Axial anomalies in external tensor fields

This calculation uses matched asymptotic expansions to show, directly from the Einstein-Maxwell equations, that a small charged body with possibly strong internal gravity moves through an electrovac region of a curved, and not necessarily asymptotically flat, external spacetime approximately according to the Lorentz force law. The dimensionless parameter $\ensuremath{\epsilon}\ensuremath{\equiv}\frac{m}{L}$ (where $m$ is the body's mass and $L$ is a curvature reference length of the external field) is assumed small, and it is found that $O(L)$ deviations from the Lorentz force law vanish over times of $O(L)$; deviations of $O(L)$ would be expected to arise only over times of $O(\frac{L}{\ensuremath{\epsilon}})$ or longer. This calculation differs from previous work in that the body may have strong internal gravity (e.g., a charged black hole), its moments are unrestricted, and the external gravitational field need not be asymptotically flat.

The equilibrium thermodynamics of a many-particle assembly in the presence of an external scalar field is examined. Two types of scalar coupling are considered: an external field coupled to the particle density and an external scalar field coupled to the energy density. It is shown that the broken translational and rotational invariance of the system due to the external field is reflected in the macroscopic physics by loss of the usual extensivity property of the system and by means of anisotropy in the response of the system to changes in the system lengths or to the system shape. In addition, the assumptions used in local equilibrium analyses are shown to be incorrect in principle. Nonlocal effects due to the external field must be included in the determination of the equation of state. Simple model calculations for a system in an external gravitational field and an externally imposed temperature field are presented as illustrations.

We consider the motion of a spinning relativistic particle in external electromagnetic and gravitational fields to first order in the external field but to arbitrary order in the spin. The influence of the spin on the particle trajectory is properly accounted for by describing the spin noncovariantly. Specific calculations are performed through second order in the spin. A simple derivation is presented for the gravitational spin-orbit and spin-spin interactions of a relativistic particle. We discuss the gravimagnetic moment (GM), a particular spin effect in general relativity. We show that for a Kerr black hole the gravimagnetic ratio, i.e., the coefficient of the GM, equals unity (just as the gyromagnetic ratio equals 2 for a charged Kerr hole). The equations of motion obtained for a spinning relativistic particle in an external gravitational field differ substantially from the Papapetrou equations.

In analogy with the Meissner effect in (super) conductors, black holes expel stationary axisymmetric external fields when approaching the extreme state. This has been studied on magnetic fields in the literature. Using the recently obtained solution describing a rotating black hole surrounded by an axisymmetric thin annular disc, we show that the effect also applies to an external gravitational field.

We extend the standard second order effective chiral Lagrangian of pions and nucleons by considering the coupling to an external gravitational field. As an application we calculate one-loop corrections to the one-nucleon matrix element of the energy-momentum tensor to fourth order in chiral counting, and next-to-leading order tree-level amplitude of the pion-production in an external gravitational field. We discuss the relation of the obtained results to experimentally measurable observables. Our expressions for the chiral corrections to the nucleon gravitational form factors differ from those in the literature. That might require to revisit the chiral extrapolation of the lattice data on the nucleon gravitational form factors obtained in the past.

We investigate the magnetic susceptibility of the QCD vacuum with the $1/{N}_{c}$ corrections taken into account, based on the instanton vacuum. Starting from the instanton liquid model, we derive the gauged light-quark partition function in the presence of the current quark mass as well as of external Abelian vector and tensor fields. We consider the $1/{N}_{c}$ meson-loop corrections which are shown to contribute to the magnetic susceptibility by around 15% for the up (and down) quarks. We also take into account the tensor terms of the quark-quark interaction from the instanton vacuum as well as the finite-width effects, both of which are of order $\mathcal{O}(1/{N}_{c})$. The effects of the tensor terms and finite width turn out to be negligibly small. The final results for the up-quarks are given as: $\ensuremath{\chi}⟨i{\ensuremath{\psi}}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\psi}{⟩}_{0}\ensuremath{\simeq}35--40\text{ }\text{ }\mathrm{MeV}$ with the quark condensate $⟨i{\ensuremath{\psi}}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\psi}{⟩}_{0}$. We also discuss the pion mass dependence of the magnetic susceptibility in order to give a qualitative guideline for the chiral extrapolation of lattice data.

