By Jaime Keller (auth.)
Within the first century after its discovery, the electron has emerge as a basic aspect within the research of actual features of nature.
This publication is dedicated to the development of a deductive idea of the electron, ranging from first rules and utilizing an easy mathematical software, geometric research. Its objective is to offer a accomplished idea of the electron to the purpose the place a connection should be made with the most techniques to the examine of the electron in physics.
The advent describes the technique. bankruptcy 2 provides the concept that of space-time-action relativity conception and in bankruptcy three the mathematical constructions describing motion are analyzed. Chapters four, five, and six take care of the idea of the electron in a sequence of features the place the geometrical research is extra appropriate. eventually in bankruptcy 7 the shape of geometrical research utilized in the e-book is gifted to clarify the huge diversity of issues that are coated and the diversity of mathematical buildings that are implicitly or explicitly incorporated.
The booklet is directed to 2 various audiences of graduate scholars and examine scientists: basically to theoretical physicists within the box of electron physics in addition to these within the extra basic box of quantum mechanics, basic particle physics, and basic relativity; secondly, to mathematicians within the box of geometric research.
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Sample text
46) Here the action of one unit of action (µ = 0, 1, 2, 3) unit of action is a null valued function with the property (i = 1, 2, 3) and In both cases the local action density is A(x) = in space– time where cd is a numerical coefficient of geometrical origin (this will be relevant to the study of the families of elementary particles and their mass), ρ the normalized density of action of the carrier. For the system we want to describe below the observer uses the START-Principle of Acceptable Choice formalism in a form in which the fields can be considered as a distribution corresponding to a ‘test’ carrier in the geometry induced by a ‘source’, for this purpose we use the solution of the equations for the STA geometry when each carrier in turn is described by applying the overall condition of null curvature RAB = 0 with for the observers’ frame of reference.
Besides the attractive gravitational term there is a (quadratic) repulsive term which will dominate at intermediate distances. This repulsive term, of the form which has been called by some experimentalists the fifth force, will act as an equivalent ‘cosmological’ constant which will force a distribution (considered to be a universe) to expand and will avoid gravitational (full) collapses of large matter densities. 2. The electric part of the interaction depends explicitly in the e/m0 ratio of the test particle, and it can then not, be a universal behavior of a test particle, even if the basic geometry has a universal form.
6) allows the direct self-consistent determination of ρ(x) and ε (see [58]). The constant ε is otherwise the rate of change of the energy in the process of removing one (average) carrier. 7) where this introduces both, the response function of the system G(x, x'), and the effective potential which would be caused either by fluctuations of the density or by differences in the local definition of energy per carrier. This reaction would propagate to all points of the distribution to achieve stability.