The exchange of spin-0 or spin-1 bosons between fermions or spin-polarised macroscopic objects gives rise to various spin-dependent potentials. We derive the coordinate-space non-relativistic potentials induced by the exchange of such bosons, including contact terms that can play an important role in atomic-scale phenomena, and correct for errors and omissions in the literature. We summarise the properties of the potentials and their relevance for various types of experiments. These potentials underpin the interpretation of experiments that search for new bosons, including spectroscopy, torsion-pendulum measurements, magnetometry, parity nonconservation and electric dipole moment experiments.

Agreement between theoretical calculations of atomic structure and spectroscopic measurements is used to constrain possible contribution of exotic spin-dependent interactions between electrons to the energy differences between states in helium-4. In particular, constraints on dipole-dipole interactions associated with the exchange of pseudoscalar bosons (such as axions or axion-like particles, ALPs) with masses 10 −2 eV m 10 4 eV are improved by a factor of ∼ 100. The first atomic-scale constraints on several exotic velocity-dependent dipole-dipole interactions are established as well. The most commonly employed framework for the purpose of comparing different experimental searches for exotic spin-dependent interactions is that introduced in Ref.[1] to describe long-range spin-dependent potentials associated with the axion and extended in Ref.[2] to encompass long-range potentials associated with any generic spin-0 or spin-1 boson. The spin-dependent potentials enumerated in Ref. [2] are characterized by dimensionless coupling constants that specify the strength of the interaction between various particles and a characteristic range λ for the interaction associated with the reduced Compton wavelength of the new boson of mass m 0 , λ = /(m 0 c), where is the reduced Planck constant and c is the speed of light. Depending on the nature of the new interaction, different particles will have different coupling constants. In the present work, we study dipole-dipole interactions between electrons at the atomic scale through investigation of the electronic structure of helium-4.Laboratory searches for exotic spin-dependent interactions mediated by new bosons are sensitive and broadly inclusive probes for global symmetries broken at high energy scales [1,2]. For example, the fundamental proper- * Electronic address: filip.ficek@student.uj.edu.pl ties of axions and the axion-like-particles (ALPs) mentioned above [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] are characterized by a symmetry breaking scale f a and an interaction scale Λ. These scales determine, for example, the mass of the ALPand the interaction of an ALP with a Standard Model fermion X is proportional to m X c 2 /f a where m X is the fermion mass. In particular, this work improves laboratory constraints on exotic spin-spin forces between electrons mediated by bosons in the mass range between 10 −2 eV and 10 4 eV by two orders of magnitude. Our research is complementary to experiments searching for an axion/ALP coupling to photons, such as the Axion Dark Matter eXperiment (ADMX) [26], the CERN Axion Solar Telescope (CAST) [27], and light-shining-throughwall experiments such as the Any Light Particle Search (ALPS) [28], since He spectroscopy probes the electron-ALP interaction as opposed to the photon-ALP interaction and is sensitive to a mass range beyond that probed by experiments such as ADMX, CAST, and ALPS. Although star cooling rates constrain certain broad classes of ALPs [29,30], there are a number of loopholes in the astrophysica...

The familiar c → ∞ nonrelativistic limit converts the Klein-Gordon equation in Minkowski spacetime to the free Schrödinger equation, and the Einstein-massive-scalar system without a cosmological constant to the Schrödinger-Newton (SN) equation. In this paper, motivated by the problem of stability of Anti-de Sitter (AdS) spacetime, we examine how this limit is affected by the presence of a negative cosmological constant Λ. Assuming for consistency that the product Λc 2 tends to a negative constant as c → ∞, we show that the corresponding nonrelativistic limit is given by the SN system with an external harmonic potential which we call the Schrödinger-Newton-Hooke (SNH) system. We then derive the resonant approximation which captures the dynamics of small amplitude spherically symmetric solutions of the SNH system. This resonant system turns out to be much simpler than its general-relativistic version, which makes it amenable to analytic methods. Specifically, in four spatial dimensions, we show that the resonant system possesses a three-dimensional invariant subspace on which the dynamics is completely integrable and hence can be solved exactly. The evolution of the two-lowest-mode initial data (an extensively studied case for the original general-relativistic system), in particular, is described by this family of solutions.

In this paper I study the stationary, spherically symmetric accretion of fluids onto a charged black hole in the presence of a cosmological constant. For some isothermal equations of state it is possible to obtain analytic solutions. For the case of a radiation fluid I derive the relation between the locations of horizons and sonic (critical) points. In specific cases the solutions form closed, binocular-like trajectories in a phase diagram of the velocity versus radius.