Conservation laws arising in the study of forward-forward Mean-Field Games

We consider forward-forward Mean Field Game (MFG) models that arise in numerical approximations of stationary MFGs. First, we establish a link between these models and a class of hyperbolic conservation laws as well as certain nonlinear wave equations. Second, we investigate existence and long-time behavior of solutions for such models

On the duality of three-dimensional superfield theories

Within the superfield approach, we consider the duality between the supersymmetric Maxwell-Chern-Simons and self-dual theories in three spacetime dimensions. Using a gauge embedding method, we construct the dual theory to the self-dual model interacting with a matter superfield, which turns out to be not the Maxwell-Chern-Simons theory coupled to matter, but a more complicated model, with a ``restricted'' gauge invariance. We stress the difficulties in dualizing the self-dual field coupled to matter into a theory with complete gauge invariance. After that, we show that the duality, achieved between these two models at the tree level, also holds up to the lowest order quantum corrections.Comment: 18 pages,2 figures, revtex4, v2: corrected reference

T-Duality in 2-D Integrable Models

The non-conformal analog of abelian T-duality transformations relating pairs of axial and vector integrable models from the non abelian affine Toda family is constructed and studied in detail.Comment: 14 pages, Latex, v.2 misprints corrected, reference added, to appear in J. Phys.

On the Nonrelativistic Limit of the phi^4 Theory in 2+1 Dimensions

We study the nonrelativistic limit of the quantum theory of a real scalar field with quartic self-interaction. The two body scattering amplitude is written in such way as to separate the contributions of high and low energy intermediary states. From this result and the two loop computation of the self energy correction, we determine an effective nonrelativistic action.Comment: 15 pages, 2 figures, revte

Noncommutative Field Theory: Nonrelativistic Fermionic Field Coupled to the Chern-Simons Field in 2+1 Dimensions

We study a noncommutative nonrelativistic fermionic field theory in 2+1 dimensions coupled to the Chern-Simons field. We perform a perturbative analysis of model and show that up to one loop the ultraviolet divergences are canceled and the infrared divergences are eliminated by the noncommutative Pauli term.Comment: Some references adde