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Four-force
About: Four-force is a research topic. Over the lifetime, 3459 publications have been published within this topic receiving 87308 citations.
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TL;DR: In this article, various physical covariance groups: SO(3), the Lorentz group, general theory of relativity group, the Clifford algebra SU(2) and the conformal group can easily be related to the quaternion group.
Abstract: The paper shows how various physical covariance groups: SO(3), the Lorentz group, the general theory of relativity group, the Clifford algebra SU(2) and the conformal group can easily be related to the quaternion group. The quaternion calculus is introduced and several physical applications: crystallography the kinematics of rigid body motion, the Thomas precession the special theory of relatively, classical electromagnetism, the equation of motion of the general theory of relativity, and Dirac's relativistic wave equation are discussed.
83 citations
TL;DR: In this paper, the authors examined a 5D space and isolated a fifth force which in principle is measurable, which is a departure from conventional dynamics is a way of testing dimensionality.
82 citations
TL;DR: This work analyzes discrete lattice general relativity and develops a canonical formalism that allows one to treat constrained theories in Lorentzian signature space-times in a manner that makes the quantization of the theories conceptually clear, albeit computationally involved.
Abstract: It has long been recognized that lattice gauge theory formulations, when applied to general relativity, conflict with the invariance of the theory under diffeomorphisms. We analyze discrete lattice general relativity and develop a canonical formalism that allows one to treat constrained theories in Lorentzian signature space-times. The presence of the lattice introduces a "dynamical gauge" fixing that makes the quantization of the theories conceptually clear, albeit computationally involved. The problem of a consistent algebra of constraints is automatically solved in our approach. The approach works successfully in other field theories as well, including topological theories. A simple cosmological application exhibits quantum elimination of the singularity at the big bang.
82 citations
TL;DR: A relativistic generalization of the classical virial theorem is obtained for any stationary and asymptotically flat spacetime as mentioned in this paper, which may be useful as a consistency check of numerical solutions of the Einstein equations.
Abstract: A relativistic generalization of the classical virial theorem is obtained for any stationary and asymptotically flat spacetime. This formulation is derived within the 3+1 formalism of general relativity. It may be useful as a consistency check of numerical solutions of the Einstein equations.
82 citations
TL;DR: In this paper, a modified self-dual action that leads to the $SO(3)$-ADM formalism without having to face the difficult second class constraints present in other approaches (for example if one starts from the Hilbert-Palatini action) is presented.
Abstract: We give in this paper a modified self-dual action that leads to the $SO(3)$-ADM formalism without having to face the difficult second class constraints present in other approaches (for example if one starts from the Hilbert-Palatini action) We use the new action principle to gain some new insights into the problem of the reality conditions that must be imposed in order to get real formulations from complex general relativity We derive also a real formulation for Lorentzian general relativity in the Ashtekar phase space by using the modified action presented in the paper
82 citations