Quantization of Constrained Systems

We present a complete derivation of the semiclassical limit of the coherent-state propagator in one dimension, starting from path integrals in phase space. We show that the arbitrariness in the path integral representation, which follows from the overcompleteness of the coherent states, results in many different semiclassical limits. We explicitly derive two possible semiclassical formulae for the propagator, we suggest a third one, and we discuss their relationships. We also derive an initial-value representation for the semiclassical propagator, based on an initial Gaussian wavepacket. It turns out to be related to, but different from, Heller's thawed Gaussian approximation. It is very different from the Herman-Kluk formula, which is not a correct semiclassical limit. We point out errors in two derivations of the latter. Finally we show how the semiclassical coherent-state propagators lead to WKB-type quantization rules and to approximations for the Husimi distributions of stationary states.

Based on the phase-space path integral (functional integral) for a system with a regular or singular Lagrangian, the generalized Ward identities for phase space generating functional under the global transformation in phase space are derived respectively. The canonical Noether theorem at the quantum level is also established. It is pointed out that the connection between the symmetries and conservation laws in classical theories, in general,is no longer preserved in quantum theories. The advantage of our formulation is that we do not need to carry out the integration over the canonical momenta as usually performed. Applying the present formulation to Yang-Mills theory, the quantal BRS conserved quantity and Ward-Takahashi identity for BRS tranformation are derived; the Ward identities for gaugeghost proper vertices and new quantal conserved quantity are also found. In comparison of quantal conservation laws with those one deriving from configuration-space path integral using the Faddeev-Popov(F-P) trick is discussed. A precise study of path-integral quantisation for a nonlinear sigma model with Hopf and Chern-Simons (CS) terms is reexamined. It has been shown that the angular momentum at the quantum level is equal to classical (Noether ) one. Applying our formulation to non-Abelian CS theory, the quantal conserved angular momentum of this system is obtained which differs from classical one in that one needs to take into account the contribution of angular momenta of ghost fields.

We consider a topological quantum mechanics described by a phase space path integral and study the 1-dimensional analog for the path integral representation of the Kontsevich formula. We see that the naive bosonic integral possesses divergences, that it is even naively non-invariant and thus is ill-defined. We then consider a superextension of the theory which eliminates the divergences and makes the theory naively invariant. This super-extension is equivalent to the correct choice of measure and was discussed in the literature. We then investigate the behavior of this extended theory under diffeomorphisms of the extended phase space and despite of its naive invariance find out that the theory possesses anomaly under nonlinear diffeomorphisms. We localize the origin of the anomaly and calculate the lowest nontrivial anomalous contribution.

Starting from the phase space path integral, we have derived the Ward identities in canonical formalism for a system with regular and singular Lagrangian. This formulation differs from the traditional discussion based on path integral in configuration space. It is pointed out that the quantum canonical equations for systems with singular Lagrangians are different from the classical ones obtained from Dirac's conjecture. The preliminary applications of Ward identities in phase space to the Yang-Mills theory are given. Some relations among the proper vertices and propagators are deduced, the PCAC, AVV vertices and generalized PCAC expressions are also obtained. We have also pointed out that some authors in their early work had ignored the treatment of the constraints.

We present a stochastic path integral formalism for continuous quantum measurement that enables the analysis of rare events using action methods. By doubling the quantum state space to a canonical phase space, we can write the joint probability density function of measurement outcomes and quantum state trajectories as a phase space path integral. Extremizing this action produces the most-likely paths with boundary conditions defined by preselected and postselected states as solutions to a set of ordinary differential equations. As an application, we analyze continuous qubit measurement in detail and examine the structure of a quantum jump in the Zeno measurement regime.

Superfield formulation of the phase space path integral

The mutual inclination between planets orbiting the same star provides key information to understand the formation and evolution of multiplanet systems. In this work, we investigate the potential of Gaia astrometry in detecting and characterizing cold Jupiters in orbits exterior to the currently known Transiting Exoplanet Survey Satellite (TESS) planet candidates. According to our simulations, out of the ∼3350 systems expected to have cold Jupiter companions, Gaia, by its nominal 5 yr mission, should be able to detect ∼200 cold Jupiters and measure the orbital inclinations with a precision of in ∼120 of them. These numbers are estimated under the assumption that the orbital orientations of the CJs follow an isotropic distribution, but these only vary slightly for less broad distributions. We also discuss the prospects from radial velocity follow-ups to better constrain the derived properties and provide a package to do quick forecasts using our Fisher matrix analysis. Overall, our simulations show that Gaia astrometry of cold Jupiters orbiting stars with TESS planets can distinguish dynamically cold (mean mutual inclination ≲5°) from dynamically hot systems (mean mutual inclination ≳20°), placing a new set of constraints on their formation and evolution.

