Axiomatic geometric formulation of electromagnetism with only one axiom: the field equation for the bivector field F with an explanation of the Trouton-Noble experiment

In this paper we present an axiomatic, geometric, formulation of electromagnetism with only one axiom: the field equation for the Faraday bivector field F. This formulation with F field is a self-contained, complete and consistent formulation that dispenses with either electric and magnetic fields or the electromagnetic potentials. All physical quantities are defined without reference frames, the absolute quantities, i.e., they are geometric four dimensional (4D) quantities or, when some basis is introduced, every quantity is represented as a 4D coordinate-based geometric quantity comprising both components and a basis. The new observer independent expressions for the stress-energy vector T(n)(1-vector), the energy density U (scalar), the Poynting vector S and the momentum density g (1-vectors), the angular momentum density M (bivector) and the Lorentz force K (1-vector) are directly derived from the field equation for F. The local conservation laws are also directly derived from that field equation. The 1-vector Lagrangian with the F field as a 4D absolute quantity is presented; the interaction term is written in terms of F and not, as usual, in terms of A. It is shown that this geometric formulation is in a full agreement with the Trouton-Noble experiment.Comment: 32 pages, LaTex, this changed version will be published in Found. Phys. Let

Competitive manufacturing with fluctuating demand and diverse technology: Mathematical proofs and illuminations on industry output-flexibility

I present an original model of competitive manufacturing with fluctuating demand and diverse technology with mathematical proofs. I discuss Aranoff's output-flexibility indicator, E(AC)-LRMC. I use the model to compute Aranoff's output-flexibility indicator to measure industry output-flexibility. I argue that a measure of industry output-flexibility is [beta]L(Q2 - Q1)/E(Q) I tie the demand-side discussion with the cost-side and show the degree of industry output-flexibility that will emerge under welfare and profit-maximizing pricing rules. I perform comparative statics of changes in technology, of demand, and of frequency of the high-peak state.Capacity planning and investment Game theory Demand fluctuations Output flexibility Equilibrium Technology choice Cost curves Competitive manufacturing Marginal cost pricing Short-run average cost curve