Solution of the Dyson--Schwinger equation on de Sitter background in IR limit

We propose an ansatz which solves the Dyson-Schwinger equation for the real scalar fields in Poincare patch of de Sitter space in the IR limit. The Dyson-Schwinger equation for this ansatz reduces to the kinetic equation, if one considers scalar fields from the principal series. Solving the latter equation we show that under the adiabatic switching on and then off the coupling constant the Bunch-Davies vacuum relaxes in the future infinity to the state with the flat Gibbons-Hawking density of out-Jost harmonics on top of the corresponding de Sitter invariant out-vacuum.Comment: 20 pages, including 4 pages of Appendix. Acknowledgements correcte

Expansion in Feynman Graphs as Simplicial String Theory

We show that the series expansion of quantum field theory in the Feynman diagrams can be explicitly mapped on the partition function of the simplicial string theory -- the theory describing embeddings of the two--dimensional simplicial complexes into the space--time of the field theory. The summation over two--dimensional geometries in this theory is obtained from the summation over the Feynman diagrams and the integration over the Schwinger parameters of the propagators. We discuss the meaning of the obtained relation and derive the one--dimensional analog of the simplicial theory on the example of the free relativistic particle.Comment: Latex, 11pp, Minor mintakes are correcte

Neutrino production coherence and oscillation experiments

Neutrino oscillations are only observable when the neutrino production, propagation and detection coherence conditions are satisfied. In this paper we consider in detail neutrino production coherence, taking \pi\to \mu \nu \ decay as an example. We compare the oscillation probabilities obtained in two different ways: (1) coherent summation of the amplitudes of neutrino production at different points along the trajectory of the parent pion; (2) averaging of the standard oscillation probability over the neutrino production coordinate in the source. We demonstrate that the results of these two different approaches exactly coincide, provided that the parent pion is considered as pointlike and the detection process is perfectly localized. In this case the standard averaging of the oscillation probability over the finite spatial extensions of the neutrino source (and detector) properly takes possible decoherence effects into account. We analyze the reason for this equivalence of the two approaches and demonstrate that for pion wave packets of finite width \sigma_{x\pi} the equivalence is broken. The leading order correction to the oscillation probability due to \sigma_{x\pi}\ne 0 is shown to be \sim [v_g/(v_g-v_\pi)]\sigma_{x\pi}/l_{osc}, where v_g and v_\pi \ are the group velocities of the neutrino and pion wave packets, and l_{osc} is the neutrino oscillation length.Comment: LaTeX, 40 pages, 4 figures. v2: minor typos correcte

Quantum field theoretic approach to neutrino oscillations in matter

We consider neutrino oscillations in non-uniform matter in a quantum field theoretic (QFT) approach, in which neutrino production, propagation and detection are considered as a single process. We find the conditions under which the oscillation probability can be sensibly defined and demonstrate how the properly normalized oscillation probability can be obtained in the QFT framework. We derive the evolution equation for the oscillation amplitude and discuss the conditions under which it reduces to the standard Schr\"odinger-like evolution equation. It is shown that, contrary to the common usage, the Schr\"odinger-like evolution equation is not applicable in certain cases, such as oscillations of neutrinos produced in decays of free pions provided that sterile neutrinos with $\Delta m^2\gtrsim 1$ eV$^2$ exist.Comment: LaTeX, 24 pages + 16 pages of appendices, 1 figure. V2: typos correcte

Floquet theory of neutrino oscillations in the earth

We review the Floquet theory of linear differential equations with periodic coefficients and discuss its applications to neutrino oscillations in matter of periodically varying density. In particular, we consider parametric resonance in neutrino oscillations which can occur in such media, and discuss implications for oscillations of neutrinos traversing the earth and passing through the earth's core.Comment: LaTeX, 28 pages, 8 eps figures. Contribution to the special issue of Yad. Fiz. dedicated to the memory of A.B. Migda

Subtleties in the quasi-classical calculation of Hawking radiation

he quasi-classical method of deriving Hawking radiation is investigated. In order to recover the original Hawking temperature one must take into account a previously ignored contribution coming from the temporal part of the action. This contribution plus a contribution coming from the spatial part of the action gives the correct temperature.Comment: 6 pages revtex. Honorable Mention in 2008 GRF essay contest, typos fixed, sign errors corrected. To be published in Special Issue of IJMP

Analysis of Gamma Radiation from a Radon Source: Indications of a Solar Influence

This article presents an analysis of about 29,000 measurements of gamma radiation associated with the decay of radon in a sealed container at the Geological Survey of Israel (GSI) Laboratory in Jerusalem between 28 January 2007 and 10 May 2010. These measurements exhibit strong variations in time of year and time of day, which may be due in part to environmental influences. However, time-series analysis reveals a number of periodicities, including two at approximately 11.2 year$^{-1}$ and 12.5 year$^{-1}$. We have previously found these oscillations in nuclear-decay data acquired at the Brookhaven National Laboratory (BNL) and at the Physikalisch-Technische Bundesanstalt (PTB), and we have suggested that these oscillations are attributable to some form of solar radiation that has its origin in the deep solar interior. A curious property of the GSI data is that the annual oscillation is much stronger in daytime data than in nighttime data, but the opposite is true for all other oscillations. This may be a systematic effect but, if it is not, this property should help narrow the theoretical options for the mechanism responsible for decay-rate variability.Comment: 9 pages, 21 figure

Exotic smooth structures on 4-manifolds with zero signature

For every integer $k\geq 2$, we construct infinite families of mutually nondiffeomorphic irreducible smooth structures on the topological $4$-manifolds $(2k-1)(S^2\times S^2)$ and (2k-1)(\CP#\CPb), the connected sums of $2k-1$ copies of $S^2\times S^2$ and \CP#\CPb.Comment: 6 page

Black Hole Motion in Entropic Reformulation of General Relativity

We consider a system of black holes -- a simplest substitute of a system of point particles in the mechanics of general relativity -- and try to describe their motion with the help of entropic action: a sum of the areas of black hole horizons. We demonstrate that such description is indeed consistent with the Newton's laws of motion and gravity, modulo numerical coefficients, which coincide but seem different from unity. Since a large part of the modern discussion of entropic reformulation of general relativity is actually based on dimensional considerations, for making a next step it is crucially important to modify the argument, so that these dimensionless parameters acquire correct values.Comment: 6 page

Comment on the Surface Exponential for Tensor Fields

Starting from essentially commutative exponential map $E(B|I)$ for generic tensor-valued 2-forms $B$, introduced in \cite{Akh} as direct generalization of the ordinary non-commutative $P$-exponent for 1-forms with values in matrices (i.e. in tensors of rank 2), we suggest a non-trivial but multi-parametric exponential ${\cal E}(B|I|t_\gamma)$, which can serve as an interesting multi-directional evolution operator in the case of higher ranks. To emphasize the most important aspects of the story, construction is restricted to backgrounds $I_{ijk}$, associated with the structure constants of {\it commutative} associative algebras, what makes it unsensitive to topology of the 2d surface. Boundary effects are also eliminated (straightfoward generalization is needed to incorporate them).Comment: 6 page