The authors give an analysis of quantum field theory of mutually interacting fields in a 3-flat Robertson-Walker universe with regard to the questions: What are the measurable quantities? What is the related calculation scheme? The classical curved spacetime acts thereby as an external gravitational field, the influence of which is taken into account without any approximation. As a case study a mathematically rigorous calculation of the decay of a massive phi particle into two massless psi particles is given in first order of the ( lambda /a) phi psi 2 mutual interaction where a is the cosmic scale factor. The particles are conformally coupled scalar particles. The interaction picture and the in-out scheme based on an S-matrix approach are used. No renormalisation is needed. Because the external field is capable of producing pairs of massive phi particles from the vacuum, the specification of the outcome of the mutual interaction is based on the registration of massless particles in the out region. A detailed analysis of the corresponding added-up probability is given. It sheds some light on the imperfection of the usual in-out approach when applied to cosmological situations. The results are used to obtain a limit for the local applicability of flat spacetime results as cross section, decay rates etc. in a cosmological situation.

We derive the distribution of the phantom dark matter in the eight classical dwarf galaxies surrounding the Milky Way, under the assumption that modified Newtonian dynamics (MOND) is the correct theory of gravity. According to their observed shape, we model the dwarfs as axisymmetric systems, rather than spherical systems, as usually assumed. In addition, as required by the assumption of the MOND framework, we realistically include the external gravitational field of the Milky Way and of the large-scale structure beyond the Local Group. For the dwarfs where the external field dominates over the internal gravitational field, the phantom dark matter has, from the star distribution, an offset of ∼0.1−0.2 kpc, depending on the mass-to-light ratio adopted. This offset is a substantial fraction of the dwarf half-mass radius. For Sculptor and Fornax, where the internal and external gravitational fields are comparable, the phantom dark matter distribution appears disturbed with spikes at the locations where the two fields cancel each other; these features have little connection with the distribution of the stars within the dwarfs. Finally, we find that the external field due to the large-scale structure beyond the Local Group has a very minor effect. The features of the phantom dark matter we find represent a genuine prediction of MOND, and could thus falsify this theory of gravity in the version we adopt here if they are not observationally confirmed.

The scattering of photons by a static gravitational field, treated as an external field, is discussed in the context of gravity with higher derivatives. It is shown that the R 2 sector of the theory does not contribute to the photon scattering, whereas the R 2 sector produces dispersive (energy-dependent) photon propagation.

Einstein’s theory of gravity — the general theory of relativity — is based on the principle that all objects accelerate identically in an external gravitational field. A triple-star system provides a stringent test of this principle. Einstein’s theory of gravity — the general theory of relativity — is based on the principle that all objects accelerate identically in an external gravitational field. A triple-star system provides a stringent test of this principle.

A functional integral solution of the Green's function of a scalar field in an external gravitational field

In Chapter II of this volume we outlined the methods for determination of the equilibrium form of the components of close binary systems in any external field of force; and in sections II-1 and 2 of Chapter III we set up equations which govern the time-response of such configurations to an arbitrary type of disturbance. The nature of such disturbances may be connected with fluctuations in external gravitational field — such as those causing forced oscillations (dynamical tides) discussed in sections III-2 and 3 — or may arise from evolutionary changes in structure of the respective stars. These may be slow or abrupt (such as the onset of a nuclear reaction in the interior, or of the ionization of hydrogen or helium in the outer layers); and the configuration must respond to them on an appropriate time-scale.

The deflection of a massive photon by an external gravitational field is energy-dependent. Interesting enough, any massive quantum particle, no matter what its spin is, undergoes dispersive deflection in external gravitational fields. Exploiting the dispersive deflection of the quantized massive electromagnetic radiation by the gravitational field of the Sun, we find an upper bound for the photon mass.

Vacuum radiation in covariant perturbation theory

We give an Atiyah-Patodi-Singer index theory construction of the bundle of fermionic Fock spaces parametrized by vector potentials in odd space dimensions and prove that this leads in a simple manner to the known Schwinger terms (Faddeev-Mickelsson cocycle) for the gauge group action. We relate the APS construction to the bundle gerbe approach discussed recently by Carey and Murray, including an explicit computation of the Dixmier-Douady class. An advantage of our method is that it can be applied whenever one has a form of the APS theorem at hand, as in the case of fermions in an external gravitational field.