Pauli-Fierz model with Kato-class potentials and exponential decays

Generalized Pauli-Fierz Hamiltonian with Kato-class potential \KPF in nonrelativistic quantum electrodynamics is defined and studied by a path measure. \KPF is defined as the self-adjoint generator of a strongly continuous one-parameter symmetric semigroup and it is shown that its bound states spatially exponentially decay pointwise and the ground state is unique.Comment: We deleted Lemma 3.1 in vol.

Signature Characters for A_2 and B_2

The signatures of the inner product matrices on a Lie algebra's highest weight representation are encoded in the representation's signature character. We show that the signature characters of a finite-dimensional Lie algebra's highest weight representations obey simple difference equations that have a unique solution once appropriate boundary conditions are imposed. We use these results to derive the signature characters of all $A_2$ and $B_2$ highest weight representations. Our results extend, and explain, signature patterns analogous to those observed by Friedan, Qiu and Shenker in the Virasoro algebra's representation theory.Comment: 22 p

Data Fusion Algorithms for Multiple Inertial Measurement Units

A single low cost inertial measurement unit (IMU) is often used in conjunction with GPS to increase the accuracy and improve the availability of the navigation solution for a pedestrian navigation system. This paper develops several fusion algorithms for using multiple IMUs to enhance performance. In particular, this research seeks to understand the benefits and detriments of each fusion method in the context of pedestrian navigation. Three fusion methods are proposed. First, all raw IMU measurements are mapped onto a common frame (i.e., a virtual frame) and processed in a typical combined GPS-IMU Kalman filter. Second, a large stacked filter is constructed of several IMUs. This filter construction allows for relative information between the IMUs to be used as updates. Third, a federated filter is used to process each IMU as a local filter. The output of each local filter is shared with a master filter, which in turn, shares information back with the local filters. The construction of each filter is discussed and improvements are made to the virtual IMU (VIMU) architecture, which is the most commonly used architecture in the literature. Since accuracy and availability are the most important characteristics of a pedestrian navigation system, the analysis of each filter’s performance focuses on these two parameters. Data was collected in two environments, one where GPS signals are moderately attenuated and another where signals are severely attenuated. Accuracy is shown as a function of architecture and the number of IMUs used

Thermal Quantum Fields without Cut-offs in 1+1 Space-time Dimensions

We construct interacting quantum fields in 1+1 dimensional Minkowski space, representing neutral scalar bosons at positive temperature. Our work is based on prior work by Klein and Landau and Hoegh-KrohnComment: 48 page