11,247 research outputs found

    Foldy-Wouthuysen Transformation, Scalar Potentials and Gravity

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    We show that care is required in formulating the nonrelativistic limit of generalized Dirac Hamiltonians which describe particles and antiparticles interacting with static electric and/or gravitational fields. The Dirac-Coulomb and the Dirac-Schwarzschild Hamiltonians, and the corrections to the Dirac equation in a non-inertial frame, according to general relativity, are used as example cases in order to investigate the unitarity of the standard and "chiral" approaches to the Foldy-Wouthuysen transformation, and spurious parity-breaking terms. Indeed, we find that parity-violating terms can be generated by unitary pseudo-scalar transformations ("chiral" Foldy-Wouthuysen transformations). Despite their interesting algebraic properties, we find that "chiral" Foldy-Wouthuysen transformations change fundamental symmetry properties of the Hamiltonian and do not conserve the physical interpretation of the operators. Supplementing the discussion, we calculate the leading terms in the Foldy-Wouthuysen transformation of the Dirac Hamiltonian with a scalar potential (of the (1/r)-form and of the confining radially symmetric linear form), and obtain compact expressions for the leading higher-order corrections to the Dirac Hamiltonian in a non-inertial rotating reference frame "Mashhoon term").Comment: 11 pages; RevTe

    Dirac Hamiltonian and Reissner-Nordstrom Metric: Coulomb Interaction in Curved Space-Time

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    We investigate the spin-1/2 relativistic quantum dynamics in the curved space-time generated by a central massive charged object (black hole). This necessitates a study of the coupling of a Dirac particle to the Reissner-Nordstrom space-time geometry and the simultaneous covariant coupling to the central electrostatic field. The relativistic Dirac Hamiltonian for the Reissner-Nordstrom geometry is derived. A Foldy-Wouthuysen transformation reveals the presence of gravitational, and electro-gravitational spin-orbit coupling terms which generalize the Fokker precession terms found for the Dirac-Schwarzschild Hamiltonian, and other electro-gravitational correction terms to the potential proportional to alpha^n G, where alpha is the fine-structure constant, and G is the gravitational coupling constant. The particle-antiparticle symmetry found for the Dirac-Schwarzschild geometry (and for other geometries which do not include electromagnetic interactions) is shown to be explicitly broken due to the electrostatic coupling. The resulting spectrum of radially symmetric, electrostatically bound systems (with gravitational corrections) is evaluated for example cases.Comment: 11 page

    Generalized Householder Transformations for the Complex Symmetric Eigenvalue Problem

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    We present an intuitive and scalable algorithm for the diagonalization of complex symmetric matrices, which arise from the projection of pseudo--Hermitian and complex scaled Hamiltonians onto a suitable basis set of "trial" states. The algorithm diagonalizes complex and symmetric (non--Hermitian) matrices and is easily implemented in modern computer languages. It is based on generalized Householder transformations and relies on iterative similarity transformations T -> T' = Q^T T Q, where Q is a complex and orthogonal, but not unitary, matrix, i.e, Q^T equals Q^(-1) but Q^+ is different from Q^(-1). We present numerical reference data to support the scalability of the algorithm. We construct the generalized Householder transformations from the notion that the conserved scalar product of eigenstates Psi_n and Psi_m of a pseudo-Hermitian quantum mechanical Hamiltonian can be reformulated in terms of the generalized indefinite inner product [integral of the product Psi_n(x,t) Psi_m(x,t) over dx], where the integrand is locally defined, and complex conjugation is avoided. A few example calculations are described which illustrate the physical origin of the ideas used in the construction of the algorithm.Comment: 14 pages; RevTeX; font mismatch in Eqs. (3) and (15) is eliminate

    Gravitational Interactions and Fine-Structure Constant

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    Electromagnetic and gravitational central-field problems are studied with relativistic quantum mechanics on curved space-time backgrounds. Corrections to the transition current are identified. Analogies of the gravitational and electromagnetic spectra suggest the definition of a gravitational fine-structure constant. The electromagnetic and gravitational coupling constants enter the Einstein-Hilbert-Maxwell Lagrangian. We postulate that the variational principle holds with regard to a global dilation transformation of the space-time coordinates. The variation suggests is consistent with a functional relationship of the form alpha_QED being proportional to alpha_G^(1/2), where alpha_QED is the electrodynamic fine-structure constant, and alpha_G its gravitational analogue.Comment: 9 pages; LaTeX; Appeared in the Proceedings to the 17th Bled workshop "What Comes Beyond the Standard Models", Bled, Slovenia, July 2-28, 2014; Editors N. S. Mankoc Borstnik, H. B. Nielsen and D. Lukman; ISSN 1580-4992; book series: Bled Workshops in Physics vol. 15, no. 2, pp. 115-122 (2014

    IL-12 and IL-4 activate a CD39-dependent intrinsic peripheral tolerance mechanism in CD8+ T cells

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    Immune responses to protein antigens involve CD4+ and CD8+ T cells, which follow distinct programs of differentiation. Naïve CD8 T cells rapidly develop cytotoxic T-cell (CTL) activity after T-cell receptor stimulation, and we have previously shown that this is accompanied by suppressive activity in the presence of specific cytokines, i.e. IL-12 and IL-4. Cytokine-induced CD8+ regulatory T (Treg) cells are one of several Treg-cell phenotypes and are Foxp3− IL-10+ with contact-dependent suppressive capacity. Here, we show they also express high level CD39, an ecto-nucleotidase that degrades extracellular ATP, and this contributes to their suppressive activity. CD39 expression was found to be upregulated on CD8+ T cells during peripheral tolerance induction in vivo, accompanied by release of IL-12 and IL-10. CD39 was also upregulated during respiratory tolerance induction to inhaled allergen and on tumor-infiltrating CD8+ T cells. Production of IL-10 and expression of CD39 by CD8+ T cells was independently regulated, being respectively blocked by extracellular ATP and enhanced by an A2A adenosine receptor agonist. Our results suggest that any CTL can develop suppressive activity when exposed to specific cytokines in the absence of alarmins. Thus negative feedback controls CTL expansion under regulation from both nucleotide and cytokine environment within tissues

    The Phenomenon of Increased Bone Conduction

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    Previous experimentation has indicated that under the following two conditions one\u27s sensitivity for bone-conducted sound is increased: (1) closure of the external auditory meatus; and (2) filling the meatus with water. There has been much discussion as to whether this \u27 increased sensitivity is apparent or real. This study attempted to investigate the phenomenon of increased bone conduction in the normal occluded ear. The experimentation was conducted in a sound proof room. The source of sound was a Western Electric 2-A audiometer, which permitted control of the intensity of eight octave frequencies, ranging from 64 to 8192 cycles. The bone conduction receiver was a vibrating button-type oscillator, part of a bone conduction hearing aid. Measurement was made with the receiver on the mastoid bones and on the forehead, and with the ears both open and occluded. Occlusion was affected with white vaseline

    Norrell H. Noble to Dr. Silver, 5 August 1962

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    Professional correspondenc
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