86 research outputs found
Reduction of Lie--Jordan algebras: Quantum
In this paper we present a theory of reduction of quantum systems in the
presence of symmetries and constraints. The language used is that of
Lie--Jordan Banach algebras, which are discussed in some detail together with
spectrum properties and the space of states. The reduced Lie--Jordan Banach
algebra is characterized together with the Dirac states on the physical algebra
of observables
Reduction of Lie-Jordan Banach algebras and quantum states
A theory of reduction of Lie-Jordan Banach algebras with respect to either a
Jordan ideal or a Lie-Jordan subalgebra is presented. This theory is compared
with the standard reduction of C*-algebras of observables of a quantum system
in the presence of quantum constraints. It is shown that the later corresponds
to the particular instance of the reduction of Lie-Jordan Banach algebras with
respect to a Lie-Jordan subalgebra as described in this paper. The space of
states of the reduced Lie-Jordan Banach algebras is described in terms of
equivalence classes of extensions to the full algebra and their GNS
representations are characterized in the same way. A few simple examples are
discussed that illustrates some of the main results
Reduction of Lie-Jordan algebras: Classical
In this paper we present a unified algebraic framework to discuss the reduction of classical and quantum systems. The underlying algebraic structure is a Lie-Jordan algebra supplemented, in the quantum case, with a Banach structure.
We discuss the reduction by symmetries, by constraints as well as the possible, non trivial, combinations of both. We finally introduce a new, general framework to perform the reduction of physical systems in an algebraic setup
Inequivalence of QFT's on Noncommutative Spacetimes: Moyal versus Wick-Voros
In this paper, we further develop the analysis started in an earlier paper on
the inequivalence of certain quantum field theories on noncommutative
spacetimes constructed using twisted fields. The issue is of physical
importance. Thus it is well known that the commutation relations among
spacetime coordinates, which define a noncommutative spacetime, do not
constrain the deformation induced on the algebra of functions uniquely. Such
deformations are all mathematically equivalent in a very precise sense. Here we
show how this freedom at the level of deformations of the algebra of functions
can fail on the quantum field theory side. In particular, quantum field theory
on the Wick-Voros and Moyal planes are shown to be inequivalent in a few
different ways. Thus quantum field theory calculations on these planes will
lead to different physics even though the classical theories are equivalent.
This result is reminiscent of chiral anomaly in gauge theories and has obvious
physical consequences. The construction of quantum field theories on the
Wick-Voros plane has new features not encountered for quantum field theories on
the Moyal plane. In fact it seems impossible to construct a quantum field
theory on the Wick-Voros plane which satisfies all the properties needed of
field theories on noncommutative spaces. The Moyal twist seems to have unique
features which make it a preferred choice for the construction of a quantum
field theory on a noncommutative spacetime.Comment: Revised version accepted for publication in Phys.Rev.D; 18 page
Positive Psychology: Supervisor Leadership in Organizational Citizenship Behaviors in Nurses
Introduction: In nursing, identifying factors encouraging positive work attitudes is ex-tremely important since a nurse’s performance directly impacts the quality of the care they provide, and, therefore, their patients’ health. Objective: The main objective of this research is to analyze whether the supervisor–nurse relationship is positively correlated with a nurse’s organizational citizenship behaviors. Thus, we established a main hypothesis as follows: the quality of the supervi-sor–nurse interpersonal relationship is positively related to the job satisfaction of the nurse, controlled by moderating the effects of psychological empowerment, the perceived organizational sup-port, and leader–leader exchange. Methodology: This is a cross-sectional descriptive study with individuals as the units of analysis. The population studied comprised all the nurses and supervisors working in nine public hospitals in the autonomous community of Aragon (Spain). The sample con-sisted of 2541 nurses, 192 supervisors, and 2500 paired dyads. Self-report questionnaires were used to ensure workers’ anonymity. The dependent variable was the nurse’s organizational citizenship behaviors; the main independent variable was the supervisor’s leadership; the moderating variables were the nurse’s empowerment, the organizational support the nurse perceived, and the quality of the supervisor–superior relationship. Results: