Abstract: We present a detailed, all-order study of gluon mass generation within the massless bound-state formalism, which constitutes the general framework for the systematic implementation of the Schwinger mechanism in non-Abelian gauge theories. The main ingredient of this formalism is the dynamical formation of bound states with vanishing mass, which give rise to effective vertices containing massless poles; these latter vertices, in turn, trigger the Schwinger mechanism, and allow for the gauge-invariant generation of an effective gluon mass. This particular approach has the conceptual advantage of relating the gluon mass directly to quantities that are intrinsic to the bound-state formation itself, such as the “transition amplitude'' and the corresponding ”bound-state wave function.'' As a result, the dynamical evolution of the gluon mass is largely determined by a Bethe-Salpeter equation that controls the dynamics of the relevant wave function, rather than the Schwinger-Dyson equation of the gluon propagator, as happens in the standard treatment. The precise structure and field-theoretic properties of the transition amplitude are scrutinized in a variety of independent ways. In particular, a parallel study within the linear-covariant (Landau) gauge and the background-field method reveals that a powerful identity, known to be valid at the level of conventional Green's functions, also relates the background and quantum transition amplitudes. Despite the differences in the ingredients and terminology employed, the massless bound-state formalism is absolutely equivalent to the standard approach based on Schwinger-Dyson equations. In fact, a set of powerful relations allows one to demonstrate the exact coincidence of the integral equations governing the momentum evolution of the gluon mass in both frameworks.

Abstract: In the development of prototype systems for positron emission tomography a valid and robust image reconstruction algorithm is required. However, prototypes often employ novel detector and system geometries which may change rapidly under optimization. In addition, developing systems generally produce highly granular, or possibly continuous detection domains which require some level of on-the-fly calculation for retention of measurement precision. In this investigation a new method of on-the-fly system matrix calculation is proposed that provides advantages in application to such list-mode systems in terms of flexibility in system modeling. The new method is easily adaptable to complicated system geometries and available computational resources. Detection uncertainty models are used as random number generators to produce ensembles of possible photon trajectories at image reconstruction time for each datum in the measurement list. However, the result of this approach is that the system matrix elements change at each iteration in a non-repetitive manner. The resulting algorithm is considered the simulation of a one-pass list (SOPL) which is generated and the list traversed during image reconstruction. SOPL alters the system matrix in use at each iteration and so behavior within the maximum likelihood-expectation maximization algorithm was investigated. A two-pixel system and a small two dimensional imaging model are used to illustrate the process and quantify aspects of the algorithm. The two-dimensional imaging system showed that, while incurring a penalty in image resolution, in comparison to a non-random equal-computation counterpart, SOPL provides much enhanced noise properties. In addition, enhancement in system matrix quality is straightforward (by increasing the number of samples in the ensemble) so that the resolution penalty can be recovered when desired while retaining improvement in noise properties. Finally the approach is tested and validated against a standard (highly accurate) system matrix using experimental data from a prototype system-the AX-PET.