Maps between standard and principal flag orders

Galois orders, introduced in 2010 by V. Futorny and S. Ovsienko, form a class of associative algebras that contain many important examples, such as the enveloping algebra of $\mathfrak{gl}_n$ (as well as its quantum deformation), generalized Weyl algebras, and shifted Yangians. The main motivation for introducing Galois orders is they provide a setting for studying certain infinite dimensional irreducible representations, called Gelfand-Tsetlin modules. Principal Galois orders, defined by J. Hartwig in 2017, are Galois orders with an extra property, which makes them easier to study. All of the mentioned examples are principal Galois orders. In 2019, B. Webster defined principal flag orders which in most situations are Morita equivalent to principal Galois orders and further simplifies their study. This paper describes some techniques to connect the study pairs of standard flag and Galois orders with data. Such techniques include: a sufficient condition for morphisms between standard flag and Galois orders to exist, a property of flag orders related to differential operators on affine varieties, and constructing tensor products of standard and principal flag and Galois orders.Comment: 10 pages, Fixed major typo

Chromosomal in situ suppression hybridization of human gonosomes and autosomes and its use in clinical cytogenetics

DNA libraries from sorted human gonosomes were used selectively to stain the X and Y chromosomes in normal and aberrant cultured human cells by chromosomal in situ suppression (CISS-) hybridization. The entire X chromosome was stained in metaphase spreads. Interphase chromosome domains of both the active and inactive X were clearly delineated. CISS-hybridization of the Y chromosome resulted in the specific decoration of the euchromatic part (Ypter-q11), whereas the heterochromatic part (Yq12) remained unlabeled. The stained part of the Y chromosome formed a compact domain in interphase nuclei. This approach was applied to amniotic fluid cells containing a ring chromosome of unknown origin (47,XY; +r). The ring chromosome was not stained by library probes from the gonosomes, thereby suggesting its autosomal origin. The sensitivity of CISS-hybridization was demonstrated by the detection of small translocations and fragments in human lymphocyte metaphase spreads after irradiation with 60Co-gamma-rays. Lymphocyte cultures from two XX-males were investigated by CISS-hybridization with Y-library probes. In both cases, metaphase spreads demonstrated a translocation of Yp-material to the short arm of an X chromosome. The translocated Y-material could also be demonstrated directly in interphase nuclei. CISS-hybridization of autosomes 7 and 13 was used for prenatal diagnosis in a case with a known balanced translocation t(7;13) in the father. The same translocation was observed in amniotic fluid cells from the fetus. Specific staining of the chromosomes involved in such translocations will be particularly important, in the future, in cases that cannot be solved reliably by conventional chromosome banding alone

Triple Compton effect: A photon splitting into three upon collision with a free electron

The process in which a photon splits into three after the collision with a free electron (triple Compton effect) is the most basic process for the generation of a high-energy multi-particle entangled state composed out of elementary quanta. The cross section of the process is evaluated in two experimentally realizable situations, one employing gamma photons and stationary electrons, and the other using keV photons and GeV electrons of an x-ray free electron laser. For the first case, our calculation is in agreement with the only available measurement of the differential cross section for the process under study. Our estimates indicate that the process should be readily measurable also in the second case. We quantify the polarization entanglement in the final state by a recently proposed multi-particle entanglement measure.Comment: 5 pages; RevTeX; to be published in Phys.Rev.Let

Radiative processes in external gravitational fields

Kinematically forbidden processes may be allowed in the presence of external gravitational fields. These ca be taken into account by introducing generalized particle momenta. The corresponding transition probabilities can then be calculated to all orders in the metric deviation from the field-free expressions by simply replacing the particle momenta with their generalized counterparts. The procedure applies to particles of any spin and to any gravitational fields. transition probabilities, emission power, and spectra are, to leading order, linear in the metric deviation. It is also shown how a small dissipation term in the particle wave equations can trigger a strong backreaction that introduces resonances in the radiative process and deeply affects the resulting gravitational background.Comment: 5 pages, 1 figur

Many worlds and modality in the interpretation of quantum mechanics: an algebraic approach

Many worlds interpretations (MWI) of quantum mechanics avoid the measurement problem by considering every term in the quantum superposition as actual. A seemingly opposed solution is proposed by modal interpretations (MI) which state that quantum mechanics does not provide an account of what `actually is the case', but rather deals with what `might be the case', i.e. with possibilities. In this paper we provide an algebraic framework which allows us to analyze in depth the modal aspects of MWI. Within our general formal scheme we also provide a formal comparison between MWI and MI, in particular, we provide a formal understanding of why --even though both interpretations share the same formal structure-- MI fall pray of Kochen-Specker (KS) type contradictions while MWI escape them.Comment: submitted to the Journal of Mathematical Physic

Radiative corrections to the Dalitz plot of K_{l3}^\pm decays

We calculate the model-independent radiative corrections to the Dalitz plot of K_{l3}^\pm decays to order (\alpha/\pi)(q/M_1), where q is the momentum transfer and M_1 is the mass of the kaon. The final results are presented, first, with the triple integration over the variables of the bremsstrahlung photon ready to be performed numerically and, second, in an analytical form. These two forms are useful to crosscheck on one another and with other calculations. This paper is organized to make it accessible and reliable in the analysis of the Dalitz plot of precision experiments and is not compromised to fixing the form factors at predetermined values. It is assumed that the real photons are kinematically discriminated. Otherwise, our results have a general model-independent applicability.Comment: RevTex4, 38 pages, 5 figures, 5 tables; some typos corrected; discussion extended to compare with other result

Fuzzy Topology, Quantization and Gauge Invariance

Dodson-Zeeman fuzzy topology considered as the possible mathematical framework of quantum geometric formalism. In such formalism the states of massive particle m correspond to elements of fuzzy manifold called fuzzy points. Due to their weak (partial) ordering, m space coordinate x acquires principal uncertainty dx. It's shown that m evolution with minimal number of additional assumptions obeys to schroedinger and dirac formalisms in norelativistic and relativistic cases correspondingly. It's argued that particle's interactions on such fuzzy manifold should be gauge invariant.Comment: 12 pages, Talk given on 'Geometry and Field Theory' conference, Porto, July 2012. To be published in Int. J. Theor. Phys. (2015

How state preparation can affect a quantum experiment: Quantum process tomography for open systems

We study the effects of preparation of input states in a quantum tomography experiment. We show that maps arising from a quantum process tomography experiment (called process maps) differ from the well know dynamical maps. The difference between the two is due to the preparation procedure that is necessary for any quantum experiment. We study two preparation procedures, stochastic preparation and preparation by measurements. The stochastic preparation procedure yields process maps that are linear, while the preparations using von Neumann measurements lead to non-linear processes, and can only be consistently described by a bi-linear process map. A new process tomography recipe is derived for preparation by measurement for qubits. The difference between the two methods is analyzed in terms of a quantum process tomography experiment. A verification protocol is proposed to differentiate between linear processes and bi-linear processes. We also emphasize the preparation procedure will have a non-trivial effect for any quantum experiment in which the system of interest interacts with its environment.Comment: 13 pages, no figures, submitted to Phys. Rev.