Researcher:
Dereli, Tekin

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Tekin

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Dereli

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Dereli, Tekin
Dereli, Dündar Tekin

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Now showing 1 - 10 of 90
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    A remarkable dynamical symmetry of the Landau problem
    (IOP Publishing Ltd, 2022) Nounahon, Philippe; Popov, Todor; Department of Physics; Dereli, Tekin; Faculty Member; Department of Physics; College of Sciences; 201358
    We show that the dynamical group of an electron in a constant magnetic feld is the group of symplectomorphisms Sp(4, R). It is generated by the spinorial realization of the conformal algebra so(2,3) considered in Dirac's seminal paper "A Remarkable Representation of the 3 + 2 de Sitter Group". The symplectic group Sp(4,R) is the double covering of the conformal group SO(2,3) of 2+1 dimensional Minkowski spacetime which is in turn the dynamical group of a hydrogen atom in 2 space dimensions. The Newton-Hooke duality between the 2D hydrogen atom and the Landau problem is explained via the Tits-Kantor-Koecher construction of the conformal symmetries of the Jordan algebra of real symmetric 2 × 2 matrices. The connection between the Landau problem and the 3D hydrogen atom is elucidated by the reduction of a Dirac spinor to a Majorana one in the Kustaanheimo-Stiefel spinorial regularization. © 2021 Published under licence by IOP Publishing Ltd.
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    A trip around octonions
    (IOP Publishing Ltd, 2022) Bilge, Ayse Humeyra; Kocak, Sahin; Department of Physics; Dereli, Tekin; Faculty Member; Department of Physics; College of Sciences; 201358
    In these expository notes, after a contemplation on the dawn of octonions, we give proofs for the Frobenius theorem and the Hurwitz theorem, we review the basics of Clifford algebras and spin groups, and exemplify the startling role played by the octonions in 7- A nd 8-dimensional phenomena such as the special 3- A nd 4-forms, the Bonan form, Spin(7) and Spin(8) groups and the mysterious triality. © 2021 Published under licence by IOP Publishing Ltd.
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    Exactly solvable pairing model using an extension of the Richardson-Gaudin approach
    (World Scientific Publ Co Pte Ltd, 2005) Balantekin, AB; Pehlivan, Y; Department of Physics; Dereli, Tekin; Faculty Member; Department of Physics; College of Sciences; 201358
    We introduce a new class of exactly solvable boson pairing models using the technique of Richardson and Gaudin. Analytical expressions for all energy eigenvalues and the first few energy eigenstates are given. In addition, another solution to Gaudin's equation is also mentioned. A relation with the Calogero-Sutherland model is suggested.
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    Newton-cartan connections with torsion
    (Istanbul Technical University, 2004) Koçak, Şahin; Limoncu, Murat; Department of Physics; Dereli, Tekin; Faculty Member; Department of Physics; College of Sciences; 201358
    We re-formulate the notion of a Newton-Cartan manifold and clarify the compatibility conditions of a connection with torsion with the Newton-Cartan structure.
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    Simple supergravity pp-waves
    (Springer/Plenum Publishers, 2022) Department of Physics; Department of Physics; Dereli, Tekin; Şenikoğlu, Yorgo; Faculty Member; Researcher; Department of Physics; College of Sciences; College of Sciences; 201358; 354435
    Non-gauge generated exact solutions of simple supergravity field equations that describe pp-waves in Rosen coordinates are presented in the language of complex quaternion valued exterior differential forms.
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    Maximal linear subspaces of strong self-dual 2-forms and the Bonan 4-form
    (Elsevier, 2011) Bilge, Ayşe Humeyra; Koçak, Şahin; Department of Physics; Dereli, Tekin; Faculty Member; Department of Physics; College of Sciences; 201358
