Clifford Space as a Generalization of Spacetime: Prospects for QFT of Point Particles and Strings
نویسنده
چکیده
The idea that spacetime has to be replaced by Clifford space (C-space) is explored. Quantum field theory (QFT) and string theory are generalized to C-space. It is shown how one can solve the cosmological constant problem and formulate string theory without central terms in the Virasoro algebra by exploiting the peculiar pseudo-Euclidean signature of C-space and the Jackiw definition of the vacuum state. As an introduction into the subject, a toy model of the harmonic oscillator in pseudo-Euclidean space is studied.
منابع مشابه
Clifford Space as a Generalization of Spacetime: Prospects for Unification in Physics
The geometric calculus based on Clifford algebra is a very useful tool for geometry and physics. It describes a geometric structure which is much richer than the ordinary geometry of spacetime. A Clifford manifold (C-space) consists not only of points, but also of 1-loops, 2-loops, etc.. They are associated with multivectors which are the wedge product of the basis vectors, the generators of Cl...
متن کاملThe 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 کاملA Novel View on the Physical Origin of E 8 Matej
We consider a straightforward extension of the 4-dimensional spacetime M4 to the space of extended events associated with strings/branes, corresponding to points, lines, areas, 3-volumes, and 4-volumes in M4. All those objects can be elegantly represented by the Clifford numbers X ≡ xγA ≡ x γa1...ar , r = 0, 1, 2, 3, 4. This leads to the concept of the so-called Clifford space C, a 16-dimension...
متن کاملPolyvector-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 کاملAlbert Einstein: A Man for the Millenium?
ion: "Abstraction by deletion ... One carefully omits parts of the data describing the mathematical concepts ... to obtain the more abstract concept" (Saunders MacLane, ibid.). By dropping the assumptions of differentiability, one can extend the principle from theories based on differentiable manifolds to those based on topological manifolds; and by dropping the assumption of continuity the pri...
متن کامل