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Register a new userAlgebraic Solution of the Supersymmetric Hydrogen Atom in d Dimensions
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In this paper the N=2 supersymmetric extension of the Schroedinger Hamiltonian with 1/r-potential in arbitrary space-dimensions is constructed. The supersymmetric hydrogen atom admits a conserved Laplace-Runge-Lenz vector which extends the rotational symmetry SO(d) to a hidden SO(d+1) symmetry. This symmetry of the system is used to determine the discrete eigenvalues with their degeneracies and the corresponding bound state wave functions.
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We find the general fully non-linear solution of topologically massive supergravity admitting a Killing spinor. It is of plane-wave type, with a null Killing vector field. Conversely, we show that all solutions with a null Killing vector are supersymmetric for one or the other choice of sign for the Chern-Simons coupling constant mu. If mu does not take the critical value mu=pm 1, these solutions are asymptotically regular on a Poincare patch, but do not admit a smooth global compactification with boundary S^1timesR. In the critical case, the solutions have a logarithmic singularity on the boundary of the Poincare patch. We derive a Nester-Witten identity, which allows us to identify the associated charges, but we conclude that the presence of the Chern-Simons term prevents us from making a statement about their positivity. The Nester-Witten procedure is applied to the BTZ black hole.
We consider general aspects of N=2 gauge theories in three dimensions, including their multiplet structure, anomalies and non-renormalization theorems. For U(1) gauge theories, we discuss the quantum corrections to the moduli space, and their relation to ``mirror symmetries of 3d N=4 theories. Mirror symmetry is given an interpretation in terms of vortices. For SU(N_c) gauge groups with N_f fundamental flavors, we show that, depending on the number of flavors, there are quantum moduli spaces of vacua with various phenomena near the origin.
While the Kerr-Schild double copy of the Coulomb solution in dimensions higher than three is the Schwarzschild black hole, it is known that it should be a non-vacuum solution in three dimensions. We show that the static black hole solution of Einstein-Maxwell theory (with one ghost sign in the action) is the double copy with the correct Newtonian limit, which provides an improvement over the previous construction with a free scalar field that does not vanish at infinity. By considering a negative cosmological constant, we also study the charged Ba~nados-Teitelboim-Zanelli black hole and find that the single copy gauge field is the Coulomb solution modified by a term which describes an electric field linearly increasing with the radial coordinate, which is the usual behaviour of the Schwarzschild-AdS black hole in higher dimensions when written around a flat background metric.
Wormholes (WH) require negative energy, and therefore an exotic matter source. Since Casimir energy is negative, it has been speculated as a good candidate to source that objects a long time ago. However only very recently a full solution for D = 4 has been found by Garattini [1], thus the Casimir energy can be a source of traversable WHs. Soon later Alencar et al [2] have shown, that this is not true in D = 3. In this paper, we show that Casimir energy can be a source of the Morris-Thorne WH for all spacetime with D > 3. Finally, we add the cosmological constant and find that for D = 3 Casimir WHs are possible, however, the space must always being AdS. For D > 3, we show that the cosmological constant invert the signal with increasing throat size.
The elastic scattering, Stark transitions and Coulomb deexcitation of excited antiprotonic hydrogen atom in collisions with hydrogenic atom have been studied in the framework of the fully quantum-mechanical close-coupling method for the first time. The total cross sections $sigma_{nl to nl}(E)$ and averaged on the initial angular momentum $l$ cross sections $sigma_{nto n}(E)$ have been calculated for the initial states of $(bar{p}p)_{n}$ atoms with the principal quantum number $n=3 - 14 $ and at the relative energies $E=0.05 - 50$ eV. The energy shifts of the $ns$ states due to the strong interaction and relativistic effects are taken into account. Some of our results are compared with the semiclassical calculations.
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