Pseudo Hermitian Interactions in the Dirac Equation

Panella, O.; Roy, Provas Kumar

doi:10.3390/sym6010103

Cited by 5 publications

(7 citation statements)

References 30 publications

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“…Although so far there are no experimental signals of a substructure of quarks and leptons, there are speculations that at some higher energy ranges beyond 1 TeV or so there might exist an : ergy scale Ac at which a substructure of quarks and leptons (preons) might become visible [150,134,165,153].…”

Section: Compositenessmentioning

confidence: 99%

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Perspectives of double beta and dark matter search as windows to new physics

Klapdor‐Kleingrothaus

2020

hnps

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Nuclear double beta decay provides an extraordinarily broad potential to search for beyond Standard Model physics, probing already now the TeV scale, on which new physics should manifest itself. These possibilities are reviewed here. First, the results of present generation experiments are presented. The most sensitive one of them - the Heidelberg-Moscow experiment in the Gran Sasso - probes the electron mass now in the sub eV region and has reached recently a limit of ~ 0.1 eV. This limit has striking influence on presently discussed neutrino mass scenarios. Basing to a large extent on the theoretical work of the Heidelberg Double Beta Group in the last two years, results are obtained also for SUSY models (R-parity breaking, sneutrino mass), leptoquarks (leptoquark-Higgs coupling), compositeness, right-handed W boson mass, test of special relativity and equivalence principle in the neutrino sector and others. These results are comfortably competitive to corresponding results from high-energy accelerators like TEVATRON, HERA, etc. One of the enriched 7Ge detectors also yields the most stringent limits for cold dark matter (WIMPs) to date by using raw data. Second, future perspectives of ßß research are discussed. A new Heidelberg experimental proposal (GENIUS) will allow to increase the sensitivity for Majorana neutrino masses from the present level of at best 0.1 eV down to 0.01 or even 0.001 eV. Its physical potential would be a breakthrough into the multi-TeV range for many beyond standard models. Its sensitivity for neutrino oscillation parameters would be larger than of all present terrestrial neutrino oscillation experiments and of those planned for the future. It could probe directly the large angle, and for almost degenerate neutrino mass scenarios even the small angle solution of the solar neutrino problem. It would further, already in a first step using only 100 kg of natural Ge detectors, cover almost the full MSSM parameter space for prediction of neutralinos as cold dark matter, making the experiment competitive to LHC in the search for supersymmetry. Finally GENIUS could be used as the first real time detector of solar pp neutrinos.

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Section: Compositenessmentioning

confidence: 99%

“…Recent theoretical work shows (see [150,168,151,169,153]) that the mass bounds for such an excited neutrino which can be derived from double beta decay are at least of the same order of magnitude as those coming from the direct search of excited states in high energy accelerators (see also Sec. 3).…”

Section: Compositenessmentioning

confidence: 99%

Perspectives of double beta and dark matter search as windows to new physics

Klapdor‐Kleingrothaus

2020

hnps

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“…The potential (22) is exactly solvable with energy eigenvalues (E n ) and wavefunctions (φ n ) given by 14 where P (a,b) n (x) denotes Jacobi polynomials. Now comparing U − (x) with (22) we find that…”

Section: Examplementioning

confidence: 99%

“…Bound states in massless Dirac equation with complex vector potential has recently been considered Ref. 22. So here we will only discuss the Lorentz scalar case.…”

Section: Dirac Equation With Lorentz Scalar Potentialmentioning

confidence: 99%

Dirac equation with complex potentials

Roy

2014

Mod. Phys. Lett. A

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We study (2 + 1) dimensional Dirac equation with complex scalar and Lorentz scalar potentials. It is shown that the Dirac equation admits exact analytical solutions with real eigenvalues for certain complex potentials while for another class of potentials zero energy solutions can be obtained analytically. For the scalar potential cases, it has also been shown that the effective Schrödinger-like equations resulting from decoupling the spinor components can be interpreted as exactly solvable energy dependent Schrödinger equations.

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“…A complete discussion of pseudo-hermiticity and its relationship to related concepts like PT -symmetry and quasi-hermiticity is provided in the monograph [27]. Recent applications of pseudo-hermitian quantum systems concern periodic Hamiltonians [21], dynamical invariants [31], relativistic models [28], random matrix theory [32], among others. While the concepts of pseudo-hermiticity and PT -symmetry have been studied extensively, they have not yet been applied to quantum systems that feature energy-dependent potentials [12].…”

mentioning

confidence: 99%

Pseudo-hermitian andPT-symmetric quantum systems with energy-dependent potentials: Bound-state solutions and energy spectra

Schulze-Halberg

Roy

2017

Annals of Physics

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We introduce generalized versions of complex Scarf and Morse-type potentials that contain energy-dependent parameters. PT -symmetry and pseudo-hermiticity of the associated quantum systems are discussed, and a modified orthogonality relation and pseudo-norm are constructed. We show that despite energy-dependence, our systems can admit real energy spectra and normalizable solutions of bound-state type.

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Pseudo Hermitian Interactions in the Dirac Equation

Cited by 5 publications

References 30 publications

Perspectives of double beta and dark matter search as windows to new physics

Perspectives of double beta and dark matter search as windows to new physics

Dirac equation with complex potentials

Pseudo-hermitian andPT-symmetric quantum systems with energy-dependent potentials: Bound-state solutions and energy spectra

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