Construction of a Complete Set of States in Relativistic Scattering Theory

The space of physical states in relativistic scattering theory is constructed, using a rigorous version of the Dirac formalism, where the Hilbert space structure is extended to a Gel'fand triple. This extension enables the construction of ``a complete set of states'', the basic concept of the original Dirac formalism, also in the cases of unbounded operators and continuous spectra. We construct explicitly the Gel'fand triple and a complete set of ``plane waves'' -- momentum eigenstates -- using the group of space-time symmetries. This construction is used (in a separate article) to prove a generalization of the Coleman-Mandula theorem to higher dimension.Comment: 30 pages, Late

Quantum Mechanical Properties of Bessel Beams

Bessel beams are studied within the general framework of quantum optics. The two modes of the electromagnetic field are quantized and the basic dynamical operators are identified. The algebra of these operators is analyzed in detail; it is shown that the operators that are usually associated to linear momentum, orbital angular momentum and spin do not satisfy the algebra of the translation and rotation group. In particular, what seems to be the spin is more similar to the helicity. Some physical consequences of these results are examined.Comment: 17 pages, no figures. New versio

Measurement and Particle Statistics in the Szilard Engine

A Szilard Engine is a hypothetical device which is able to extract work from a single thermal reservoir by measuring the position of particles within the engine. We derive the amount of work that can be extracted from such a device in the low temperature limit. Interestingly, we show this work is determined by the information gain of the initial measurement rather than by the number and type of particles which constitute the working substance. Our work provides another clear connection between information gain and extractable work in thermodynamical processes.Comment: 4 page

Infraparticle Scattering States in Non-Relativistic QED: II. Mass Shell Properties

We study the infrared problem in the usual model of QED with non-relativistic matter. We prove spectral and regularity properties characterizing the mass shell of an electron and one-electron infraparticle states of this model. Our results are crucial for the construction of infraparticle scattering states, which are treated in a separate paper.Comment: AMS Latex, 45 pages, 2 figure

On the forward cone quantization of the Dirac field in "longitudinal boost-invariant" coordinates with cylindrical symmetry

We obtain a complete set of free-field solutions of the Dirac equation in a (longitudinal) boost-invariant geometry with azimuthal symmetry and use these solutions to perform the canonical quantization of a free Dirac field of mass $M$. This coordinate system which uses the 1+1 dimensional fluid rapidity $\eta = 1/2 \ln [(t-z)/(t+z)]$ and the fluid proper time $\tau = (t^2-z^2)^{1/2}$ is relevant for understanding particle production of quarks and antiquarks following an ultrarelativistic collision of heavy ions, as it incorporates the (approximate) longitudinal "boost invariance" of the distribution of outgoing particles. We compare two approaches to solving the Dirac equation in curvilinear coordinates, one directly using Vierbeins, and one using a "diagonal" Vierbein representation

Intrinsic Entanglement Degradation by Multi-Mode Detection

Relations between photon scattering, entanglement and multi-mode detection are investigated. We first establish a general framework in which one- and two-photon elastic scattering processes can be discussed, then we focus on the study of the intrinsic entanglement degradation caused by a multi-mode detection. We show that any multi-mode scattered state cannot maximally violate the Bell-CHSH inequality because of the momentum spread. The results presented here have general validity and can be applied to both deterministic and random scattering processes.Comment: 12 pages, 4 figures, v3: minor changes. Phys. Rev. A (2004), to be publishe

Transcriptomes reflect the phenotypes of undifferentiated, granulocyte and macrophage forms of HL-60/S4 cells

