Acausality in Gowdy spacetimes

We present a parametrization of T ³ and S ¹ × S ² Gowdy cosmological models which allows us to study both types of topologies simultaneously. We show that there exists a coordinate system in which the general solution of the linear polarized special case (with both topologies) has exactly the same functional dependence. This unified parametrization is used to investigate the existence of Cauchy horizons at the cosmological singularities, leading to a violation of the strong cosmic censorship conjecture. Our results indicate that the only acausal spacetimes are described by the Kantowski-Sachs and the Kerr-Gowdy metrics.     

Local Anomalies and Local Equivariant Cohomology

The locality conditions for the vanishing of local anomalies in field theory are shown to admit a geometrical interpretation in terms of local equivariant cohomology. This interpretation allows us to solve the problem proposed by Singer in [31], and consists in defining an adequate notion of local cohomology to deal with the problem of locality in the geometrical approaches to the study of local anomalies based on the Atiyah-Singer index theorem. Moreover, using the relation between local cohomology and the cohomology of jet bundles studied in [19] we obtain necessary and sufficient conditions for the cancellation of local gravitational and mixed anomalies.     

Local gravitomagnetism

In a simple two-body system, we calculate the gravitomagnetic components of the metric in the local quasi-inertial frame of one of the bodies. The local geometry in this frame which is freely falling along the geodesic but is directionally fixed with respect to distant stars is primarily denned by the gravitomagnetic components of the local metric. This metric serves to track down the various contributions from the local and distant source and thus provides further insight to the nature of gravitomagnetism. As a result we show that in the quasi-inertial frame geodetic precession is a gravitomagnetic phenomenon. Furthermore we establish a connection between local gravitomagnetic effects and Einstein's principle of equivalence.     

Local State and Sector Theory in Local Quantum Physics

We define a new concept of local states in the framework of algebraic quantum field theory (AQFT). Local states are a natural generalization of states and give a clear vision of localization in the context of QFT. In terms of them, we can find a condition from which follows automatically the famous DHR selection criterion in DHR-DR theory. As a result, we can understand the condition as consequences of physically natural state preparations in vacuum backgrounds. Furthermore, a theory of orthogonal decomposition of completely positive (CP) maps is developed. It unifies a theory of orthogonal decomposition of states and order structure theory of CP maps. Using it, localized version of sectors is formulated, which gives sector theory for local states with respect to general reference representations.     

Nonlinear Local Lyapunov Exponent and Quantification of Local Predictability

Nonlinear local Lyapunov exponent （NLLE） is applied to quantitatively determine the local predictability limit of chaotic systems. As an example, we find that the local predictability limit of Henon attractor varies considerably with time, and some underlying phase-spatial structure does not appear. The local predictability limit of initially adjacent points in phase space may be completely different. This will cause difficulties in making the long-time analogue forecast.     

Local nonlinear electrodynamics

The propagation of electromagnetic waves in dielectric media characterized by the coefficients and is examined in the eikonal approximation of electrodynamics. Employing the techniques Hadamard-Papapetrou (HPD) and Spacetime Integration (STI), we derive the dispersion relation, the polarization modes and effective geometry associated to the model.     

Local quantum entropy

It is shown that it is possible to define true local entropy in velocity space, in an approximate version of the two-fluid formulation of quantum theory introduced by the present author in earlier papers. Using this definition, it is then shown that it is possible to define finite forms for total entropy at all points in configuration space. This important step is achieved by the introduction of a responding velocity space. The use of a basis system which responds to occupation number density, makes possible a clear separation of the statistics and the dynamics of the underlying quantum process, and also makes possible the unambiguous use of certain divergent and oscillatory integrals.     

Local current commutators

The predictive power of current algebra relations is discussed using models for the spectral functions of current commutator matrix elements. The functions constructed fulfill the requirements of covariance, locality and spectrum conditions. Thus, the current algebra constraints can easily be imposed. In these models the formfactors are described by superpositions of poles. For simplicity only spin zero states are taken into account.     

