Neutron Acceleration in Uniform Electromagnetic Fields

The question as to whether neutron acceleration can occur in uniform electromagnetic fields is examined. Although such an effect has been predicted using the canonical equations of motion some doubt has been raised recently as to whether it is in principle observable for a spin 1/2 particle. To resolve this issue a gedanken experiment is proposed and analyzed using a wave packet construction for the neutron beam. By allowing arbitrary orientation for the neutron spin as well as for the electric and magnetic fields a non vanishing acceleration of the center of the neutron wave packet is found which confirms the predictions of the canonical formalism.Comment: 11 page

Berry phase for oscillating neutrinos

We show the presence of a topological (Berry) phase in the time evolution of a mixed state. For the case of mixed neutrinos, the Berry phase is a function of the mixing angle only.Comment: 7 pages, Revte

Classical and Quantum Interaction of the Dipole

A unified and fully relativistic treatment of the interaction of the electric and magnetic dipole moments of a particle with the electromagnetic field is given. New forces on the particle due to the combined effect of electric and magnetic dipoles are obtained. Four new experiments are proposed, three of which would observe topological phase shifts.Comment: 10 pages, Latex/Revtex. Some minor errors have been correcte

Gravitational Phase Operator and Cosmic Strings

A quantum equivalence principle is formulated by means of a gravitational phase operator which is an element of the Poincare group. This is applied to the spinning cosmic string which suggests that it may (but not necessarily) contain gravitational torsion. A new exact solution of the Einstein- Cartan-Sciama-Kibble equations for the gravitational field with torsion is obtained everywhere for a cosmic string with uniform energy density, spin density and flux. A novel effect due to the quantized gravitational field of the cosmic string on the wave function of a particle outside the string is used to argue that spacetime points are not meaningful in quantum gravity.Comment: 22 pages, to be published Phys. Rev. D. Some minor changes have been made and a reference has been added to the paper of D.V. Gal'tsov and P.S. Letelier, Phys. Rev. D 47 (1993) 4273, which first contained the metric (2.2) external to the cosmic string. The present paper extends this solution to a regular solution inside the string as wel

Action principle formulation for motion of extended bodies in General Relativity

We present an action principle formulation for the study of motion of an extended body in General Relativity in the limit of weak gravitational field. This gives the classical equations of motion for multipole moments of arbitrary order coupling to the gravitational field. In particular, a new force due to the octupole moment is obtained. The action also yields the gravitationally induced phase shifts in quantum interference experiments due to the coupling of all multipole moments.Comment: Revised version derives Octupole moment force. Some clarifications and a reference added. To appear in Phys. Rev.

Topology, Locality, and Aharonov-Bohm Effect with Neutrons

Recent neutron interferometry experiments have been interpreted as demonstrating a new topological phenomenon similar in principle to the usual Aharonov-Bohm (AB) effect, but with the neutron's magnetic moment replacing the electron's charge. We show that the new phenomenon, called Scalar AB (SAB) effect, follows from an ordinary local interaction, contrary to the usual AB effect, and we argue that the SAB effect is not a topological effect by any useful definition. We find that SAB actually measures an apparently novel spin autocorrelation whose operator equations of motion contain the local torque in the magnetic field. We note that the same remarks apply to the Aharonov-Casher effect.Comment: 9 page

On the measurement problem for a two-level quantum system

A geometric approach to quantum mechanics with unitary evolution and non-unitary collapse processes is developed. In this approach the Schrodinger evolution of a quantum system is a geodesic motion on the space of states of the system furnished with an appropriate Riemannian metric. The measuring device is modeled by a perturbation of the metric. The process of measurement is identified with a geodesic motion of state of the system in the perturbed metric. Under the assumption of random fluctuations of the perturbed metric, the Born rule for probabilities of collapse is derived. The approach is applied to a two-level quantum system to obtain a simple geometric interpretation of quantum commutators, the uncertainty principle and Planck's constant. In light of this, a lucid analysis of the double-slit experiment with collapse and an experiment on a pair of entangled particles is presented.Comment: for related papers, see http://www.uwc.edu/dept/math/faculty/kryukov

Background Independent Quantum Mechanics, Metric of Quantum States, and Gravity: A Comprehensive Perspective

This paper presents a comprehensive perspective of the metric of quantum states with a focus on the background independent metric structures. We also explore the possibilities of geometrical formulations of quantum mechanics beyond the quantum state space and Kahler manifold. The metric of quantum states in the classical configuration space with the pseudo-Riemannian signature and its possible applications are explored. On contrary to the common perception that a metric for quantum state can yield a natural metric in the configuration space with the limit when Planck constant vanishes, we obtain the metric of quantum states in the configuration space without imposing this limiting condition. Here, Planck constant is absorbed in the quantity like Bohr radii. While exploring the metric structure associated with Hydrogen like atom, we witness another interesting finding that the invariant lengths appear in the multiple of Bohr radii.Comment: 25 Pages;journal reference added:Published in- Int. J. Theor. Phys. 46 (2007) 3216-3229. References revise

Geometric Phase and Modulo Relations for Probability Amplitudes as Functions on Complex Parameter Spaces

We investigate general differential relations connecting the respective behavior s of the phase and modulo of probability amplitudes of the form \amp{\psi_f}{\psi}, where $\ket{\psi_f}$ is a fixed state in Hilbert space and $\ket{\psi}$ is a section of a holomorphic line bundle over some complex parameter space. Amplitude functions on such bundles, while not strictly holomorphic, nevertheless satisfy generalized Cauchy-Riemann conditions involving the U(1) Berry-Simon connection on the parameter space. These conditions entail invertible relations between the gradients of the phase and modulo, therefore allowing for the reconstruction of the phase from the modulo (or vice-versa) and other conditions on the behavior of either polar component of the amplitude. As a special case, we consider amplitude functions valued on the space of pure states, the ray space ${\cal R} = {\mathbb C}P^n$, where transition probabilities have a geometric interpretation in terms of geodesic distances as measured with the Fubini-Study metric. In conjunction with the generalized Cauchy-Riemann conditions, this geodesic interpretation leads to additional relations, in particular a novel connection between the modulus of the amplitude and the phase gradient, somewhat reminiscent of the WKB formula. Finally, a connection with geometric phases is established.Comment: 11 pages, 1 figure, revtex