Empirical evidence demonstrates that the quality of the supervisor–nurse relationship is positively correlated with organizational citizenship behaviors. The results also confirm the moderating effect of nurses’ empowerment and of the organizational support they perceive. Discussion: Our research shows how important it is for organizations to es-tablish management practices promoting high-quality nurse–supervisor relationships; thus, hospital management should monitor both the supervisors’ performance and leadership. Conclusions: The quality of the relationship the supervisor establishes with their nurses is vitally important since it is a necessary requirement for beneficial results for the organization as a result of citizenship behavior practice
Quantum tomography, phase space observables, and generalized Markov kernels
We construct a generalized Markov kernel which transforms the observable
associated with the homodyne tomography into a covariant phase space observable
with a regular kernel state. Illustrative examples are given in the cases of a
'Schrodinger cat' kernel state and the Cahill-Glauber s-parametrized
distributions. Also we consider an example of a kernel state when the
generalized Markov kernel cannot be constructed.Comment: 20 pages, 3 figure
Covariant Quantum Fields on Noncommutative Spacetimes
A spinless covariant field on Minkowski spacetime \M^{d+1} obeys the
relation where
is an element of the Poincar\'e group \Pg and is its unitary representation on quantum vector states. It
expresses the fact that Poincar\'e transformations are being unitary
implemented. It has a classical analogy where field covariance shows that
Poincar\'e transformations are canonically implemented. Covariance is
self-reproducing: products of covariant fields are covariant. We recall these
properties and use them to formulate the notion of covariant quantum fields on
noncommutative spacetimes. In this way all our earlier results on dressing,
statistics, etc. for Moyal spacetimes are derived transparently. For the Voros
algebra, covariance and the *-operation are in conflict so that there are no
covariant Voros fields compatible with *, a result we found earlier. The notion
of Drinfel'd twist underlying much of the preceding discussion is extended to
discrete abelian and nonabelian groups such as the mapping class groups of
topological geons. For twists involving nonabelian groups the emergent
spacetimes are nonassociative.Comment: 20 page
Generalized Jacobi structures
Jacobi brackets (a generalization of standard Poisson brackets in which
Leibniz's rule is replaced by a weaker condition) are extended to brackets
involving an arbitrary (even) number of functions. This new structure includes,
as a particular case, the recently introduced generalized Poisson structures.
The linear case on simple group manifolds is also studied and non-trivial
examples (different from those coming from generalized Poisson structures) of
this new construction are found by using the cohomology ring of the given
group.Comment: Latex2e file. 11 pages. To appear in J. Phys.
Mutually unbiased bases: tomography of spin states and star-product scheme
Mutually unbiased bases (MUBs) are considered within the framework of a
generic star-product scheme. We rederive that a full set of MUBs is adequate
for a spin tomography, i.e. knowledge of all probabilities to find a system in
each MUB-state is enough for a state reconstruction. Extending the ideas of the
tomographic-probability representation and the star-product scheme to
MUB-tomography, dequantizer and quantizer operators for MUB-symbols of spin
states and operators are introduced, ordinary and dual star-product kernels are
found. Since MUB-projectors are to obey specific rules of the star-product
scheme, we reveal the Lie algebraic structure of MUB-projectors and derive new
relations on triple- and four-products of MUB-projectors. Example of qubits is
considered in detail. MUB-tomography by means of Stern-Gerlach apparatus is
discussed.Comment: 11 pages, 1 table, partially presented at the 17th Central European
Workshop on Quantum Optics (CEWQO'2010), June 6-11, 2010, St. Andrews,
Scotland, U
Optical tomography of Fock state superpositions
We consider optical tomography of photon Fock state superpositions in
connection with recent experimental achievements. The emphasis is put on the
fact that it suffices to represent the measured tomogram as a main result of
the experiment. We suggest a test for checking the correctness of experimental
data. Explicit expressions for optical tomograms of Fock state superpositions
are given in terms of Hermite polynomials. Particular cases of vacuum and low
photon-number state superposition are considered as well as influence of
thermal noise on state purity is studied.Comment: 5 pages, 2 figure
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