    The notion of self-duality of 2-forms in 4-dimensions plays an eminent role in many areas of mathematics and physics, but although the 2-forms have a genuine meaning related to curvature and gauge-field-strength in higher dimensions also, their "self-duality" is something which is almost avoided above 4-dimensions. We show that self-duality of 2-forms is a very natural notion in higher (even) dimensions also and we prove the equivalence of some scattered and rarely used definitions in the literature. We demonstrate the usefulness of this higher self-duality by studying it in 8-dimensions and we derive a natural expression for the Bonan form in terms of self-dual 2-forms and we give an explicit expression of the local action of SO(8) on the Bonan form. (C) 2010 Elsevier Inc. All rights reserved.
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    Degenerate spin structures and the Lévy-Leblond equation
    (TÜBİTAK , 2006) Koçak, Ş.; Limoncu, M.; Department of Physics; Dereli, Tekin; Faculty Member; Department of Physics; College of Sciences; 201358
    Newton-Cartan manifolds and the Galilei group are defined by the use of co-rank one degenerate metric tensor. Newton-Cartan connection is lifted to the degenerate spinor bundle over a Newton-Cartan 4-manifold by the aid of degenerate spin group. Levy-Leblond equation is constructed with the lifted connection.
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    Electric charge screening by non-minimal couplings of electromagnetic fields to gravity
    (Iop Publishing Ltd, 2020) Department of Physics; Department of Physics; Dereli, Tekin; Şenikoğlu, Yorgo; Faculty Member; Researcher; Department of Physics; College of Sciences; College of Sciences; 201358; 354435
    A case of non-minimal couplings between gravity and electromagnetic fields is presented. The field equations are worked out in the language of exterior differential forms. A class of exact charge screening solutions is given with a specific discussion on the polarisation and magnetisation of space-time. The consequences of non-minimal couplings to gravity are examined.
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    Dark range of ω in Brans-Dicke gravity
    (IOP Publishing Ltd, 2022) Senikoǧlu, Yorgo; Department of Physics; Dereli, Tekin; Faculty Member; Department of Physics; College of Sciences; 201358
    The variational field equations of Brans-Dicke scalar-tensor theory of gravitation that is coupled to a mass-varying sterile neutrino field are presented in Riemannian and non-Riemannian setting in the language of exterior differential forms over four-dimensional spacetime. In a gravitational plane wave geometry in Rosen coordinates, with the scalar field set equal to a constant, the field equations admit ghost neutrino solutions. These correspond to Majorana spinor configurations for which the total neutrino stress-energy-momentum tensor vanishes. We show here that in the absence of a sterile neutrino in the gravitational wave geometry, there are scalar field configurations for which the total scalar field stress-energy-momentum tensor vanishes for negative values of the Brans-Dicke parameter-3/2 < ω < 0. © 2021 Published under licence by IOP Publishing Ltd.
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    ACDM cosmology with a quiescent anisotropy in a higher dimensional steady state universe
    (IOP Publishing Ltd, 2022) Akarsu, Ozgur; Katırcı, Nihan; Department of Physics; Dereli, Tekin; Faculty Member; Department of Physics; College of Sciences; 201358
    In this work, which follows a series of studies on the higher-dimensional steady state universe idea and prepared for Professor Tekin Dereli's Festschrift, we show the infuence of the dynamical internal (unobservable) space on the evolution of the possible anisotropy of the external (observable) space. We obtain mathematically exactly the same Friedmann equation of the standard ΛCDM model for the external space, but with some remarkable physical diferences. In particular, the higher-dimensional negative cosmological constant plays the role of the four-dimensional positive cosmological constant and the expansion anisotropy, viz., the shear scalar, of the external space mimics a negative cosmological constant; it would mimic a stif fuid when allowed on top of the standard ΛCDM model. This latter feature gives us the opportunity to manipulate the CMB quadrupole temperature fuctuation, suggesting a possible answer to the fact that its observed value is lower than that predicted by the standard ΛCDM model. © 2021 Published under licence by IOP Publishing Ltd.