Author Posting. © The Author(s), 2017. This is the author's version of the work. It is posted here by permission of Taylor & Francis for personal use, not for redistribution. The definitive version was published in Nucleus 8 (2017): 222-237, doi:10.1080/19491034.2017.1285989.In order to understand the chromatin changes underlying differential gene expression during induced differentiation of human leukemic HL-60/S4 cells, we conducted RNA-Seq analysis on quadruplicate cultures of undifferentiated, granulocytic- and macrophage-differentiated cell forms. More than half of mapped genes exhibited altered transcript levels in the differentiated cell forms. In general, more genes showed increased mRNA levels in the granulocytic form and in the macrophage form, than showed decreased levels. The majority of Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways were significantly enriched in genes that exhibited differential transcript levels after either RA or TPA treatment. Changes in transcript levels for groups of genes with characteristic protein phenotypes, such as genes encoding cytoplasmic granular proteins, nuclear envelope and cytoskeletal proteins, cell adhesion proteins, and proteins involved in the cell cycle and apoptosis illustrate the profound differences among the various cell states. In addition to the transcriptome analyses, companion karyotyping by M-FISH of undifferentiated HL-60/S4 cells revealed a plethora of chromosome alterations, compared to normal human cells. The present mRNA profiling provides important information related to nuclear shape changes (e.g., granulocyte lobulation), deformability of the nuclear envelope and linkage between the nuclear envelope and cytoskeleton during induced myeloid chromatin differentiation.DMW thanks the Bay and Paul Foundations for support. ALO and DEO thank the College of Pharmacy at UNE for their support. ALO and DEO are recipients of a 2015 UNE Mini- Grant from the Vice President for Research and Scholarship. ALO and DEO thank the German Cancer Research Center (Heidelberg) for the awards of Guest Scientist fellowships.2018-02-0

A novel approach to light-front perturbation theory

We suggest a possible algorithm to calculate one-loop n-point functions within a variant of light-front perturbation theory. The key ingredients are the covariant Passarino-Veltman scheme and a surprising integration formula that localises Feynman integrals at vanishing longitudinal momentum. The resulting expressions are generalisations of Weinberg's infinite-momentum results and are manifestly Lorentz invariant. For n = 2 and 3 we explicitly show how to relate those to light-front integrals with standard energy denominators. All expressions are rendered finite by means of transverse dimensional regularisation.Comment: 10 pages, 5 figure

Angular momentum of non-paraxial light beam: Dependence of orbital angular momentum on polarization

It is shown that the momentum density of free electromagnetic field splits into two parts. One has no contribution to the net momentum due to the transversality condition. The other yields all the momentum. The angular momentum that is associated with the former part is spin, and the angular momentum that is associated with the latter part is orbital angular momentum. Expressions for the spin and orbital angular momentum are given in terms of the electric vector in reciprocal space. The spin and orbital angular momentum defined this way are used to investigate the angular momentum of nonparaxial beams that are described in a recently published paper [Phys. Rev. A 78, 063831 (2008)]. It is found that the orbital angular momentum depends, apart from an $l$-dependent term, on two global quantities, the polarization represented by a generalized Jones vector and a new characteristic represented by a unit vector $\mathbf{I}$, though the spin depends only on the polarization. The polarization dependence of orbital angular momentum through the impact of $\mathbf{I}$ is obtained and discussed. Some applications of the result obtained here are also made. The fact that the spin originates from the momentum density that has no contribution to the net momentum is used to show that there does not exist the paradox on the spin of circularly polarized plane wave. The polarization dependence of both spin and orbital angular momentum is shown to be the origin of conversion from the spin of a paraxial Laguerre-Gaussian beam into the orbital angular momentum of the focused beam through a high numerical aperture.Comment: 21 pages including an appendi

Transcriptomes Reflect The Phenotypes Of Undifferentiated, Granulocyte And Macrophage Forms Of HL-60/S4 Cells

To understand the chromatin changes underlying differential gene expression during induced differentiation of human leukemic HL-60/S4 cells, we conducted RNA-Seq analysis on quadruplicate cultures of undifferentiated, granulocytic- and macrophage-differentiated cell forms. More than half of mapped genes exhibited altered transcript levels in the differentiated cell forms. In general, more genes showed increased mRNA levels in the granulocytic form and in the macrophage form, than showed decreased levels. The majority of Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways were significantly enriched in genes that exhibited differential transcript levels after either RA or TPA treatment. Changes in transcript levels for groups of genes with characteristic protein phenotypes, such as genes encoding cytoplasmic granular proteins, nuclear envelope and cytoskeletal proteins, cell adhesion proteins, and proteins involved in the cell cycle and apoptosis illustrate the profound differences among the various cell states. In addition to the transcriptome analyses, companion karyotyping by M-FISH of undifferentiated HL-60/S4 cells revealed a plethora of chromosome alterations, compared with normal human cells. The present mRNA profiling provides important information related to nuclear shape changes (e.g., granulocyte lobulation), deformability of the nuclear envelope and linkage between the nuclear envelope and cytoskeleton during induced myeloid chromatin differentiation