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

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

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

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

Renormalizable quantum field theory as a limit of a quantum field model on the loop space

A nonlocal generalization of quantum field theory in which momentum space is the space of continuous maps of a circle into $\mathbf{R}^4$ is proposed. Functional integrals in this theory are proved to exist. Renormalized quantum field model is obtained as a local limit of the proposed theory.Comment: 9 pages, LaTe

Evidence for Two Early Accretion Events That Built the Milky Way Stellar Halo

The Gaia Sausage is the major accretion event that built the stellar halo of the Milky Way galaxy. Here, we provide dynamical and chemical evidence for a second substantial accretion episode, distinct from the Gaia Sausage. The Sequoia Event provided the bulk of the high energy retrograde stars in the stellar halo, as well as the recently discovered globular cluster FSR 1758. There are up to 6 further globular clusters, including $\omega$~Centauri, as well as many of the retrograde substructures in Myeong et al. (2018), associated with the progenitor dwarf galaxy, named the Sequoia. The stellar mass in the Sequoia galaxy is $\sim 5 \times 10^{7} M_\odot$, whilst the total mass is $\sim 10^{10} M_\odot$, as judged from abundance matching or from the total sum of the globular cluster mass. Although clearly less massive than the Sausage, the Sequoia has a distinct chemo-dynamical signature. The strongly retrograde Sequoia stars have a typical eccentricity of $\sim0.6$, whereas the Sausage stars have no clear net rotation and move on predominantly radial orbits. On average, the Sequoia stars have lower metallicity by $\sim 0.3$ dex and higher abundance ratios as compared to the Sausage. We conjecture that the Sausage and the Sequoia galaxies may have been associated and accreted at a comparable epoch.Comment: MNRAS, revised version in light of referee's comments. Minor modifications and clarifications to the argument, as well as an updated list of Sausage Globular Cluster