A Non-Principal Value Prescription for the Temporal Gauge

A non-principal value prescription is used to define the spurious singularities of Yang-Mills theory in the temporal gauge. Typical one-loop dimensionally-regularized temporal-gauge integrals in the prescription are explicitly calculated, and a regularization for the spurious gauge divergences is introduced. The divergent part of the one-loop self-energy is shown to be local and has the same form as that in the spatial axial gauge with the principal-value prescription. The renormalization of the theory is also briefly mentioned.Comment: 13 pages, NCKU-HEP/93-0

Evolutionary multiplayer games on graphs with edge diversity

Evolutionary game dynamics in structured populations has been extensively explored in past decades. However, most previous studies assume that payoffs of individuals are fully determined by the strategic behaviors of interacting parties and social ties between them only serve as the indicator of the existence of interactions. This assumption neglects important information carried by inter-personal social ties such as genetic similarity, geographic proximity, and social closeness, which may crucially affect the outcome of interactions. To model these situations, we present a framework of evolutionary multiplayer games on graphs with edge diversity, where different types of edges describe diverse social ties. Strategic behaviors together with social ties determine the resulting payoffs of interactants. Under weak selection, we provide a general formula to predict the success of one behavior over the other. We apply this formula to various examples which cannot be dealt with using previous models, including the division of labor and relationship- or edge-dependent games. We find that labor division facilitates collective cooperation by decomposing a many-player game into several games of smaller sizes. The evolutionary process based on relationship-dependent games can be approximated by interactions under a transformed and unified game. Our work stresses the importance of social ties and provides effective methods to reduce the calculating complexity in analyzing the evolution of realistic systems.Comment: 50 pages, 7 figure

The UL(3)×UR(3)U_L(3) \times U_R(3) Extended Nambu--Jona-Lasinio Model in Differential Regularization

We employ the method of differential regularization to calculate explicitly the one-loop effective action of a bosonized $U_L(3)\times U_R(3)$ extended Nambu--Jona-Lasinio model consisting of scalar, pseudoscalar, vector and axial vector fields.Comment: LaTeX, 17 page