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A vector product formulation of special relativity and electromagnetism

Charles P. Poole, Horacio A. Farach & Yakir Aharonov

Foundations of Physics 10 (7-8):531-553 (1980)

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Extension of trigonometric and hyperbolic functions to vectorial arguments and its application to the representation of rotations and Lorentz transformations.H. Yamasaki - 1983 - Foundations of Physics 13 (11):1139-1154.details The use of the axial vector representing a three-dimensional rotation makes the rotation representation much more compact by extending the trigonometric functions to vectorial arguments. Similarly, the pure Lorentz transformations are compactly treated by generalizing a scalar rapidity to a vector quantity in spatial three-dimensional cases and extending hyperbolic functions to vectorial arguments. A calculation of the Wigner rotation simplified by using the extended functions illustrates the fact that the rapidity vector space obeys hyperbolic geometry. New representations bring a Lorentz-invariant (...) Download Export citation Bookmark 1 citation
The introduction of Superluminal Lorentz transformations: A revisitation. [REVIEW]G. D. Maccarrone & Erasmo Recami - 1984 - Foundations of Physics 14 (5):367-407.details We revisit the introduction of the Superluminal Lorentz transformations which carry from “bradyonic” inertial frames to “tachyonic” inertial frames, i.e., which transform time-like objects into space-like objects, andvice versa. It has long been known that special relativity can be extended to Superluminal observers only by increasing the number of dimensions of the space-time or—which is in a sense equivalent—by releasing the reality condition (i.e., introducing also imaginary quantities). In the past we always adopted the latter procedure. Here we show the (...) Download Export citation Bookmark 1 citation
Algebraic field descriptions in three-dimensional Euclidean space.Nikos Salingaros & Yehiel Ilamed - 1984 - Foundations of Physics 14 (8):777-797.details In this paper, we use the differential forms of three-dimensional Euclidean space to realize a Clifford algebra which is isomorphic to the algebra of the Pauli matrices or the complex quaternions. This is an associative vector-antisymmetric tensor algebra with division: We provide the algebraic inverse of an eight-component spinor field which is the sum of a scalar + vector + pseudovector + pseudoscalar. A surface of singularities is defined naturally by the inverse of an eight-component spinor and corresponds to a (...) Download Export citation Bookmark 1 citation

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