The shape of the Galactic halo with GaiaGaia DR2 RR Lyrae. Anatomy of an ancient major merger

We use the $Gaia$ DR2 RR Lyrae sample to gain an uninterrupted view of the Galactic stellar halo. We dissect the available volume in slices parallel to the Milky Way's disc to show that within $\sim30$ kpc from the Galactic centre the halo is triaxial, with the longest axis misaligned by $\sim70^{\circ}$ with respect to the Galactic $x$-axis. This anatomical procedure exposes two large diffuse over-densities aligned with the semi-major axis of the halo: the Hercules-Aquila Cloud and the Virgo Over-density. We reveal the kinematics of the entire inner halo by mapping out the amplitudes and directions of the RR Lyrae proper motions. These are then compared to simple models with different anisotropies to demonstrate that the inner halo is dominated by stars on highly eccentric orbits. We interpret the shape of the density and the kinematics of the $Gaia$ DR2 RR Lyrae as evidence in favour of a scenario in which the bulk of the halo was deposited in a single massive merger event.Comment: 12 pages, 7 figures; Accepted for publication in MNRA

The Exact Solution of the Schwarzian Theory

The explicit evaluation of the partition function in the Schwarzian theory is presented.Comment: 3 page

Correlation functions in the Schwarzian theory

A mathematically correct approach to study theories with infinite-dimensional groups of symmetries is presented. It is based on quasi-invariant measures on the groups. In this paper, the properties of the measure on the group of diffeomorphisms are used to evaluate the functional integrals in the Schwarzian theory. As an important example of the application of the new technique, we explicitly evaluate the correlation functions in the Schwarzian theory.Comment: 29 pages, 3 figure

Paths with singularities in functional integrals of quantum field theory

In the toy model ($\phi^{4}$-interacting quantum field theory in one-dimensional "Euclidean" space-time) we prove that the functional integrals of the free field theory evaluated over the space of continuous functions are equal to the functional integrals of the interacting field theory evaluated over a set of spaces containing the spaces of discontinuous functions

A quantum mechanical model of "dark matter"

The role of singular solutions in some simple quantum mechanical models is studied. The space of the states of two-dimensional quantum harmonic oscillator is shown to be separated into sets of states with different properties.Comment: 9 pages, LaTex, 4 figure

Quantum restoration of broken symmetries

A certain non-linear non-local substitution is shown to transform the action of the self-interacting quantum field to the free one. The functional integrals in both theories are equal to each other. However, the integrations are performed over different functional spaces. The classical action and the classical limit of the corresponding quantum theory turn out to be different. And the symmetry originally broken in the classical theory is restored in the classical limit of the quantum theory.Comment: LaTex 5 page

Peculiar spaces of relativistic quantum fields

We study how quantum field theory models are modified under the reparametrizations of the space-time coordinates and some simultaneous transformations of the field function. The transformations that turn the action of the massive field in the Minkowski space-time into the action of the massless field in some curved space are presented.Comment: 7 page

On the local limit of quantum field theories defined on the loop space

The local limit of a quantum field theory on the loop space is studied. It is proved that the invariance of the theory with respect to the group of diffeomorphisms leads to Feynman diagrams convergence in the local limit

A class of exactly solvable quantum models of scalar gravity

Exactly solvable quantum theory of a singular at the origin scalar field with the self-interaction of Liouville type is proposed. The mean value of the scale factor in the FLRW metric as a function of conformal time is evaluated explicitly.Comment: 5 page

A Prototype for Science Alerts

Many of the science goals of the GAIA mission, especially for bursting or time-varying phenomena like supernovae or microlensing, require an early identification, analysis and release of preliminary data. The alerting on rare and unusual events is the scientific equivalent of the finding of needles in haystacks or the panning for gold-dust in rivers. In modern signal processing, such novelty detection is routinely performed with self-organising maps (SOMs), which are an unsupervised clustering algorithm invented by Kohonen. Here, we describe the application of SOMS to the classification of data provided by large-scale surveys such as GAIA and to the despatching of scientific alerts. We illustrate our ideas by processing the publically available OGLE II dataset towards the Bulge, identifying major classes of variable stars (such as novae, small amplitude red giant variables, eclipsing binaries and so on) and extracting the rare, discrepant lightcurves from which the alerts can be drawn.Comment: 8 pages, 10 figures, invited review for "The Three Dimensional Universe with GAIA", eds M. Perryman, C. Turon (ESA SP-576