Effective action on the hyperbolic plane in a constant external field

view Abstract Citations (753) References (12) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Does the missing mass problem signal the breakdown of Newtonian gravity? Bekenstein, J. ; Milgrom, M. Abstract A nonrelativistic potential theory for gravity is considered which differs from the Newtonian theory. The theory is built on the basic assumptions of the modified dynamics, which were shown earlier to reproduce dynamical properties of galaxies and galaxy aggregates without having to assume the existence of hidden mass. The theory involves a modification of the Poisson equation and can be derived from a Lagrangian. The total momentum, angular momentum, and (properly defined) energy of an isolated system are conserved. The center-of-mass acceleration of an arbitrary bound system in a constant external gravitational field is independent of any property of the system. In other words, all isolated objects fall in exactly the same way in a constant external gravitational field (the weak equivalence principle is satisfied). However, the internal dynamics of a system in a constant external field is different from that of the same system in the absence of the external field, in violation of the strong principle of equivalence. These two results are consistent with the phenomenological requirements of the modified dynamics. A toy relativistic theory is sketched which has a nonrelativistic limit satisfying the requirements of the modified dynamics. Publication: The Astrophysical Journal Pub Date: November 1984 DOI: 10.1086/162570 Bibcode: 1984ApJ...286....7B Keywords: Galactic Rotation; Gravitation Theory; Mass Distribution; Missing Mass (Astrophysics); Newton Theory; Nonrelativistic Mechanics; Potential Theory; Computational Astrophysics; Cosmology; Equivalence; Poisson Equation; Astrophysics full text sources ADS |

We find dispersion laws for the photon propagating in the presence of mutually orthogonal constant external electric and magnetic fields in the context of the $\theta $-expanded noncommutative QED. We show that there is no birefringence to the first order in the noncommutativity parameter $% \theta .$ By analyzing the group velocities of the photon eigenmodes we show that there occurs superluminal propagation for any direction. This phenomenon depends on the mutual orientation of the external electromagnetic fields and the noncommutativity vector. We argue that the propagation of signals with superluminal group velocity violates causality in spite of the fact that the noncommutative theory is not Lorentz-invariant and speculate about possible workarounds.

The exact solution for the chiral field superpropagator in a constant external Abelian field is given.

This work explores the conditions that allow the injection and pinning of different magnetic domain walls (DWs) in Permalloy nanostripes with notches of different shapes. The injection is done under a constant external field by applying a 10 ns current pulse through an adjacent current line. The type of DW is identified by its anisotropic magnetoresistance (AMR). We find that, while a quasi-static pinning (nucleating at zero field and propagating the DW to the notch by slowly increasing the external field) would allow to distinguish different types of DWs pinned at the notch, a dynamic pinning (nucleating, propagating, and pinning the DW under a constant non-zero magnetic field) makes the discrimination of different DWs very difficult. Micromagnetic simulations indicate that the AMR of the different types of DWs become quite similar to each other as the injection field increases. This might explain why at large injection fields, usually only one or two values of resistance are detected, depending on the shape of the notch. Therefore, caution should be taken when establishing a one-to-one relationship between a type of DW and a value of resistance, especially if the injection is done under a non-zero external magnetic field.

Quantum electrodynamics in an external constant field

Within the QCD sum-rule approach in an external field, we calculate the baryon matrix element of isovector-scalar current, $H_{\rm B}=\langle B|\overline{u}u- \overline{d}d|B\rangle/2M_{\rm B}$, for octet baryons, which appears in the response of the correlator of baryon interpolating fields to a constant isovector-scalar external field. The sum rules are obtained for a general baryon interpolating field with an appropriate form for the phenomenological ansatz of the spectral density. The key phenomenological input is the response of the quark condensates to the external field. To first order in the quark mass difference $\delta m=m_d-m_u$, the non-electromagnetic part of the baryon isospin mass splitting is given by the product of $\delta m$ and $H_{\rm B}$. Therefore, QCD sum-rule calculation of $H_{\rm B}$ leads to an estimate of the octet baryon isospin mass splittings. The resulting values are comparable to the experimental values; however, the sum-rule predictions for $H_{\rm B}$ are sensitive to the values of the response of the quark condensates to the external source, which are not well determined.

We study exact solutions of Dirac and Klein–Gordon equations and Green functions in d-dimensional QED and in an external electromagnetic field with constant and homogeneous field invariants. The cases of even and odd dimensions are considered separately; they are essentially different. We direct attention to the asymmetry of the quasienergy spectrum, which appears in odd dimensions. The in and out classification of the exact solutions as well as the completeness and orthogonality relations is strictly proven. Different Green functions in the form of sums over the exact solutions are constructed. The Fock–Schwinger proper time integral representations of these Green functions are found. As physical applications, we consider the calculations of different quantum effects related to the vacuum instability in the external field. For example, we present mean values of particles created from the vacuum, the probability of the vacuum remaining a vacuum, the effective action, and the expectation values of the current and energy-momentum tensor.

The dynamical stability of disk galaxies is sensitive to whether their anomalous rotation curves are caused by dark matter halos or Milgromian dynamics (MOND). We investigate this by setting up a MOND model of M33. We first simulate it in isolation for 6 Gyr, starting from an initial good match to the rotation curve (RC). Too large a bar and bulge form when the gas is too hot, but this is avoided by reducing the gas temperature. A strong bar still forms in 1 Gyr, but rapidly weakens and becomes consistent with the observed weak bar. Previous work showed this to be challenging in Newtonian models with a live dark matter halo, which developed strong bars. The bar pattern speed implies a realistic corotation radius of 3 kpc. However, the RC still rises too steeply, and the central line-of-sight velocity dispersion (LOSVD) is too high. We then add a constant external acceleration field of 8.4 × 10−12 m s−2 at 30° to the disk as a first-order estimate for the gravity exerted by M31. This suppresses buildup of material at the center, causing the RC to rise more slowly and reducing the central LOSVD. Overall, this simulation bears good resemblance to several global properties of M33, and highlights the importance of including even a weak external field on the stability and evolution of disk galaxies. Further simulations with a time-varying external field, modeling the full orbit of M33, will be needed to confirm its resemblance to observations.

