The Causal Phase in QED3QED_{3}

The operator ${\bf S}$ in Fock space which describes the scattering and particle production processes in an external time-dependent electromagnetic potential $A$ can be constructed from the one-particle S-matrix up to a physical phase $\lambda [A]$. In this work we determine this phase for $QED$ in (2+1) dimensions, by means of causality, and show that no ultraviolet divergences arise, in contrast to the usual formalism of $QED$.Comment: LaTex, 11 pages, no figure

Remarks on Infrared Dynamics in QED3

In this work we study how the infrared sector of the interaction Hamiltonian can affect the construction of the S matrix operator of QED in (2+1) dimensions.Comment: 9 page

Propagating Torsion in 3D-Gravity and Dynamical Mass Generation

In this paper, fermions are minimally coupled to 3D-gravity where a dynamical torsion is introduced. A Kalb-Ramond field is non-minimally coupled to these fermions in a gauge-invariant way. We show that a 1-loop mass generation mechanism takes place for both the 2-form gauge field and the torsion. As for the fermions, no mass is dynamically generated: at 1-loop, there is only a mass shift proportional to the Yukawa coupling whenever the fermions have a non-vanishing tree-level mass.Comment: 13 pages, latex file, no figures, some corrections adde

Wave Equation Numerical Resolution: a Comprehensive Mechanized Proof of a C Program

We formally prove correct a C program that implements a numerical scheme for the resolution of the one-dimensional acoustic wave equation. Such an implementation introduces errors at several levels: the numerical scheme introduces method errors, and floating-point computations lead to round-off errors. We annotate this C program to specify both method error and round-off error. We use Frama-C to generate theorems that guarantee the soundness of the code. We discharge these theorems using SMT solvers, Gappa, and Coq. This involves a large Coq development to prove the adequacy of the C program to the numerical scheme and to bound errors. To our knowledge, this is the first time such a numerical analysis program is fully machine-checked.Comment: No. RR-7826 (2011

Symmetry aspects of fermions coupled to torsion and electromagnetic fields

We study and explore the symmetry properties of fermions coupled to dynamical torsion and electromagnetic fields. The stability of the theory upon radiative corrections as well as the presence of anomalies are investigated.Comment: 9 pages, LaTe

Vector Supersymmetry of 2D Yang-Mills Theory

The vector supersymmetry of the 2D topological BF model is extended to 2D Yang-Mills. The consequences of the corresponding Ward identity on the ultraviolet behavior of the theory are analyzed.Comment: Some references adde

Observables in Topological Yang-Mills Theories

Using topological Yang-Mills theory as example, we discuss the definition and determination of observables in topological field theories (of Witten-type) within the superspace formulation proposed by Horne. This approach to the equivariant cohomology leads to a set of bi-descent equations involving the BRST and supersymmetry operators as well as the exterior derivative. This allows us to determine superspace expressions for all observables, and thereby to recover the Donaldson-Witten polynomials when choosing a Wess-Zumino-type gauge.Comment: 39 pages, Late

A Formally Verified Floating-Point Implementation of the Compact Position Reporting Algorithm

The Automatic Dependent Surveillance-Broadcast (ADS-B) system allows aircraft to communicate their current state, including position and velocity information, to other aircraft in their vicinity and to ground stations. The Compact Position Reporting (CPR) algorithm is the ADS-B module responsible for the encoding and decoding of aircraft positions. CPR is highly sensitive to computer arithmetic since it heavily relies on functions that are intrinsically unstable such as floor and modulo. In this paper, a formally-verified double-precision floating-point implementation of the CPR algorithm is presented. The verification proceeds in three steps. First, an alternative version of CPR, which reduces the floating-point rounding error is proposed. Then, the Prototype Verification System (PVS) is used to formally prove that the ideal real-number counterpart of the improved algorithm is mathematically equivalent to the standard CPR definition. Finally, the static analyzer Frama-C is used to verify that the double-precision implementation of the improved algorithm is correct with respect to its operational requirement. The alternative algorithm is currently being considered for inclusion in the revised version of the ADS-B standards document as the reference implementation of the CPR algorithm

Supersymmetric Extension of the Lorentz and CPT-Violating Maxwell-Chern-Simons Model

Focusing on gauge degrees of freedom specified by a 1+3 dimensions model hosting a Maxwell term plus a Lorentz and CPT non-invariant Chern-Simons-like contribution, we obtain a minimal extension of such a system to a supersymmetric environment. We comment on resulting peculiar self-couplings for the gauge sector, as well as on background contribution for gaugino masses. Furthermore, a non-polynomial generalization is presented.Comment: revtex4, 4 pages, no figure