We construct the covariant nonlocal action for recently suggested long-distance modifications of gravity theory motivated by the cosmological constant and cos-mological acceleration problems. This construction is based on the special non-local form of the Einstein-Hilbert action explicitly revealing the fact that this action within the covariant curvature expansion begins with curvature-squared...

Many problems of current interest in atomic interferometry lend themselves to a path integral treatment. We present a practical guide to solving such problems, taking as examples the gravitational experiments of Kasevich and Chu, and the atomic equivalents of the Sagnac and Aharonov-Bohm effects.

K e y w o r d s E l l i p t i c system, Transmission problem, Positive solution. 1. I N T R O D U C T I O N Let 12 be a smooth bounded domain of R n, n > 2, and let ~1 c gl be a subdomain with smooth boundary ~ satisfying ~1 C i2. Writing F = c9~ and gl2 = ~\~l l we have ~ = ~1 tJ 122 and 0i'~2 = ~, tJ F. We are concerned with the existence of positive solutions to the following system of nonli...

We discuss the unitarity relation of the Aharonov-Bohm scattering amplitude with the hope that it distinguishes between the differing treatments which employ different incident waves. We find that the original Aharonov-Bohm scattering amplitude satisfies the unitarity relation under the regularization prescription whose theoretical foundation does not appear to be understood. On the other hand,...

The motion of spectator quarks in decay of a beauty hadron is a nonperturbative effect which can usually be neglected. We find that the motion in some decay channels, which contribute total decay widths of beauty hadrons, can not be neglected. The contributions from these decay channels to decay widths are proportional to certain averages of the squared inverse of the momentum carried by a spec...

Using a simple version of the model for the quantum measurement of a two level system, the contention of Aharonov, Anandan, and Vaidman that one must in certain circumstances give the wavefunction an ontological as well as an epistemological significance is examined. I decide that their argument that the wave function of a system can be measured on a single system fails to establish the key poi...

correct. We shall modify this result for linear-invariant families. Families of closeto-convex functions and of functions of bounded boundary rotation will be showed to be linear-invariant. Because of the coefficient estimate for close-to-convex functions and functions of bounded boundary rotation derived by Aharonov and Friedland [1], it is possible to get the distortion theorem for the n-th. ...

An analysis is given of the spectral properties of perturbations of the magnetic bi-harmonic operator ∆A in L(R), n=2,3,4, where A is a magnetic vector potential of Aharonov-Bohm type, and bounds for the number of negative eigenvalues are established. Key elements of the proofs are newly derived Rellich inequalities for ∆A which are shown to have a bearing on the limiting cases of embedding the...

The path integral for relativistic three-dimensional spinless Aharonov-Bohm-Coulomb system is solved, and the energy spectra are extracted from the resulting amplitude.

We study the long time behavior of solutions to the nonlocal quasilinear dissipative wave equation utt − φ(x)‖∇u(t)‖∆u+ δut + |u|u = 0, in RN , t ≥ 0, with initial conditions u(x, 0) = u0(x) and ut(x, 0) = u1(x). We consider the case N ≥ 3, δ > 0, and (φ(x))−1 a positive function in LN/2(RN ) ∩ L∞(RN ). The existence of a global attractor is proved in the strong topology of the space D1,2(RN )×...