By Fabio Cardone, Roberto Mignani
This publication discusses intimately the mathematical features and actual functions of a brand new geometrical constitution of space-time. it's in keeping with a generalization ("deformation") of the standard Minkowski area, supposedly endowed with a metric whose coefficients depend upon the power. power and Geometry: Geometrical Description of Interactions is acceptable for researchers, teachers and scholars in mathematical and theoretical physics.
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This ebook discusses intimately the mathematical features and actual purposes of a brand new geometrical constitution of space-time. it really is in keeping with a generalization ("deformation") of the standard Minkowski house, supposedly endowed with a metric whose coefficients rely on the strength. power and Geometry: Geometrical Description of Interactions is acceptable for researchers, lecturers and scholars in mathematical and theoretical physics.
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Extra resources for Energy and Geometry: An Introduction to: Geometrical Description of Interactions
E. in this subcase (unlike the previous one, see Eqs. 25)) one can state a proportionality relation by an overall factor (even if dependent on the metric coeﬃcients) between uiDSR,II (E) and |uDSR,II (E)|∗ . We have therefore shown that the two diﬀerent procedures of directional separation lead to two diﬀerent mathematical deﬁnitions of maximal causal velocity, an isotropic (w, Eq. 26)) and an anisotropic (u, Eq. 24)) one. The choice between them must be done on a physical basis (see Subsec. 3).
M. d Let us clarify the latter statement. The carriers of a given interaction propagating with the speed u typical of that interaction are expected to be strictly massless only inside the space whose metric is determined by the interaction considered. A priori, nothing forbids that such “deformed photons” may acquire a nonvanishing mass in a deformed Minkowski space related to a diﬀerent interaction. This might be the case of the massive bosons W + , W − and Z 0 , carriers of the weak interaction, which would therefore be massless in the ˜ (ηweak (E)) related to the weak interaction, but would acquire a space M mass when considered in the standard Minkowski space M of SR (that, as already stressed, is strictly connected to the electromagnetic interaction,e ruling the operation of the measuring devices).
8) Therefore, the generalized expression of the momentum fourvector (in the case of spatial isotropy) is pµ = m0 V µ (E) = (m0 γ˜ (E)u(E), m0 γ˜ (E)v k ). 31) for the interaction considered. e. at energies such that vi ui (E). 10) yields the following NR expression of the energy corresponding to the given interaction: ENR = mu2i (E) = mc2 b20 (E) . g. in the xy plane, at angles θ, θ in frames K, K ) with dispersion relation u = λν = λ ν , where ν, ν are the wave frequencies in K, K . 13) Relativistic Kinematics in a Deformed Minkowski Space 39 • Aberration law: tgθ = sin θ .