Superselection Sectors and General Covariance.I

This paper is devoted to the analysis of charged superselection sectors in the framework of the locally covariant quantum field theories. We shall analize sharply localizable charges, and use net-cohomology of J.E. Roberts as a main tool. We show that to any 4-dimensional globally hyperbolic spacetime it is attached a unique, up to equivalence, symmetric tensor \Crm^*-category with conjugates (in case of finite statistics); to any embedding between different spacetimes, the corresponding categories can be embedded, contravariantly, in such a way that all the charged quantum numbers of sectors are preserved. This entails that to any spacetime is associated a unique gauge group, up to isomorphisms, and that to any embedding between two spacetimes there corresponds a group morphism between the related gauge groups. This form of covariance between sectors also brings to light the issue whether local and global sectors are the same. We conjecture this holds that at least on simply connected spacetimes. It is argued that the possible failure might be related to the presence of topological charges. Our analysis seems to describe theories which have a well defined short-distance asymptotic behaviour.Comment: 66 page

Schwinger, Pegg and Barnett approaches and a relationship between angular and Cartesian quantum descriptions II: Phase Spaces

Following the discussion -- in state space language -- presented in a preceding paper, we work on the passage from the phase space description of a degree of freedom described by a finite number of states (without classical counterpart) to one described by an infinite (and continuously labeled) number of states. With that it is possible to relate an original Schwinger idea to the Pegg and Barnett approach to the phase problem. In phase space language, this discussion shows that one can obtain the Weyl-Wigner formalism, for both Cartesian {\em and} angular coordinates, as limiting elements of the discrete phase space formalism.Comment: Subm. to J. Phys A: Math and Gen. 7 pages, sequel of quant-ph/0108031 (which is to appear on J.Phys A: Math and Gen

Quasiprobability distribution functions for periodic phase-spaces: I. Theoretical Aspects

An approach featuring $s$-parametrized quasiprobability distribution functions is developed for situations where a circular topology is observed. For such an approach, a suitable set of angle-angular momentum coherent states must be constructed in appropriate fashion.Comment: 13 pages, 3 figure

Quantum charges and spacetime topology: The emergence of new superselection sectors

In which is developed a new form of superselection sectors of topological origin. By that it is meant a new investigation that includes several extensions of the traditional framework of Doplicher, Haag and Roberts in local quantum theories. At first we generalize the notion of representations of nets of C*-algebras, then we provide a brand new view on selection criteria by adopting one with a strong topological flavour. We prove that it is coherent with the older point of view, hence a clue to a genuine extension. In this light, we extend Roberts' cohomological analysis to the case where 1--cocycles bear non trivial unitary representations of the fundamental group of the spacetime, equivalently of its Cauchy surface in case of global hyperbolicity. A crucial tool is a notion of group von Neumann algebras generated by the 1-cocycles evaluated on loops over fixed regions. One proves that these group von Neumann algebras are localized at the bounded region where loops start and end and to be factorial of finite type I. All that amounts to a new invariant, in a topological sense, which can be defined as the dimension of the factor. We prove that any 1-cocycle can be factorized into a part that contains only the charge content and another where only the topological information is stored. This second part resembles much what in literature are known as geometric phases. Indeed, by the very geometrical origin of the 1-cocycles that we discuss in the paper, they are essential tools in the theory of net bundles, and the topological part is related to their holonomy content. At the end we prove the existence of net representations

The Wigner function associated to the Rogers-Szego polynomials

We show here that besides the well known Hermite polynomials, the q-deformed harmonic oscillator algebra admits another function space associated to a particular family of q-polynomials, namely the Rogers-Szego polynomials. Their main properties are presented, the associated Wigner function is calculated and its properties are discussed. It is shown that the angle probability density obtained from the Wigner function is a well-behaved function defined in the interval [-Pi,Pi), while the action probability only assumes integer values greater or equal than zero. It is emphasized the fact that the width of the angle probability density is governed by the free parameter q characterizing the polynomial.Comment: 12 pages, 2 (mathemathica) figure

