Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a nondifferentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a...

We investigate generators of local transformations in the covariant canonical formalism (CCF). The CCF treats space and time on an equal footing regarding differential forms as basic variables. conjugate $\pi_A$ are defined derivatives Lagrangian $d$-form $L(\psi^A, d\psi^A)$ with respect to $d\psi^A$, namely $\pi_A := \partial L/\partial d\psi^A$, where $\psi^A $ $p$-form dynamical fields. for...

In this article we present a mechanism in which we find new non-perturbative solutions of quantum electrodynamics in four dimensions. Two non-perturbative solutions are found for approximate Schwinger-Dyson equations. The mass ratio of the three solutions (one is ordinary solution) is approximately 1 : (8π/α) : 8π/α, which is close to the realistic mass ratio of e, μ and τ. e-mail: [email protected]...

We present an implementation of absorbing boundary conditions for the Einstein equations based on the recent work of Buchman and Sarbach. In this paper, we assume that spacetime may be linearized about Minkowski space close to the outer boundary, which is taken to be a coordinate sphere. We reformulate the boundary conditions as conditions on the gauge-invariant ReggeWheeler-Zerilli scalars. Hi...