Would-Be Local Fields

General quantum field theory is formulated for the case when the Wightman distributions can grow in momentum space as the exponential of a covariant polynomial. Appropriate spaces of test functions are introduced, and it is shown that the vacuumexpectation values can be written in terms of various associated tempered distributions, which enjoy some of the properties of ordinary Wightman distributions; in particular, they can be represented as boundary values of functions holomorphic in the usual extended tubes. Notions of locality for the tempered distributions can be introduced, which are sufficient to imply the PCT theorem and theorems on the connection between spin and statistic for the non-tempered fields. It is shown how a Haag-Ruelle theory of asymptotic states and fields may be set up. A possible line of generalisation is illustrated by the special example of fields of the type χ (□) A (x), where A is a tempered field, and χ an entire analytic function of finite exponential order.     

Local spin II

Equations are discussed for computing, from ah initio wavefunctions, average values of quantities like S_A. S_B which appear in the Heisenberg model Hamiltonian of magnetism. These equations are based on projection operators onto local regions of space. They result in local spin operators S_A which obey the definition of angular momentum operators and commute with each other. These averages are evaluated for UHF and CI wavefunctions for a few examples of closed and open shell molecules. The calculations are compared with the assumptions made in the Noodleman method for evaluating the parameters in the Heisenberg Hamiltonian and with various definitions of bond order.     

Polarization Attack on Continuous-Variable Quantum Key Distribution with a Local Local Oscillator

The estimation of phase noise of continuous-variable quantum key distribution protocol with a local local oscillator (LLO CVQKD), as a major process in quantifying the secret key rate, is closely relevant to the intensity of the phase reference. However, the transmission of the phase reference through the insecure quantum channel is prone to be exploited by the eavesdropper (Eve) to mount attacks. Here, we introduce a polarization attack scheme against the phase reference. Presently, in a practical LLO CVQKD system, only part of the phase reference pulses are measured to compensate for the polarization drift of the quantum signal pulses in a compensation cycle due to the limited polarization measurement rate, while the other part of the phase reference pulses are not measured. We show that Eve can control the phase noise by manipulating the polarization direction of the unmeasured phase reference to hide her attack on the quantum signal. Simulations show that Eve can obtain partial or total key rates information shared between Alice and Bob as the transmission distance increases. Improving the polarization measurement rate to 100% or monitoring the phase reference intensity in real-time is of great importance to protect the LLO CVQKD from polarization attack.     

Local Heterotic Torsional Models

We present a class of smooth supersymmetric heterotic solutions with a non-compact Eguchi-Hanson space. The non-compact geometry is embedded as the base of a six-dimensional non-Kähler manifold with a non-trivial torus fiber. We solve the non-linear anomaly equation in this background exactly. We also define a new charge that detects the non-Kählerity of our solutions.     

Local and global gravity

Our long experience with Newtonian potentials has inured us to the view that gravity only produces local effects. In this paper we challenge this quite deeply ingrained notion and explicitly identify some intrinsically global gravitational effects. In particular we show that the global cosmological Hubble flow can actually modify the motions of stars and gas within individual galaxies, and even do so in a way which can apparently eliminate the need for galactic dark matter. Also we show that a classical light wave acquires an observable, global, pathdependent phase in traversing a gravitational field. Both of these effects serve to underscore the intrinsic difference between nonrelativistic and relativistic gravity.     

Local conformal field algebras

The local conformal field algebras with the multiplication corresponding to the regularized pointwise product of fields in the operator algebras of the quantum conformal field theory are investigated.     

Local detection of entanglement

We construct an explicit model where it can be established if a two mode pure Gaussian system is entangled or not by acting only on one of the parts that constitute the system. Measuring the dispersion in momentum and the time evolution of the dispersion in position of one particle we can tell if entanglement is present as well as the degree of entanglement of the system.