A dynamical inconsistency of Horava gravity

The dynamical consistency of the non-projectable version of Horava gravity is investigated by focusing on the asymptotically flat case. It is argued that for generic solutions of the constraint equations the lapse must vanish asymptotically. We then consider particular values of the coupling constants for which the equations are tractable and in that case we prove that the lapse must vanish everywhere -- and not only at infinity. Put differently, the Hamiltonian constraints are generically all second-class. We then argue that the same feature holds for generic values of the couplings, thus revealing a physical inconsistency of the theory. In order to cure this pathology, one might want to introduce further constraints but the resulting theory would then lose much of the appeal of the original proposal by Horava. We also show that there is no contradiction with the time reparametrization invariance of the action, as this invariance is shown to be a so-called "trivial gauge symmetry" in Horava gravity, hence with no associated first-class constraints.Comment: 28 pages, 2 references adde

Self-adjoint extensions and spectral analysis in the generalized Kratzer problem

We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional nonrelativistic motion of a particle in the potential field $V(x)=g_{1}x^{-1}+g_{2}x^{-2}$. For $g_{2}>0$ and $g_{1}<0$, the potential is known as the Kratzer potential and is usually used to describe molecular energy and structure, interactions between different molecules, and interactions between non-bonded atoms. We construct all self-adjoint Schrodinger operators with the potential $V(x)$ and represent rigorous solutions of the corresponding spectral problems. Solving the first part of the problem, we use a method of specifying s.a. extensions by (asymptotic) s.a. boundary conditions. Solving spectral problems, we follow the Krein's method of guiding functionals. This work is a continuation of our previous works devoted to Coulomb, Calogero, and Aharonov-Bohm potentials.Comment: 31 pages, 1 figur

Quantum properties of general gauge theories with composite and external fields

The generating functionals of Green's functions with composite and external fields are considered in the framework of BV and BLT quantization methods for general gauge theories. The corresponding Ward identities are derived and the gauge dependence is investigatedComment: 24 pages, LATEX, slightly changed to clarify the essential new aspect concerning composite fields depending on external ones; added formulas showing lack of (generalized) nilpotence of operators appearing in the Ward identitie

Dirac equation in the magnetic-solenoid field

We consider the Dirac equation in the magnetic-solenoid field (the field of a solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using von Neumann's theory of deficiency indices. We find self-adjoint extensions of the Dirac Hamiltonian in both above dimensions and boundary conditions at the AB solenoid. Besides, for the first time, solutions of the Dirac equation in the magnetic-solenoid field with a finite radius solenoid were found. We study the structure of these solutions and their dependence on the behavior of the magnetic field inside the solenoid. Then we exploit the latter solutions to specify boundary conditions for the magnetic-solenoid field with Aharonov-Bohm solenoid.Comment: 23 pages, 2 figures, LaTex fil

Reduction of quantum noise in optical interferometers using squeezed light

We study the photon counting noise in optical interferometers used for gravitational wave detection. In order to reduce quantum noise a squeezed vacuum state is injected into the usually unused input port. Here, we specifically investigate the so called `dark port case', when the beam splitter is oriented close to 90{\deg} to the incoming laser beam, such that nearly all photons go to one output port of the interferometer, and only a small fraction of photons is seen in the other port (`dark port'). For this case it had been suggested that signal amplification is possible without concurrent noise amplification [R.Barak and Y.Ben-Aryeh, J.Opt.Soc.Am.B25(361)2008]. We show that by injection of a squeezed vacuum state into the second input port, counting noise is reduced for large values of the squeezing factor, however the signal is not amplified. Signal strength only depends on the intensity of the laser beam.Comment: 8 pages, 1 figur

Higher Derivative Quantum Gravity with Gauss-Bonnet Term

Higher derivative theory is one of the important models of quantum gravity, renormalizable and asymptotically free within the standard perturbative approach. We consider the $4-\epsilon$ renormalization group for this theory, an approach which proved fruitful in $2-\epsilon$ models. A consistent formulation in dimension $n=4-\epsilon$ requires taking quantum effects of the topological term into account, hence we perform calculation which is more general than the ones done before. In the special $n=4$ case we confirm a known result by Fradkin-Tseytlin and Avramidi-Barvinsky, while contributions from topological term do cancel. In the more general case of $4-\epsilon$ renormalization group equations there is an extensive ambiguity related to gauge-fixing dependence. As a result, physical interpretation of these equations is not universal unlike we treat $\epsilon$ as a small parameter. In the sector of essential couplings one can find a number of new fixed points, some of them have no analogs in the $n=4$ case.Comment: LaTeX file, 30 pages, 5 figures. Several misprints in the intermediate expressions correcte