Regularized Green's Function for the Inverse Square Potential

A Green's function approach is presented for the D-dimensional inverse square potential in quantum mechanics. This approach is implemented by the introduction of hyperspherical coordinates and the use of a real-space regulator in the regularized version of the model. The application of Sturm-Liouville theory yields a closed expression for the radial energy Green's function. Finally, the equivalence with a recent path-integral treatment of the same problem is explicitly shown.Comment: 10 pages. The final section was expande

Two-Pion Exchange Nucleon-Nucleon Potential: Model Independent Features

A chiral pion-nucleon amplitude supplemented by the HJS subthreshold coefficients is used to calculate the the long range part of the two-pion exchange nucleon-nucleon potential. In our expressions the HJS coefficients factor out, allowing a clear identification of the origin of the various contributions. A discussion of the configuration space behaviour of the loop integrals that determine the potential is presented, with emphasis on cancellations associated with chiral symmetry. The profile function for the scalar-isoscalar component of the potential is produced and shown to disagree with those of several semi-phenomenological potentials.Comment: 16 pages, 9 embedded figures, Latex 2.09, Revtex.sty, epsf.st

Effective Field Theory Program for Conformal Quantum Anomalies

The emergence of conformal states is established for any problem involving a domain of scales where the long-range, SO(2,1) conformally invariant interaction is applicable. Whenever a clear-cut separation of ultraviolet and infrared cutoffs is in place, this renormalization mechanism produces binding in the strong-coupling regime. A realization of this phenomenon, in the form of dipole-bound anions, is discussed.Comment: 15 pages. Expanded, with additional calculational details. To be published in Phys. Rev.

A Survey on Quantum Computational Finance for Derivatives Pricing and VaR

[Abstract]: We review the state of the art and recent advances in quantum computing applied to derivative pricing and the computation of risk estimators like Value at Risk. After a brief description of the financial derivatives, we first review the main models and numerical techniques employed to assess their value and risk on classical computers. We then describe some of the most popular quantum algorithms for pricing and VaR. Finally, we discuss the main remaining challenges for the quantum algorithms to achieve their potential advantages.Xunta de Galicia; ED431G 2019/01All authors acknowledge the European Project NExt ApplicationS of Quantum Computing (NEASQC), funded by Horizon 2020 Program inside the call H2020-FETFLAG-2020-01 (Grant Agreement 951821). Á. Leitao, A. Manzano and C. Vázquez wish to acknowledge the support received from the Centro de Investigación de Galicia “CITIC”, funded by Xunta de Galicia and the European Union (European Regional Development Fund- Galicia 2014-2020 Program), by Grant ED431G 2019/01

Conformal Enhancement of Holographic Scaling in Black Hole Thermodynamics: A Near-Horizon Heat-Kernel Framework

Standard thermodynamic treatments of quantum field theory in the presence of black-hole backgrounds reproduce the black hole entropy by usually specializing to the leading order of the heat-kernel or the high-temperature expansion. By contrast, this work develops a hybrid framework centered on geometric spectral asymptotics whereby these assumptions are shown to be unwarranted insofar as black hole thermodynamics is concerned. The approach--consisting of the concurrent use of near-horizon and heat-kernel asymptotic expansions--leads to a proof of the holographic scaling of the entropy as a universal feature driven by conformal quantum mechanics.Comment: 13 pages, JHEP style. Added section 3 in the new version and a few typos were correcte

Black Hole Thermodynamics from Near-Horizon Conformal Quantum Mechanics

The thermodynamics of black holes is shown to be directly induced by their near-horizon conformal invariance. This behavior is exhibited using a scalar field as a probe of the black hole gravitational background, for a general class of metrics in D spacetime dimensions (with $D \geq 4$). The ensuing analysis is based on conformal quantum mechanics, within a hierarchical near-horizon expansion. In particular, the leading conformal behavior provides the correct quantum statistical properties for the Bekenstein-Hawking entropy, with the near-horizon physics governing the thermodynamic properties from the outset. Most importantly: (i) this treatment reveals the emergence of holographic properties; (ii) the conformal coupling parameter is shown to be related to the Hawking temperature; and (iii) Schwarzschild-like coordinates, despite their ``coordinate singularity,''can be used self-consistently to describe the thermodynamics of black holes.Comment: 16 pages. Sections 2 and 3 and sections 4 and 5 of version 1 were merged and reduced; a few typos were corrected. The original central results and equations remain unchange