It is shown that Berry's phase appears in a more general context than realized so far. The evolution of the quantum system need be neither unitary nor cyclic and may be interrupted by quantum measurements. A key ingredient in this generalization is the use of some ideas introduced by Pancharatnam in his study of the interference of polarized light, which, when carried over to quantum mechanics, allow a meaningful comparison of the phase between any two nonorthogonal vectors in Hilbert space.PACS numbers: 03.65. Bz, 02.40.4m Three years ago, Berry made a rather perceptive and interesting observation regarding the behavior of quantum-mechanical systems in a slowly changing environment. If the system is initially in an eigenstate of the instantaneous Hamiltonian, the adiabatic theorem guarantees that it remains so. This, however, determines the state of the system only up to a phase. Berry asked the question "What is the phase of the system?" and got a somewhat unexpected answer. If the environment (more precisely, the Hamiltonian) returns to its initial state, the system also does, but it acquires an extra phase over and above the dynamical phase, which can be calculated and allowed for. This effect has been studied and measured in various contexts.Simon 2 gave a simple geometrical interpretation of Berry's phase. If one regards the space of normalized states as a fiber bundle over the space of rays 3 (a ray is defined as an equivalence class of states differing only in phase), then this bundle has a natural connection. This connection permits a comparison of the phases of states on two neighboring rays. Simon observed that when the dynamical phase factor is removed, the evolution of the system as determined by the Schrodinger equation is a parallel transport of the phase of the system according to this natural connection. Berry's phase is then a consequence of the curvature of this connection.Recently, Aharanov and Anandan 4 generalized Berry's results by giving up the assumption of adiabaticity. The key step in this work is their identification of the integral of the expectation value of the Hamiltonian as the dynamical phase. Once this dynamical phase is removed, the evolution of the phase of the system is again determined by the natural connection and one recovers Berry's phase for any cyclic evolution of the quantum system.The purpose of this Letter is to point out that Berry's phase appears in a still more general context. The evolution of the system need be neither unitary (norm preserving) nor cyclic (returning to the original ray). This generalization is based on the work of Pancharatnam 5 on the interference of polarized light. Carrying Pancharatnam's ideas over to quantum mechanics yields a fairly general setting for a discussion of Berry's phase. We briefly describe Pancharatnam's work before developing the subject of the present paper.Pancharatnam posed the following question: Given two beams of polarized light, is there a natural way to compare the phases of these beams? His physically motivated an...

2+1 Einstein gravity is used as a toy model for testing a program for nonperturbative canonical quantisation of the 3+1 theory. The program can be successfully implemented in the model and leads to a surprisingly rich quantum theory.

The role of spatial topology in the Hamiltonian description of Bianchi models is analysed. It turns out that, in general, the number of degrees of freedom of these models is not uniquely determined by the isometry group but depends in addition on the choice of topology. Consequently, the quantum theory is quite sensitive to this choice. Contrary to one's initial expectation, subtleties arise in the spatially open models-say with topology R3-rather than closed. Finally, it is shown that class B models cannot occur with closed topologies.

In a double slit interference experiment, the wave function at the screen with both slits open is not exactly equal to the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well-known text books in quantum mechanics implicitly and/or explicitly use this assumption that is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from nonclassical paths in quantum interference experiments that provide a measurable deviation from a naive application of the superposition principle. A direct experimental demonstration for the existence of these nonclassical paths is difficult to present. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence.

No abstract

We present a method for solving the wormlike chain model for semiflexible polymers to any desired accuracy over the entire range of polymer lengths. Our results are in excellent agreement with recent computer simulations and reproduce important qualitatively interesting features observed in simulations of polymers of intermediate lengths. We also make a number of predictions that can be tested in a variety of concrete experimental realizations. The expected level of finite size fluctuations in force-extension curves is also estimated. This study is relevant to mechanical properties of biological molecules.

This letter is a critique of Barbero's constrained Hamiltonian formulation of General Relativity on which current work in Loop Quantum Gravity is based. We show that if one tries to interpret Barbero's real SO(3) connection as a space-time gauge field, the theory is not diffeomorphism invariant. In this respect, Barbero's connection is quite different from Ashtekar's, which does admit a space-time interpretation as a complex SU (2) gauge field. We conclude that Barbero's formulation is not a gauge theory of gravity in the sense that Ashtekar's Hamiltonian formulation is. The advantages of Barbero's real connection formulation have been bought at the price of giving up the description of gravity as a gauge field.1

We revisit the action principle for general relativity, motivated by the path integral approach to quantum gravity. We consider a spacetime region whose boundary has piecewise C 2 components, each of which can be spacelike, timelike or null and consider metric variations in which only the pullback of the metric to the boundary is held fixed. Allowing all such metric variations we present a unified treatment of the spacelike, timelike and null boundary components using Cartan's tetrad formalism. Apart from its computational simplicity, this formalism gives us a simple way of identifying corner terms. We also discuss "creases" which occur when the boundary is the event horizon of a black hole. Our treatment is geometric and intrinsic and we present our results both in the computationally simpler tetrad formalism as well as the more familiar metric formalism. We recover known results from a simpler and more general point of view and find some new ones. arXiv:1612.00149v2 [gr-qc] 1 Feb 2017