12 found
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  1.  14
    Putting Continuous Metaheuristics to Work in Binary Search Spaces.Broderick Crawford, Ricardo Soto, Gino Astorga, José García, Carlos Castro & Fernando Paredes - 2017 - Complexity:1-19.
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  2.  66
    The Extended Relativity Theory in Born-Clifford Phase Spaces with a Lower and Upper Length Scales and Clifford Group Geometric Unification.Carlos Castro - 2005 - Foundations of Physics 35 (6):971-1041.
    We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upperR and lower length λ scales. The invariance symmetry leads naturally to the real Clifford algebra Cl and complexified Clifford ClC algebra related to Twistors. A unified theory of all Noncommutative branes in Clifford-spaces is developed based on the Moyal-Yang star product deformation quantization whose deformation parameter involves the lower/upper scale \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document}. Previous work led us to show from first principles (...)
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  3.  35
    The String Uncertainty Relations Follow From the New Relativity Principle.Carlos Castro - 2000 - Foundations of Physics 30 (8):1301-1316.
    Stringy corrections to the ordinary Heisenberg uncertainty relations have been known for some time. However, a proper understanding of the underlying new physical principle modifying the ordinary Heisenberg uncertainty relations has not yet emerged. The author has recently proposed a new scale relativity theory as a physical foundation of string and M theories. In this work the stringy uncertainty relations, and corrections thereof, are rigorously derived from this new relativity principle without any ad-hoc assumptions. The precise connection between the Regge (...)
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  4.  26
    On Superluminal Particles and the Extended Relativity Theories.Carlos Castro - 2012 - Foundations of Physics 42 (9):1135-1152.
    Superluminal particles are studied within the framework of the Extended Relativity theory in Clifford spaces (C-spaces). In the simplest scenario, it is found that it is the contribution of the Clifford scalar component π of the poly-vector-valued momentum which is responsible for the superluminal behavior in ordinary spacetime due to the fact that the effective mass $\mathcal{M} = \sqrt{ M^{2} - \pi^{2} }$ is imaginary (tachyonic). However, from the point of view of C-space, there is no superluminal (tachyonic) behavior because (...)
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  5.  32
    On Weyl Geometry, Random Processes, and Geometric Quantum Mechanics.Carlos Castro - 1992 - Foundations of Physics 22 (4):569-615.
    This paper discusses some of the technical problems related to a Weylian geometrical interpretation of the Schrödinger and Klein-Gordon equations proposed by E. Santamato. Solutions to these technical problems are proposed. A general prescription for finding out the interdependence between a particle's effective mass and Weyl's scalar curvature is presented which leads to the fundamental equation of geometric quantum mechanics, $$m(R)\frac{{dm(R)}}{{dR}} = \frac{{\hbar ^2 }}{{c^2 }}$$ The Dirac equation is rigorously derived within this formulation, and further problems to be solved (...)
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  6. Born’s Reciprocal Gravity in Curved Phase-Spaces and the Cosmological Constant.Carlos Castro - 2012 - Foundations of Physics 42 (8):1031-1055.
    The main features of how to build a Born’s Reciprocal Gravitational theory in curved phase-spaces are developed. By recurring to the nonlinear connection formalism of Finsler geometry a generalized gravitational action in the 8D cotangent space (curved phase space) can be constructed involving sums of 5 distinct types of torsion squared terms and 2 distinct curvature scalars ${\mathcal{R}}, {\mathcal{S}}$ which are associated with the curvature in the horizontal and vertical spaces, respectively. A Kaluza-Klein-like approach to the construction of the curvature (...)
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  7. On Nonlinear Quantum Mechanics, Noncommutative Phase Spaces, Fractal-Scale Calculus and Vacuum Energy.Carlos Castro - 2010 - Foundations of Physics 40 (11):1712-1730.
    A (to our knowledge) novel Generalized Nonlinear Schrödinger equation based on the modifications of Nottale-Cresson’s fractal-scale calculus and resulting from the noncommutativity of the phase space coordinates is explicitly derived. The modifications to the ground state energy of a harmonic oscillator yields the observed value of the vacuum energy density. In the concluding remarks we discuss how nonlinear and nonlocal QM wave equations arise naturally from this fractal-scale calculus formalism which may have a key role in the final formulation of (...)
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  8. On Dark Energy, Weyl’s Geometry, Different Derivations of the Vacuum Energy Density and the Pioneer Anomaly.Carlos Castro - 2007 - Foundations of Physics 37 (3):366-409.
    Two different derivations of the observed vacuum energy density are presented. One is based on a class of proper and novel generalizations of the de Sitter solutions in terms of a family of radial functions R that provides an explicit formula for the cosmological constant along with a natural explanation of the ultraviolet/infrared entanglement required to solve this problem. A nonvanishing value of the vacuum energy density of the order of ${10^{- 123} M_{\rm Planck}^4}$ is derived in agreement with the (...)
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  9.  60
    Extended Scale Relativity, P-Loop Harmonic Oscillator, and Logarithmic Corrections to the Black Hole Entropy.Carlos Castro & Alex Granik - 2003 - Foundations of Physics 33 (3):445-466.
    An extended scale relativity theory, actively developed by one of the authors, incorporates Nottale's scale relativity principle where the Planck scale is the minimum impassible invariant scale in Nature, and the use of polyvector-valued coordinates in C-spaces (Clifford manifolds) where all lengths, areas, volumes⋅ are treated on equal footing. We study the generalization of the ordinary point-particle quantum mechanical oscillator to the p-loop (a closed p-brane) case in C-spaces. Its solution exhibits some novel features: an emergence of two explicit scales (...)
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  10.  51
    On Clifford Space Relativity, Black Hole Entropy, Rainbow Metrics, Generalized Dispersion and Uncertainty Relations.Carlos Castro - 2014 - Foundations of Physics 44 (9):990-1008.
    An analysis of some of the applications of Clifford space relativity to the physics behind the modified black hole entropy-area relations, rainbow metrics, generalized dispersion and minimal length stringy uncertainty relations is presented.
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  11.  16
    Research, Development, and Innovation in Extremadura: A GNU/Linex Case Study.Andoni Alsonso, Luis Casas, Carlos Castro & Fernando Solís - 2004 - Philosophy Today 48 (9999):16-22.
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  12.  27
    The Charge–Mass–Spin Relation of Clifford Polyparticles, Kerr–Newman Black Holes and the Fine Structure Constant.Carlos Castro - 2004 - Foundations of Physics 34 (7):1091-1113.
    A Clifford-algebraic interpretation is proposed of the charge, mass, spin relationship found recently by Cooperstock and Faraoini, which was based on the Kerr–Newman metric solutions of the Einstein–Maxwell equations. The components of the polymomentum associated with a Clifford polyparticle in four dimensions provide for such a charge, mass, spin relationship without the problems encountered in Kaluza–Klein compactifications which furnish an unphysically large value for the electron charge. A physical reasoning behind such charge, mass, spin relationship is provided, followed by a (...)
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