On the reconstruction of a unitary matrix from its moduli

We study the problem of reconstructing a unitary matrix from the knowledge of the moduli of its matrix elements, first in the case of a symmetric matrix, which could be theS matrix forn coupled channels, second in the case of a non-symmetric matrix like the Cabibbo-Kobayashi-Maskawa matrix forn generations of quarks and leptons. In the symmetric case we find conditions under which the problem has solutions differing in a non-trivial way, but also situations where one has continuous ambiguities.In the non-symmetric case we show that forn>3 there may be continuous ambiguities, of which we give an exhaustic list forn=4. We give indications that there is also a set of moduli for which one has discrete solutions, but no rigorous proof.Unité associée au CNRS n^o 040768     

A mathematica program for constructing quantum circuits and computing their unitary matrices

In this paper we briefly describe a Mathematica program for simulation of quantum circuits and illustrate some of its facilities by simple examples. Unlike other Mathematica-based quantum simulators, our program provides a user-friendly graphical interface for generating quantum circuits and computing the circuit unitary matrices. In addition to standard linear algebra-based tools, our program implements special computer-algebra technique for constructing the multivariate polynomial system that, for a circuit composed from the Toffoli and Hadamard gates, uniquely defines the circuit matrix.     

Calculations of atomic spin-orbit matrix elements in the unitary group approach

We present detailed closed-form expressions for the evaluation and numerical calculation of atomic spin-orbit matrix elements in the unitary group approach. A minicomputer implementation of the calculations is described.     

Gaussian ensembles of random hermitian matrices intermediate between orthogonal and unitary ones

Communications in Mathematical Physics - A Gaussian ensemble of Hermitian matrices depending on a parameter α is considered. When α=0, the ensemble is Gaussian Orthogonal, and when...     

On the Mickelsson-Faddeev extension and unitary representations

The Mickelsson-Faddeev extension is a 3-space analogue of a Kac-Moody group, where the central charge is replaced by a space of functions of the gauge potential. This extension is a pullback of a universal extension, where the gauge potentials are replaced by operators in a Schatten ideal, as in non-commutative differential geometry. Our main result is that the universal extension cannot be faithfully represented by unitary operators on a separable Hilbert space. We also examine potential consequences of the existence of unitary representations for the Mickelsson-Faddeev extension.     

On unitary subsectors of polycritical gravities

We study higher-derivative gravity theories in arbitrary space–time dimension $d$ with a cosmological constant at their maximally critical points where the masses of all linearized perturbations vanish. These theories have been conjectured to be dual to logarithmic conformal field theories in the $(d-1)$ -dimensional boundary of an AdS solution. We determine the structure of the linearized perturbations and their boundary fall-off behaviour. The linearized modes exhibit the expected Jordan block structure and their inner products are shown to be those of a non-unitary theory. We demonstrate the existence of consistent unitary truncations of the polycritical gravity theory at the linearized level for odd rank.     

On unitary implementability of conformal transformations

We show that the only projective representations of the conformal group in a Hilbert space which, when restricted to the Poincaré subgroup, are unitary irreducible of mass zero and discrete helicity, are the usual unitary representations of SU(2, 2) often called ladder representations. Some physical consequences are also discussed.     

On moduli spaces of graded bundles

This is a review of the main topological properties of moduli spaces of graded bundles. These spaces consist of such elements of the cohomology H ¹(M, GL(n, E)), where E»M is a vector bundle, which are identical when restricted to ⁰ M=M × . Some explicit formulae in the case when M = P ^m and M is a torus are quoted. Applications to instantons and supergravity are discussed.     

On the “vector coupling” of unitary spins

The problem of the vector coupling of unitary spins, i.e., the decomposition of the direct product of the irreducible representations D^[o] × D^[w] of the group U(3) into irreducible components D^[1] is considered. Using the projection operators for the group U(3), we have devised a procedure which allows one to construct systematically a complete set of vectors belonging to the irreducible representation D^[j], including those cases where this direct product D^[5] × D^[w] is not simply reducible.     

On the absence of homogeneous scalar unitary cellular automata

Failure to find homogeneous scalar unitary cellular automata (CA) in one dimension led to consideration of only “approximately unitary” CA - which motivated our recent proof of a No-go Lemma in one dimension. In this note we extend the one dimensional result to prove the absence of nontrivial homogeneous scalar unitary CA on Euclidean lattices in any dimension.     

Construction of non-Abelian walls and their complete moduli space

We present a systematic method to construct exactly all Bogomol'nyi-Prasad-Sommerfield multiwall solutions in supersymmetric U(N(C)) gauge theories in five dimensions with N(F) hypermultiplets in the fundamental representation for infinite gauge coupling. The moduli space of these non-Abelian walls is found to be the complex Grassmann manifold SU(N(F)) divided by SU(N(C))xSU(N(F)-N(C))xU(1) endowed with a deformed metric.     

Implications of equalities among the elements of CKM and PMNS matrices

Investigating the CKM matrix in different parameterization schemes, it is noticed that those schemes can be divided into a few groups where the sine values of the C P phase for each group are approximately equal i.e. there exist several relations among the C P phases. Using those relations, several approximate equalities among the elements of CKM matrix are established. The case can also be generalized to the PMNS matrix for the lepton sector. Assuming them to be exact, there are infinite numbers of solutions and by choosing special values for the free parameters in those solutions, several textures presented in the literature are obtained. Other authors have derived several mixing textures by using presumed symmetries; amazingly, some, though not all, of their forms are the same as those we obtained. This hints at the existence of a hidden symmetry which is broken in the practical world. Nature makes its own selection of the underlying symmetry and the way to break it, while we just guess what it is.     

On the generation of operator equivalents and the calculation of their matrix elements.

To find all components T((k))(+/-q) = N(k,q)J(q)(+/-) summation operator(k-q)(m=0) (+/-1)(k-m)a(k, q; m)J(m)(z) (0 相似文献