LEE Fizik Mühendisliği Lisansüstü Programı
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Konu "Alan kuramı" ile LEE Fizik Mühendisliği Lisansüstü Programı'a göz atma
Sayfa başına sonuç
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ÖgeNonrelativistic gravity in threedimensions(Lisansüstü Eğitim Enstitüsü, 2021) Zorba, Utku ; Özdemir, Neşe ; 692464 ; Fizik MühendisliğiIn this thesis, we examined the nonrelativistic threedimensional $\mathcal{N}=2$ supergravity theories. These gravity theories are based on a symmetry algebra in which Lie algebra admits nondegenerate, invariant, and symmetric Killing form. We considered a supersymmetric extension of nonrelativistic symmetry algebras from which we constructed ChernSimons 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 NewtonCartan geometry, NewtonCartan gravity, threedimensional Einstein gravity, ChernSimons formalism, and finally basics of spinors in three dimensions. Having collected these tools, we apply the corresponding formalism into threedimensional nonrelativistic symmetries. With the term nonrelativistic 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 nonrelativistic. In Ch. 2, we establish the supersymmetric extension of the extended NewtonHooke, Lifshitz and Schrödinger algebras and construct the corresponding ChernSimons supergravity models. The extended NewtonHooke superalgebra admits two distinct nondegenerate invariant bilinear 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 nonrelativistic model such that parityeven field equations arise from a parityodd Lagrangian. We then showed that it is possible to improve the extended Bargmann superalgebra with dilatations (without including nonrelativistic special conformal symmetry) which we called the extended Lifshitz superalgebra and also established the ChernSimons extended Lifshitz supergravity action. In the final step, we include the nonrelativistic special conformal symmetry and establish the extended Schrödinger superalgebra and the corresponding ChernSimons extended Schrödinger supergravity action. We consider our result as a first step to construct an offshell formulation for the extended Bargmann supergravity and its matter couplings. In Ch. 3, we present a threedimensional nonrelativistic 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 threedimensional model is the contraction of a bimetric 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 ChernSimons 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 nonrelativistic supergravity. In Ch 4, we present a Lie algebra expansion method to generate higherorder threedimensional Schrödinger algebras. Our construction relies on a recent novel threedimensional nonrelativistic 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 higherorder Schrödinger algebra which we refer to as the enhanced Schrödinger algebra. We, next, truncate the nonrelativistic conformal symmetry generators and find a new algebra that goes beyond the threedimensional 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 Bargmanninvariant sense to the extended theory.