Ascertaining the values of sigma x,sigma y,and sigma z of a polarization qubit

In the 1987 spin-retrodiction puzzle of Vaidman, Aharonov, and Albert one is challenged to ascertain the values of sigma(x), sigma(y), and sigma(z) of a spin-1/2 particle by utilizing entanglement. We report the experimental realization of a quantum-optical version in which the outcome of an intermediate polarization projection is inferred by exploiting single-photon two-qubit quantum gates. The experimental success probability is consistently above the 90.2% threshold of the optimal one-qubit strategy, with an average success probability of 95.6%.     

Topological sigma models

A variant of the usual supersymmetric nonlinear sigma model is described, governing maps from a Riemann surface to an arbitrary almost complex manifoldM. It possesses a fermionic BRST-like symmetry, conserved for arbitrary, and obeyingQ ²=0. In a suitable version, the quantum ground states are the 1+1 dimensional Floer groups. The correlation functions of the BRST-invariant operators are invariants (depending only on the homotopy type of the almost complex structure ofM) similar to those that have entered in recent work of Gromov on symplectic geometry. The model can be coupled to dynamical gravitational or gauge fields while preserving the fermionic symmetry; some observations by Atiyah suggest that the latter coupling may be related to the Jones polynomial of knot theory. From the point of view of string theory, the main novelty of this type of sigma model is that the graviton vertex operator is a BRST commutator. Thus, models of this type may correspond to a realization at the level of string theory of an unbroken phase of quantum gravity.On leave from Department of Physics, Princeton University. Supported in part by NSF Grants No. 80-19754, 86-16129, 86-20266     

The topological sigma model

We obtain the invariants of Witten's topologicalσ-model by gauge fixing a topological action and using BRST symmetry. The fields and the BRST formalism are interpreted geometrically.     

Topological massive sigma models

In this paper we construct topological sigma models which include a potential and are related to twisted massive supersymmetric sigma models. Contrary to a previous construction these models have no central charge and do not require the manifold to admit a Killing vector. We use the topological massive sigma model constructed here to simplify the calculation of the observables. Lastly it is noted that this model can be viewed as interpolating between topological massless sigma models and topological Landau-Ginzburg models.     

Noncommutative linear sigma models

We examine noncommutative linear sigma models with U(N) global symmetry groups at the one-loop quantum level, and contrast the results with our previous study of the noncommutative O(N) linear sigma models where we have shown that Nambu–Goldstone symmetry realization is inconsistent with continuum renormalization. Specifically we find no violation of Goldstone's theorem at one-loop for the U(N) models with the quartic term ordering consistent with possible noncommutative gauging of the model. The difference is due to terms involving noncommutative commutator interactions, which vanish in the commutative limit. We also examine the U(2), and O(4) linear sigma models with matter in the adjoint representation, and find that the former is consistent with Goldstone's theorem at one-loop if we include only trace invariants consistent with possible noncommutative gauging of the model, while the latter exhibits violations of Goldstone's theorem of the kind seen in the fundamental of O(N) for N>2.     

Noise-driven nonlinear sigma model

We present a noise-driven model for obtaining the gap and line-width as functions of the temperature in the nonlinear sigma model. The method is phenomenological and rests on the following physical idea: a classical external stochastic field is introduced representing the coupling of the sigma field with a noise source. Moreover, we assume that the inelastic scattering length is much longer than the elastic one, justifying the neglect of dissipation for temperatures such that the nonlinear sigma model is a good approximation for antiferromagnetic spin chains. This phenomenological approach is justified by comparison with other theoretical predictions and with experiment.     

Hypernuclei with sigma particles

The production of Σ particles in the (K⁻, π⁻) on ⁹Be at 720 MeV/c has been studied at the CERN proton synchrotron (PS). The missing-mass spectrum shows structures in the Σ region, which have been interpreted as belonging to hypernuclei with sigma particles. An upper limit of 8 MeV for the width of these states has been estimated.     

On classicalization in nonlinear sigma models

We consider the phenomenon of classicalization in nonlinear sigma models with both positive and negative target space curvature and with any number of derivatives. We find that the theories with only two derivatives exhibit a weak form of classicalization, and that the quantitative results depend on the sign of the curvature. Nonlinear sigma models with higher derivatives show a strong form of the phenomenon which is independent of the sign of curvature. We argue that weak classicalization may actually be equivalent to asymptotic safety, whereas strong classicalization seems to be a genuinely different phenomenon. We also discuss possible ambiguities in the definition of the classical limit.     

Chiral symmetry breaking andKN sigma commutator

KN sigma commutator has been calculated in the framework of the (6, )+( , 6) model. It is found that though this model could not be discarded in favour of the (3, )+( , 3) or (8, 8) model, a very large value forKN sigma term is required to get a positive value ofπN sigma term.     

Geometric sigma model of the Universe

The purpose of this work is to demonstrate how an arbitrarily chosen background of the Universe can be made a solution of a simple geometric sigma model.Geometric sigma models are purely geometric theories in which spacetime coordinates are seen as scalar fields coupled to gravity.Although they look like ordinary sigma models,they have the peculiarity that their complete matter content can be gauged away.The remaining geometric theory possesses a background solution that is predefined in the process of constructing the theory.The fact that background configuration is specified in advance is another peculiarity of geometric sigma models.In this paper,I construct geometric sigma models based on different background geometries of the Universe.Whatever background geometry is chosen,the dynamics of its small perturbations is shown to have a generic classical stability.This way,any freely chosen background metric is made a stable solution of a simple model.Three particular models of the Universe are considered as examples of how this is done in practice.