The interaction and the transformation of the electromagnetic and gravitational waves and the variation of those amplitudes are analyzed theoretically, where the Einstein-Maxwell field is assumed. Two waves are defined such that the electromagnetic vector potentials and the gravitational tensor potentials and their first derivatives are continuous while their second derivatives are discontinuous at a wave front. It is proved that the concomitant electromagnetic and gravitational waves can interact with each other if an external electromagnetic field exists. The global behaviors of interaction and transformation of the two concomitant waves are also investigated, where a Lorentz metric space-time is assumed. The variation formulas for amplitude are derived. The amplitudes may grow or decay according to a factor depending on the mean and Gaussian curvatures of an initial wave front and to a factor depending on the external electromagnetic field. When there is no external electromagnetic field, there is no interaction between the two waves and they propagate independently, while when an external field exists, the electromagnetic wave may transform into the gravitational wave and vice versa. In a case of a weak constant external electromagnetic field, where a flat space may be assumed, the amplitude of a wave varies sinusoidally with respect to the distance measured along its ray. The length of interchangeability is defined by the length in which a wave is completely transformed into its dual wave, and it is inversely proportional to the strength of an external electromagnetic field.

A recent computation of the (nonlocal) covariant effective action of QED in weak constant external electromagnetic fields is generalized to general Lorentz gauges and its gauge dependence is displayed, and it is then removed by the prescription for a gauge and parametrization independent effective action according to Vilkovisky. The geometry, which in this framework is ascribed to the field configuration space of QED, is made explicit, and it is shown that Vilkovisky’s effective action coincides with the conventional Landau gauge case.

The nonlinear mathematical model of behavior of controllable viscosity fluid (CVF) under applied external field is presented. A large family of these fluids is commonly used to control responding forces of dampers in vibration control applications. The responding force of a damper with CVF has two components. The first one - uncontrollable - is proportional to the viscosity of a base fluid and velocity of its motion, the second one, which is controllable, depends on the strength of the applied external field. Both are involved in the process of dissipation of unwanted energy from the vibrating systems. An equivalent damping factor based on the principle of energy dissipated during one cycle of damper work under a constant strength external field was calculated. When mass or stiffness is variable the equivalent damping factor can be set accordingly by adjusting the strength of external field to have vibrating damped system purposely/continuously working in the critical or other chosen state. This paper also presents cases of applying periodically changing strengths of an external field synchronized with cycles of periodical motion of the vibrating system to continuously control the damping force within each cycle.

Pair production of open strings — relativistic versus dissipative dynamics

There exists a clear physical motivation for theoretical studies of the vacuum instability related to the production of electron-positron pairs from a vacuum due to strong external electric fields. Various nonperturbative (with respect to the external fields) calculation methods were developed. Some of these methods are based on possible exact solutions of the Dirac equation. Unfortunately, there are only few cases when such solutions are known. Recently, an approximate but still nonperturbative approach to treat the vacuum instability caused by slowly varying $t$-electric potential steps (time dependent external fields that vanish as $|t|\rightarrow\infty$), which does not depend on the existence of the corresponding exact solutions, was formulated in Ref. [S. P. Gavrilov, D. M. Gitman, Phys. Rev. D \textbf{95}, 076013 (2017)]. Here, we present an approximate calculation method to treat nonperturbatively the vacuum instability in arbitrary weakly inhomogeneous $x$-electric potential steps (time-independent electric fields of a constant direction that are concentrated in restricted space areas, which means that the fields vanish as $|x|\rightarrow\infty$) in the absence of the corresponding exact solutions. Defining the weakly inhomogeneous regime in general terms, we demonstrate the universal character of the vacuum instability. This universality is associated with a large density of states excited from the vacuum by the electric field. Such a density appears in our approach as a large parameter. We derive universal representations for the total number and current density of the created particles. Relations of these representations with a locally constant field approximation for Schwinger's effective action are found.

Single core MgB2 tape has been made by the powder-in-tube (PIT) method using commercial MgB2 powder (Alfa Aesar) and two-axial rolling deformation in an Fe/Cu sheath. Transport currents were measured at temperatures 4.2 K–15 K in parallel and perpendicular to the external magnetic field B = 0–5.5 T and at a constant field B = 1 T of variable orientation to the tape surface (0–180°). The transport current anisotropy of the tape with different orientations of the tape surface with respect to the external magnetic field was measured, showing higher currents in perpendicular field orientation. The Ic anisotropy of MgB2/Fe/Cu tape was observed only for low external fields (0–2.5 T). This behaviour is explained by the Fe sheath magnetization and confirmed by the isotropic behaviour of MgB2/Cu tape prepared by the similar PIT process and by hysteretic Ic(B) curves measured for increased and decreased external field in MgB2/Fe/Cu. The presence of the ferromagnetic barrier in MgB2 composite wire influences the Ic(B) characteristics and may lead to increased hysteretic losses for possible future ac applications.

We have studied the problem of particle–antiparticle pair creation from vacuum in external fields considering Schwinger's method. The effective action is calculated respectively for scalar and spinor quantum electrodynamics (QED) in the presence of a constant electromagnetic field plus a Volkov plane wave. It is shown that the plane wave has no influence on the process of pair creation.