The Extended Relativity Theory in Born-Clifford Phase Spaces with a Lower and Upper Length Scales and Clifford Group Geometric Unification

نویسنده

  • Carlos Castro
چکیده

We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper and lower length scales (infrared/ultraviolet cutoff ). The invariance symmetry leads naturally to the real Clifford algebra Cl(2, 6, R) and complexified Clifford ClC(4) algebra related to Twistors. We proceed with an extensive review of Smith’s 8D model based on the Clifford algebra Cl(1, 7) that reproduces at low energies the physics of the Standard Model and Gravity; including the derivation of all the coupling constants, particle masses, mixing angles, ....with high precision. Further results by Smith are discussed pertaining the interplay among Clifford, Jordan, Division and Exceptional Lie algebras within the hierarchy of dimensions D = 26, 27, 28 related to bosonic string, M,F theory. Two Geometric actions are presented like the Clifford-Space extension of Maxwell’s Electrodynamics, Brandt’s action related the 8D spacetime tangent-bundle involving coordinates and velocities ( Finsler geometries ) followed by a discussion ( based on results by Cho et al ) why Einstein’s gravity in m + n dimensions is equivalent to an m-dim Yang-Mills-like theory of diffemorphisms of an internal n-dim space which admits a holographic reduction to lower dimensions in the case of AdSm×S and dSm×H backgrounds. Finally we outline the reasons why a Clifford-Space Geometric Unification of all forces is a very reasonable avenue to consider and propose an Einstein-Hilbert type action in Clifford-Phase spaces (associated with the 8D Phase space) as a Unified Field theory action candidate that should reproduce the physics of the Standard Model plus Gravity in the low energy limit.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Extended Relativity Theory in Clifford Phase Spaces and Modifications of Gravity at the Planck/Hubble scales

We extend the construction of Born’s Reciprocal Phase Space Relativity to the case of Clifford Spaces which involve the use of polyvectors and a lower/upper length scale. We present the generalized polyvector-valued velocity and acceleration/force boosts in Clifford Phase Spaces and find an explicit Clifford algebraic realization of the velocity and acceleration/force boosts. Finally, we provid...

متن کامل

The Extended Relativity Theory in Clifford Spaces

An introduction to some of the most important features of the Extended Relativity theory in Clifford-spaces (C-spaces) is presented whose ”point” coordinates are non-commuting Clifford-valued quantities which incorporate lines, areas, volumes, hyper-volumes.... degrees of freedom associated with the collective particle, string, membrane, p-brane,... dynamics of p-loops (closed p-branes) in targ...

متن کامل

Polyvector-valued Gauge Field Theories and Quantum Mechanics in Noncommutative Clifford Spaces

The basic ideas and results behind polyvector-valued gauge field theories and Quantum Mechanics in Noncommutative Clifford spaces are presented. The star products are noncommutative but associative up to second order only. The construction of Noncommutative Clifford-space gravity as polyvector-valued gauge theories of twisted diffeomorphisms in Clifford-spaces would require quantum Hopf algebra...

متن کامل

On n-ary Algebras, Branes and Polyvector Gauge Theories in Noncommutative Clifford Spaces

Polyvector-valued gauge field theories in noncommutative Clifford spaces are presented. The noncommutative star products are associative and require the use of the Baker-Campbell-Hausdorff formula. Actions for pbranes in noncommutative (Clifford) spaces and noncommutative phase spaces are provided. An important relationship among the n-ary commutators of noncommuting spacetime coordinates [X, X...

متن کامل

On the Fischer-Clifford matrices of a maximal subgroup of the Lyons group Ly

The non-split extension group $overline{G} = 5^3{^.}L(3,5)$ is a subgroup of order 46500000 and of index 1113229656 in Ly. The group $overline{G}$ in turn has L(3,5) and $5^2{:}2.A_5$ as inertia factors. The group $5^2{:}2.A_5$ is of order 3 000 and is of index 124 in L(3,5). The aim of this paper is to compute the Fischer-Clifford matrices of $overline{G}$, which together with associated parti...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005