Localization in Nets of Standard Spaces

Starting from a real standard subspace of a Hilbert space and a representation of the translation group with natural properties, we construct and analyze for each endomorphism of this pair a local, translationally covariant net of standard subspaces, on the lightray and on two-dimensional Minkowski space. These nets share many features with low-dimensional quantum field theory, described by corresponding nets of von Neumann algebras. Generalizing a result of Longo and Witten to two dimensions and massive multiplicity free representations, we characterize these endomorphisms in terms of specific analytic functions. Such a characterization then allows us to analyze the corresponding nets of standard spaces, and in particular compute their minimal localization length. The analogies and differences to the von Neumann algebraic situation are discussed.Comment: 34 pages, 1 figur

The role of positivity and causality in interactions involving higher spin

It is shown that the recently introduced positivity and causality preserving string-local quantum field theory (SLFT) resolves most No-Go situations in higher spin problems. This includes in particular the Velo–Zwanziger causality problem which turns out to be related in an interesting way to the solution of zero mass Weinberg–Witten issue. In contrast to the indefinite metric and ghosts of gauge theory, SLFT uses only positivity-respecting physical degrees of freedom. The result is a fully Lorentz-covariant and causal string field theory in which light- or space-like linear strings transform covariant under Lorentz transformation. The cooperation of causality and quantum positivity in the presence of interacting particles leads to remarkable conceptual changes. It turns out that the presence of H-selfinteractions in the Higgs model is not the result of SSB on a postulated Mexican hat potential, but solely the consequence of the implementation of positivity and causality. These principles (and not the imposed gauge symmetry) account also for the Lie-algebra structure of the leading contributions of selfinteracting vector mesons. Second order consistency of selfinteracting vector mesons in SLFT requires the presence of H-particles; this, and not SSB, is the raison d'être for H. The basic conceptual and calculational tool of SLFT is the S-matrix. Its string-independence is a powerful restriction which determines the form of interaction densities in terms of the model-defining particle content and plays a fundamental role in the construction of pl observables and sl interpolating fields

LocNet: Global localization in 3D point clouds for mobile vehicles

Global localization in 3D point clouds is a challenging problem of estimating the pose of vehicles without any prior knowledge. In this paper, a solution to this problem is presented by achieving place recognition and metric pose estimation in the global prior map. Specifically, we present a semi-handcrafted representation learning method for LiDAR point clouds using siamese LocNets, which states the place recognition problem to a similarity modeling problem. With the final learned representations by LocNet, a global localization framework with range-only observations is proposed. To demonstrate the performance and effectiveness of our global localization system, KITTI dataset is employed for comparison with other algorithms, and also on our long-time multi-session datasets for evaluation. The result shows that our system can achieve high accuracy.Comment: 6 pages, IV 2018 accepte

On the Euler characteristic of Kronecker moduli spaces

Combining the MPS degeneration formula for the Poincar\'e polynomial of moduli spaces of stable quiver representations and localization theory, it turns that the determination of the Euler characteristic of these moduli spaces reduces to a combinatorial problem of counting certain trees. We use this fact in order to obtain an upper bound for the Euler characteristic in the case of the Kronecker quiver. We also derive a formula for the Euler characteristic of some of the moduli spaces appearing in the MPS degeneration formula.Comment: 15 page

Nonperturbative Tests of Three-Dimensional Dualities

We test several conjectural dualities between strongly coupled superconformal field theories in three dimensions by computing their exact partition functions on a three-sphere as a function of Fayet-Iliopoulos and mass parameters. The calculation is carried out using localization of the path integral and the matrix model previously derived for superconformal N = 2 gauge theories. We verify that the partition functions of quiver theories related by mirror symmetry agree provided the mass parameters and the Fayet-Iliopoulos parameters are exchanged, as predicted. We carry out a similar calculation for the mirror of N = 8 super-Yang-Mills theory and show that its partition function agrees with that of the ABJM theory at unit Chern-Simons level. This provides a nonperturbative test of the conjectural equivalence of the two theories in the conformal limit

Localized Frames and Compactness

We introduce the concept of weak-localization for generalized frames and use this concept to define a class of weakly localized operators. This class contains many important operators, including: Short Time Fourier Transform multipliers, Calderon-Toeplitz operators, Toeplitz operators on various functions spaces, Anti-Wick operators, and many others. In this paper, we study the boundedness and compactness of weakly localized operators. In particular, we provide a characterization of compactness for weakly localized operators in terms of the behavior of their Berezin transform