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  • Öge
    Non-relativistic gravity in three-dimensions
    (Lisansüstü Eğitim Enstitüsü, 2021) Zorba, Utku ; Özdemir, Neşe ; 692464 ; Fizik Mühendisliği
    In this thesis, we examined the non-relativistic three-dimensional $\mathcal{N}=2$ supergravity theories. These gravity theories are based on a symmetry algebra in which Lie algebra admits non-degenerate, invariant, and symmetric Killing form. We considered a supersymmetric extension of non-relativistic symmetry algebras from which we constructed Chern-Simons actions, and as a result, we have obtained their gauge transformations and field equations, and the matter couplings. In addition, we developed a framework to construct Lie algebra expansion to obtain extended Schrödinger algebra for the first time in the literature, and this result will be used for our future plan for constructing matter multiplets that transform under supersymmetric extended Schrödinger symmetries. The first chapter of the thesis presents a sufficient groundwork for the following sections. Our purpose is to elaborate on Newton-Cartan geometry, Newton-Cartan gravity, three-dimensional Einstein gravity, Chern-Simons formalism, and finally basics of spinors in three dimensions. Having collected these tools, we apply the corresponding formalism into three-dimensional non-relativistic symmetries. With the term non-relativistic symmetry we imply that all the algebras that we will consider next sections are an extension of Galilei algebra, since we designate the symmetry algebras as non-relativistic. In Ch. 2, we establish the supersymmetric extension of the extended Newton-Hooke, Lifshitz and Schrödinger algebras and construct the corresponding Chern-Simons supergravity models. The extended Newton-Hooke superalgebra admits two distinct non-degenerate invariant bi-linear forms that gives rise to two different supergravity models with the same equations of motion. These two models are particularly different in terms of the parity of the bosonic actions. In particular, we showed that there is an exotic non-relativistic model such that parity-even field equations arise from a parity-odd Lagrangian. We then showed that it is possible to improve the extended Bargmann superalgebra with dilatations (without including non-relativistic special conformal symmetry) which we called the extended Lifshitz superalgebra and also established the Chern-Simons extended Lifshitz supergravity action. In the final step, we include the nonrelativistic special conformal symmetry and establish the extended Schrödinger superalgebra and the corresponding Chern-Simons extended Schrödinger supergravity action. We consider our result as a first step to construct an off-shell formulation for the extended Bargmann supergravity and its matter couplings. In Ch. 3, we present a three-dimensional non-relativistic model of gravity that is invariant under the central extension of the symmetry group that leaves the recently constructed Newtonian gravity action invariant. In particular, we show that the three-dimensional model is the contraction of a bi-metric model that is the sum of the Einstein gravity in Lorentzian and the Euclidean signatures. Moreover, the model is distinct from the Newtonian gravity both at the level of action and the matter coupling. By choosing fields appropriately, we show that this action can be obtained by a contraction procedure. Our model is of the Chern-Simons type, which allowes us to establish the supersymmetric completion by extending the algebra with five supersymmetry generators. The supersymmetric completion of this action provides one of the very few examples of action for non-relativistic supergravity. In Ch 4, we present a Lie algebra expansion method to generate higher-order three-dimensional Schrödinger algebras. Our construction relies on a recent novel three-dimensional non-relativistic conformal Galilei algebra that we used as a core algebra. By employing the Lie algebra expansions, we first recovered the extended Schrödinger algebra and obtained a new higher-order Schrödinger algebra which we refer to as the enhanced Schrödinger algebra. We, next, truncate the non-relativistic conformal symmetry generators and find a new algebra that goes beyond the three-dimensional extended Bargmann algebra. In particular, we show that the symmetry algebra that was proposed as the symmetry algebra of action for Newtonian gravity is not uniquely defined but can be closed with three parameters. We also show that for a particular choice of these parameters the Bargmann algebra becomes a subalgebra of the extended algebra and one can introduce a mass current in a Bargmann-invariant sense to the extended theory.
  • Öge
    Development of a segmented detector for reactor antineutrinos
    ( 2020) Kandemir, Mustafa ; Çakır, Muammer Altan ; 621467 ; Fizik Mühendisliği ; Physics Engineering