Topological features of massive bosons on two dimensional Einstein space-time

In this paper we tackle the problem of constructing explicit examples of topological cocycles of Roberts' net cohomology, as defined abstractly by Brunetti and Ruzzi. We consider the simple case of massive bosonic quantum field theory on the two dimensional Einstein cylinder. After deriving some crucial results of the algebraic framework of quantization, we address the problem of the construction of the topological cocycles. All constructed cocycles lead to unitarily equivalent representations of the fundamental group of the circle (seen as a diffeomorphic image of all possible Cauchy surfaces). The construction is carried out using only Cauchy data and related net of local algebras on the circle.Comment: 41 pages, title changed, minor changes, typos corrected, references added. Accepted for publication in Ann. Henri Poincare

Representations of Conformal Nets, Universal C*-Algebras and K-Theory

We study the representation theory of a conformal net A on the circle from a K-theoretical point of view using its universal C*-algebra C*(A). We prove that if A satisfies the split property then, for every representation \pi of A with finite statistical dimension, \pi(C*(A)) is weakly closed and hence a finite direct sum of type I_\infty factors. We define the more manageable locally normal universal C*-algebra C*_ln(A) as the quotient of C*(A) by its largest ideal vanishing in all locally normal representations and we investigate its structure. In particular, if A is completely rational with n sectors, then C*_ln(A) is a direct sum of n type I_\infty factors. Its ideal K_A of compact operators has nontrivial K-theory, and we prove that the DHR endomorphisms of C*(A) with finite statistical dimension act on K_A, giving rise to an action of the fusion semiring of DHR sectors on K_0(K_A)$. Moreover, we show that this action corresponds to the regular representation of the associated fusion algebra.Comment: v2: we added some comments in the introduction and new references. v3: new authors' addresses, minor corrections. To appear in Commun. Math. Phys. v4: minor corrections, updated reference

Quasi-probability representations of quantum theory with applications to quantum information science

This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional quantum theory. We focus on both the characteristics and applications of these representations with an emphasis toward quantum information theory. We discuss the recently proposed unification of the set of possible quasi-probability representations via frame theory and then discuss the practical relevance of negativity in such representations as a criteria for quantumness.Comment: v3: typos fixed, references adde

Heterogeneity Governs 3D-Cultures of Clinically Relevant Microbial Communities

The intrinsic heterogeneity of bacterial niches should be retained in in vitrocultures to represent the complex microbial ecology. As a case study,mucin-containing hydrogels -CF-Mu3Gel - are generated by diffusion-inducedgelation, bioinspired on cystic fibrosis (CF) mucus, and a microbial nichechallenging current therapeutic strategies. At breathing frequency, CF-Mu3Gelexhibits aG′andG′′equal to 24 and 3.2 Pa, respectively. Notably, CF-Mu3Gelexhibits structural gradients with a gradual reduction of oxygen tensionacross its thickness (280–194μmol L−1). Over the culture period, a steepdecline in oxygen concentration occurs just a few millimeters below theair–mucus interface in CF-Mu3Gel, similar to those of CF airway mucus.Importantly, the distinctive features of CF-Mu3Gel significantly influencebacterial organization and antimicrobial tolerance in mono- and co-cultures ofStaphylococcus aureusandPseudomonas aeruginosathat standard culturesare unable to emulate. The antimicrobial susceptibility determined inCF-Mu3Gel corroborates the mismatch on the efficacy of antimicrobialtreatment between planktonically cultured bacteria and those in patients.With this example-based research, new light is shed on the understanding ofhow the substrate influences microbial behavior, paving the way for improvedfundamental microbiology studies and more effective drug testing anddevelopment

Framed Hilbert space: hanging the quasi-probability pictures of quantum theory

Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an alternate approach to defining a set of quasi-probability representations, based on a more natural generalization of a classical representation, is equivalent to our earlier approach based on frames, and therefore is also subject to our no-go theorem for a non-negative representation. Furthermore, we clarify the relationship between the contextuality of quantum theory and the necessity of negativity in quasi-probability representations and discuss their relevance as criteria for non-classicality. We also provide a comprehensive overview of known quasi-probability representations and their expression within the frame formalism.Comment: 46 pages, 1 table, contains a review of finite dimensional quasi-probability function