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Showing 1 to 15 of 15 for “"Minkowski space"”.
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The free particle on q-Minkowski space
… abzubilden. In dieser Arbeit wird der q-Minkowski Raum als ein konkretes Modell solch eines betrachtet. Das besondere dieser q-deformierten Räume ist, daß sie eine so genannte Quantengruppe als Hintergrundsymmetrie besitzen. Dies macht es möglich sich die in der Physik äußerst wichtigen …
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Self-similar solutions to the mean curvature flow in Euclidean and Minkowski space
… motions of immersed hypersurfaces in Euclidean space under the mean curvature flow and derive the corresponding hypersurface equations. Then we present a new two-parameter family of immersed helicoidal surfaces that rotate/translate with constant velocity under the flow. We look at their …
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Conformal symmetries in special and general relativity.The derivation and interpretation of conformal symmetries and asymptotic conformal symmetries in Minkowski space-time and in some space-times of general relativity.
… conformal Killing vectors in asymptotically-flat space-times of general relativity. This problem has been examined by two different methods; in Chapter 5 the asymptotic expansion technique originated by Newman and Unti [31] leads to a solution for asymptotically-flat spacetimes which admit an …
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Scattering and stability properties of nonlinear wave equations on asymptotically flat spacetimes
… equations (PDEs) in asymptotically flat spacetimes. Each project focuses on the behaviour of solutions nearby special ones and are therefore part of a perturbative understanding of these PDEs. Furthermore, all projects are connected by the search for a geometric understanding of the …
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Radiation field for Einstein vacuum equations
… Einstein Vacuum equations, which are close to Minkowski space, at null infinity. By imposing harmonic gauge, the Einstein Vacuum equations reduce to a system of quasilinear wave equations on R"j". We show that if the space dimension n > 5 the Moller wave operator is an isomorphism from Cauchy …
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Worldsheet methods for perturbative quantum field theory
… symmetries of the asymptotic null boundary of Minkowski space, called $\scri$, and scattering amplitudes. The first part begins with a review of the CHY formulas for scattering amplitudes, the scattering equations and the ambitwistor string including its pure spinor version. Next are the …
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Infinite derivative gravity : a ghost and singularity-free theory
… calculated, before being linearised around both Minkowski space and de Sitter space. The theory is then constrained so as to avoid ghosts and tachyons by appealing to the modified propagator, which is also derived. Finally, the Raychaudhuri Equation is employed in order to describe the …
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The standard model in 5D : theoretical consistency and experimental constraints
The four-dimensional Minkowski space is known to be a good description for space-time down to the length scales probed by the latest high-energy experiments. Nevertheless, there is the viable and exciting possibility that additional space-time structure will be observable in the next generation of …
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Does the Causal Structure of Space-Time Determine its Geometry
… it possible to construe the causal structure of space-time as basic and from it to reconstruct the topological and metrical structure of space-time? The problem is first examined within the context of Minkowski space-time (Chapter II) and then generalized to the class of space-time models …
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Convexity and curvature in Lorentzian geometry
A space-time satisfies $\mathcal{R} \geq K $ if the sectional curvatures are bounded below by $K$ for spacelike planes and above by $K$ for timelike planes (similarly, a space-time satisfies $\mathcal{R} \leq K$ if the aforementioned inequalities are reversed). We demonstrate that these curvature …
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Constraint preserving boundary conditions for the linearized Einstein equations
… work we consider the linearization around the Minkowski space-time in Cartesian coordinates of the generalized Einstein-Christoffel system and analyze different kinds of boundary conditions that are designed to ensure that the constraints vanish throughout the computational domain: the Neumann, …
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Geometric aspects of gauge and spacetime symmetries
… of these groups to physical properties of the spacetimes. We then make group deformation local, generalising deformed special relativity (DSR) by describing gravity as a gauge theory of the de Sitter group. We find that in our construction Minkowski space has a connection with torsion; physical …
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Non-collapsing on Hypersurfaces of Prescribed Curvature
… study is the mean convex mean curvature flow in Minkowski space $\mathbb{L}^{n,1}$. Of particular interest is the study of co-compact mean convex embedded spacelike hypersurfaces evolving by the mean curvature flow into $\mathbb{L}^{n,1}$. In particular, we deduce a non-collapsing estimate by …
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Non-collapsing on Hypersurfaces of Prescribed Curvature
… study is the mean convex mean curvature flow in Minkowski space $\mathbb{L}^{n,1}$. Of particular interest is the study of co-compact mean convex embedded spacelike hypersurfaces evolving by the mean curvature flow into $\mathbb{L}^{n,1}$. In particular, we deduce a non-collapsing estimate by …
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The broken non-abelian X-ray transform and inverse problems for connections at high fixed frequency
… the case where M = D\Ω is a causal diamond D in Minkowski space to which a small neighbourhood Ω of the observer's worldline has been removed, g is the induced Lorentzian metric, and the set of broken geodesics are the broken light rays that start and end in Ω. This transform was introduced by …