We construct a number of explicit examples of hyperbolic monopoles, with various charges and often with some platonic symmetry. The fields are obtained from instanton data in four-dimensional Euclidean space that are invariant under a circle action, and in most cases the monopole charge is equal to the instanton charge. A key ingredient is the identification of a new set of constraints on ADHM instanton data that are sufficient to ensure the circle invariance. Unlike for Euclidean monopoles, the formulae for the squared Higgs field magnitude in the examples we construct are rational functions of the coordinates. Using these formulae, we compute and illustrate the energy density of the monopoles. We also prove, for particular monopoles, that the number of zeros of the Higgs field is greater than the monopole charge, confirming numerical results established earlier for Euclidean monopoles. We also present some one-parameter families of monopoles analogous to known scattering events for Euclidean monopoles within the geodesic approximation.

Today human services organizations are faced with rapidly changing demands. In the 1980's, referred to as the decade of accountability, powerful new forces have entered into what was a neatly packaged human service operating environment. Accountability has led divergent human service stakeholders to impose new sets of constraints and expectations on the human service organization.

In this paper we describe the development of a multi-modal scheme for preventing the loss of control of aircraft in the presence of control effector failures. The proposed scheme, referred to as the Multi-Modal Lossof-control Prevention System (MM-LPS), rapidly identifies the failure, reconfigures the control law to achieve effective failure accommodation, and calculates an appropriate measure for the resulting closed-loop system to predict if the system will enter an unsafe mode of operation, such as that corresponding to position or rate saturation of the control effectors that result in an uncontrollable system. The role of the MM-LPS is to stabilize the system and achieve graceful degradation of the closed-loop performance. One of the major elements of the proposed approach is on-line calculation and prediction of Achievable Trim Points (ATP), i.e. the trim points that can be achieved with the available control authority, and the use of the ATP measure post-failure to calculate a new set of constraints and a new control law that brings the system from one trim point to another. The MM-LPS system integrates on-line Failure Detection, Identification and Reconfiguration (FDIR) algorithms, ATP calculation module, and constrained multi-modal control laws. Its performance was evaluated on a difficult example where the objective was to assure the closed-loop stability of a F/A-18 aircraft in the presence of full stabilator hard-over failure.

Constraint programming for solving various assembly line balancing problems

Computer-aided analysis of integrated circuit devices has played a critical role for more than three decades of technology evolution. In the 1950s and early 1960s simulation was used extensively to characterize the operating principles of both bipolar and MOS devices. Bipolar effects such as base-width modulation and base pushout were characterized as well as MOS phenomena including gradual channel and channel-length modulation effects. During the late 1960s and throughout the 1970s simulation provided critical insight in the scaling of devices leading to the advent of very large scale integration (VLSI). Starting in the mid-1970s the modeling of fabrication technology became an important adjunct to device analysis. The need to control threshold and subthreshold behavior of scaled devices played a significant role in this synergistic coupling. Now in the mid-1980s the role of both device and process analysis have each come to new plateaus of both performance and utility. The scaling of submicrometer channel-length MOS devices poses a new set of constraints and challenges. This paper traces the evolution of computer-aided analysis over the past three decades. Unique aspects of the device physics and the role of device and process analysis at each phase of development will be presented. The progression from device conception towards stabilizing the technologies for large-scale product are presented. Problems of submicrometer technology including both production issues as well as new physical requirements for both process and device modeling will be dealt with, including the opportunity presented with the rapid advances in computer technology and the seemingly inevitable computational bottleneck posed by the growing needs for three-dimensional simulation.

Bounds on R-parity violating SUSY Yukawa couplings from semileptonic decays of baryons

Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation Ramsagar Vooradi, Munawar A. Shaik, Nikhil M. Gupta; Three‐index Model for Westenberger‐Kallrath Benchmark Scheduling Problem. AIP Conference Proceedings 26 October 2010; 1298 (1): 380–385. https://doi.org/10.1063/1.3516335 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAIP Publishing PortfolioAIP Conference Proceedings Search Advanced Search |Citation Search

A useless variable is one whose value contributes nothing to the final outcome of a computation. Such variables are unlikely to occur in human-produced code, but may be introduced by various program transformations. We would like to eliminate useless parameters from procedures and eliminate the corresponding actual parameters from their call sites. This transformation is the extension to higher-order programming of a variety of dead-code elimination optimizations that are important in compilers for first-order imperative languages.Shivers has presented such a transformation. We reformulate the transformation and prove its correctness. We believe that this correctness proof can be a model for proofs of other analysis-based transformations. We proceed as follows: We reformulate Shivers' analysis as a set of constraints; since the constraints are conditional inclusions, they can be solved using standard algorithms.We prove that any solution to the constraints is sound: that two computations that differ only on variables marked as useless give the same answer up to useless variables, and hence the same answer when the answer is a constant.We observe that this notion of soundness is too weak to support the transformation of the analyzed program. We add additional closure conditions to the analysis and show that any solution to the new set of constraints justifies the transformation. The proof is by tree surgery: we show that from any computation of the original program, we can construct a computation of the transformed program that yields an answer related to the original, and the same answer when the original answer is a constant.