479 research outputs found

    Deformed Clifford algebra and supersymmetric quantum mechanics on a phase space with applications in quantum optics

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    In order to realize supersymmetric quantum mechanics methods on a four dimensional classical phase-space, the complexified Clifford algebra of this space is extended by deforming it with the Moyal star-product in composing the components of Clifford forms. Two isospectral matrix Hamiltonians having a common bosonic part but different fermionic parts depending on four real-valued phase space functions are obtained. The Hamiltonians are doubly intertwined via matrix-valued functions which are divisors of zero in the resulting Moyal-Clifford algebra. Two illustrative examples corresponding to Jaynes-Cummings-type models of quantum optics are presented as special cases of the method. Their spectra, eigen-spinors and Wigner functions as well as their constants of motion are also obtained within the autonomous framework of deformation quantization.Comment: 22 pages. published versio

    Massive hematuria due to a congenital renal arteriovenous malformation mimicking a renal pelvis tumor: a case report

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    <p>Abstract</p> <p>Introduction</p> <p>Congenital renal arteriovenous malformations (AVMs) are very rare benign lesions. They are more common in women and rarely manifest in elderly people. In some cases they present with massive hematuria. Contemporary treatment consists of transcatheter selective arterial embolization which leads to resolution of the hematuria whilst preserving renal parenchyma.</p> <p>Case presentation</p> <p>A 72-year-old man, who was heavy smoker, presented with massive hematuria and flank pain. CT scan revealed a filling defect caused by a soft tissue mass in the renal pelvis, which initially led to the suspicion of a transitional cell carcinoma (TCC) of the upper tract, in view of the patient's age and smoking habits. However a subsequent retrograde study could not depict any filling defect in the renal pelvis. Selective right renal arteriography confirmed the presence of a renal AVM by demonstrating abnormal arterial communication with a vein with early visualization of the venous system. At the same time successful selective transcatheter embolization of the lesion was performed.</p> <p>Conclusion</p> <p>This case highlights the importance of careful diagnostic work-up in the evaluation of upper tract hematuria. In the case presented, a congenital renal AVM proved to be the cause of massive upper tract hematuria and flank pain in spite of the initial evidence indicating the likely diagnosis of a renal pelvis tumor.</p

    Gravity, Two Times, Tractors, Weyl Invariance and Six Dimensional Quantum Mechanics

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    Fefferman and Graham showed some time ago that four dimensional conformal geometries could be analyzed in terms of six dimensional, ambient, Riemannian geometries admitting a closed homothety. Recently it was shown how conformal geometry provides a description of physics manifestly invariant under local choices of unit systems. Strikingly, Einstein's equations are then equivalent to the existence of a parallel scale tractor (a six component vector subject to a certain first order covariant constancy condition at every point in four dimensional spacetime). These results suggest a six dimensional description of four dimensional physics, a viewpoint promulgated by the two times physics program of Bars. The Fefferman--Graham construction relies on a triplet of operators corresponding, respectively to a curved six dimensional light cone, the dilation generator and the Laplacian. These form an sp(2) algebra which Bars employs as a first class algebra of constraints in a six-dimensional gauge theory. In this article four dimensional gravity is recast in terms of six dimensional quantum mechanics by melding the two times and tractor approaches. This "parent" formulation of gravity is built from an infinite set of six dimensional fields. Successively integrating out these fields yields various novel descriptions of gravity including a new four dimensional one built from a scalar doublet, a tractor vector multiplet and a conformal class of metrics.Comment: 27 pages, LaTe

    Wigner phase space distribution as a wave function

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    We demonstrate that the Wigner function of a pure quantum state is a wave function in a specially tuned Dirac bra-ket formalism and argue that the Wigner function is in fact a probability amplitude for the quantum particle to be at a certain point of the classical phase space. Additionally, we establish that in the classical limit, the Wigner function transforms into a classical Koopman-von Neumann wave function rather than into a classical probability distribution. Since probability amplitude need not be positive, our findings provide an alternative outlook on the Wigner function's negativity.Comment: 6 pages and 2 figure

    Deformation Quantization of Fermi Fields

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    Deformation quantization for any Grassmann scalar free field is described via the Weyl-Wigner-Moyal formalism. The Stratonovich-Weyl quantizer, the Moyal ⋆\star-product and the Wigner functional are obtained by extending the formalism proposed recently in [35] to the fermionic systems of infinite number of degrees of freedom. In particular, this formalism is applied to quantize the Dirac free field. It is observed that the use of suitable oscillator variables facilitates considerably the procedure. The Stratonovich-Weyl quantizer, the Moyal ⋆\star-product, the Wigner functional, the normal ordering operator, and finally, the Dirac propagator have been found with the use of these variables.Comment: 19+1 pages, no figures, revtex4 file styl
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