follow from duality? Specifically the symmetries which follow from duality must be consistent with the equivalence relations. We argue such consistency may be obtaine...

Unitary transformations, Weyl's association and the role of canonical transformations

Abstract: Quantum mechanical operators can be associated with functions of p, q through the Weyl or Wigner transform. In this paper we develop alternative associations through the use of unitary transformations, and study the relation between unitary transformations and canonical transformations of the p, q labels.

The Establishment of the Kingdom of Italy as a Unitary State: A Case Study in Regime Formation

Abstract: This article examines the establishment of a highly centralized unitary state in the newly formed Kingdom of Italy during 1848-1870. This study analyzes the general theoretical problem that underlies the Italian case, namely, the factors that play a key role in determining whether a centralized unitary system, a decentralized unitary system, or a federal system will emerge during the process of regime formation in a nation that has followed a more centerto-periphery model rather than an e pluribus unum model of state formation. Certain conditions that encourage federalism or decentralization are discussed, including the difusion of a cultural sense of community among elites and masses; a resulting sense of confidence among elites that federalism or decentralization will not endanger regime survival; a nonthreatening international environment; a strongly asymmetrical relationship between the state, which has led the unification process, and the states it has annexed; and possibly the presence of an important and influential neighboring state with federal institutions or regional autonomy.

Patterns of Diffusion in Japan and America

Abstract: Japan is a small, homogeneous, unitary state. The United States is a large, diverse, federal state. One would expect that diffusion among Japanese prefectures would be (1) faster, 2) more complete, and (3) more influenced by the central government than is diffusion among the American states. These three hypotheses are tested with mixed results. In some respects diffusion may follow a dynamic of its own, producing similar results in vastly different contexts.

Using finite unitary geometry to construct a class of pbib designs

Abstract: In this paper the author considers the n-dimensional(n≥3)unitary geometry over finite field F_(q~2),where q is a power of a prime,The author takesthe set of all one-dimensional non-isotropic subspaces as the set of treatments,and obtainsan association scheme and PBIB designs with q associate classes,whose parameters are also computed

Generators of s1-bordism

Abstract: In this paper generators are found for the rings US1* (the unitary S1-bordism ring) and U*(S1,{ZS}) (the unitary bordism ring with actions of the group S1 without fixed points). The generators found are S1-manifolds of the form (S3)k × CPn/(S1)k. By an obvious construction the ring US1* allows one to establish a relation between numerical invariants of manifolds with unitary actions of S1 and the set of fixed points, without using a theorem of the type of an integrality theorem. In particular, we obtain a new proof of the Atiyah-Hirzebruch formula for the generalized Todd genus of S1-manifolds. Bibliography: 9 titles.