55495910
Homogeneous Field and WKB Approximation in Deformed Quantum Mechanics with Minimal Length
In the framework of the deformed quantum mechanics with a minimal length, we consider the motion of a nonrelativistic particle in a homogeneous external field. We find the integral representation for the physically acceptable wave function in the position representation. Using the method of steepest descent, we obtain the asymptotic expansions of the wave function at large positive and negative arguments. We then employ the leading asymptotic expressions to derive the WKB connection formula, which proceeds from classically forbidden region to classically allowed one through a turning point. By the WKB connection formula, we prove the Bohr-Sommerfeld quantization rule up to . We also show that if the slope of the potential at a turning point is too steep, the WKB connection formula is no longer valid around the turning point. The effects of the minimal length on the classical motions are investigated using the Hamilton-Jacobi method. We also use the Bohr-Sommerfeld quantization to study statistical physics in deformed spaces with the minimal length.
15618734
Solving Witten's SFT by insertion of operators on projectors
Following Okawa, we insert operators at the boundary of regulated star algebra projectors to construct the leading order tachyon vacuum solution of open string field theory. We also calculate the energy density of the solution and the ratio between the kinetic and the cubic terms. A universal relationship between these two quantities is found. We show that for any twist invariant projector, the energy density can account for at most 68.46% of the D25-brane tension. The general results are then applied to regulated slivers and butterflies, and the next-to-leading order solution for regulated sliver states is constructed.
119289762
Quantum gravity effects on compact star cores
Abstract Using the Tolman–Oppenheimer–Volkoff equation and the equation of state of zero temperature ultra-relativistic Fermi gas based on generalized uncertainty principle (GUP), the quantum gravitational effects on the cores of compact stars are discussed. Our results show that 2 m ( r ) / r varies with r. Quantum gravity plays an important role in the region r ∼ 10 3 r 0 , where r 0 ∼ β 0 l p , l p is the Planck length and β 0 is a dimensionless parameter accounting for quantum gravity effects. Furthermore, near the center of compact stars, we find that the metric components are g t t ∼ r 4 and g r r = [ 1 − r 2 / ( 6 r 0 2 ) ] − 1 . All these effects are different from those obtained from classical gravity. These results can be applied to neutron stars or denser ones like quark stars. The observed masses of neutron stars ( ⩽ 2 M ⊙ ) indicate that β 0 can not exceed 1037, not as good as the upper bound β 0 10 34 from simple electroweak consideration. This means that incorporating either quantum gravity effects or nuclear interactions, one obtains almost the same mass limits of neutron stars.
117792048
Superluminal neutrinos and domain walls
In this letter, we propose that the recent measurement of superluminal neutrinos in OPERA could be explained by the existence of a domain wall which is left behind after the phase transition of some scalar field in the universe. The scalar field couples to the neutrino and photon field with different effective couplings. It causes different effective metrics and the emergence of superluminal neutrinos. Moreover, if the supernova and the earth are in the same plane parallel to the wall, or the thickness of the wall is much smaller than the distance from the supernova to the earth, the contradiction between OPERA and SN1987a can be reconciled.
118539816
Superluminal Neutrinos and Monopoles
In this letter, we show that superluminal neutrinos announced by OPERA could be explained by the existence of a monopole, which is left behind after the spontaneous symmetry breaking (SSB) phase transition of some scalar fields in the universe. We assume the 't Hooft-Polyakov monopole couples to the neutrinos but not photon fields. The monopole introduces a different effective metric to the neutrinos from the one experienced by photons. We find that the superluminal propagation only exists in a very short distance from the monopole, about $10^3$ cm in OPERA. No matter how far they travel, neutrinos always arrive earlier than photons by the same amount of time, provided a monopole existing on or close to their trajectories. This conclusion can be tested by future experiments. The result reconciles the contradiction between OPERA and supernova neutrinos. We further exclude cosmic strings as a possible theoretical explanation.
1719078
Rolling closed string tachyons and the big crunch
We study the low-energy effective field equations that couple gravity, the dilaton, and the bulk closed string tachyon of bosonic closed string theory. We establish that whenever the tachyon induces the rolling process, the string metric remains fixed while the dilaton rolls to strong coupling. For negative definite potentials we show that this results in an Einstein metric that crunches the universe in finite time. This behavior is shown to be rather generic even if the potentials are not negative definite. The solutions are reminiscent of those in the collapse stage of a cyclic universe cosmology where scalar field potentials with negative energies play a central role.
118994703
Intersecting D-branes in Type IIB Plane Wave Background
We study intersecting D-branes in a type IIB plane wave background using the Green-Schwarz worldsheet formulation. We consider all possible ${\mathrm{D}}_{\ifmmode\pm\else\textpm\fi{}}$-branes intersecting at angles in the plane wave background and identify their residual supersymmetries. We find, in particular, that ${\mathrm{D}}_{\ensuremath{\mp}}\ensuremath{-}{\mathrm{D}}_{\ifmmode\pm\else\textpm\fi{}}$ brane intersections preserve no supersymmetry. We also present the explicit worldsheet expressions of conserved supercharges and their supersymmetry algebras.
42909303
Instantons and emergent geometry
We show that self-dual electromagnetism in noncommutative spacetime is equivalent to self-dual Einstein gravity.
119092503
Anyonic physical observables and spin phase transition
The quantization of charged matter system coupled to Chern-Simons gauge fields is analyzed in a covariant gauge fixing, and gauge invariant physical anyon operators satisfying fractional statistics are constructed in a symmetric phase, based on Dirac's recipe performed on QED. This method provides us a definite way of identifying physical spectrums free from gauge ambiguity and constructing physical anyon operators under a covariant gauge fixing. We then analyze the statistical spin phase transition in a symmetry-broken phase and show that the Higgs mechanism transmutes an anyon satisfying fractional statistics into a canonical boson, a spin 0 Higgs boson or a topologically massive photon.
15090356
Dark Energy and Emergent Spacetime
A natural geometric framework of noncommutative spacetime is symplectic geometry rather than Riemannian geometry. The Darboux theorem in symplectic geometry then admits a novel form of the equivalence principle such that the electromagnetism in noncommutative spacetime can be regarded as a theory of gravity. Remarkably the emergent gravity reveals a noble picture about the origin of spacetime, dubbed as emergent spacetime, which is radically different from any previous physical theory all of which describe what happens in a given spacetime. In particular, the emergent gravity naturally explains the dynamical origin of flat spacetime, which is absent in Einstein gravity: A flat spacetime is not free gratis but a result of Planck energy condensation in a vacuum. This emergent spacetime picture, if it is correct anyway, turns out to be essential to resolve the cosmological constant problem, to understand the nature of dark energy and to explain why gravity is so weak compared to other forces.
12059305
Superstrings and D-branes in A Plane Wave
We carefully analyze the supersymmetry algebra of closed strings and open strings in a type IIB plane wave background. We use eight component chiral spinors, SO(8) MajoranaWeyl spinors, in light-cone gauge to provide a useful basis of string field theory calculation in the plane wave. We consider the two classes of D-branes, D±-branes, and give a worldsheet derivation of conserved supercurrents for all half BPS D-branes preserving 16 supersymmetries in the type IIB plane wave background. We exhaustively provide the supersymmetry algebra of the half BPS branes as well. We also point out that the supersymmetry algebra distinguishes the two SO(4) directions with relative sign which is consistent with the Z2 symmetry of the string action.