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151.
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. 相似文献
152.
Hitoshi Konno 《Czechoslovak Journal of Physics》2005,55(11):1455-1460
We give a level-2 representation of the elliptic algebra
in terms of one free boson and one free fermion. We show that
-modules have a natural direct sum decomposition into the irreducible (deformed) super-Virasoro modules associated with the
coset
.
Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005. 相似文献
153.
Carlos Castro 《Foundations of Physics》2005,35(6):971-1041
We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper R and lower length λ 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. 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
. Previous work led us to show from first principles why the observed value of the vacuum energy density (cosmological constant) is given by a geometric mean relationship
, and can be obtained when the infrared scale R is set to be of the order of the present value of the Hubble radius. 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. Geometric actions are presented like the Clifford-Space extension of Maxwell’s Electrodynamics, and Brandt’s action related to the 8D spacetime tangent-bundle involving coordinates and velocities (Finsler geometries). 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. 相似文献
154.
The real and quaternionic charge conjugation operators invariant under the infinite-dimensional Clifford algebra, or compatible with the Fermi algebra, are determined. There results a maze of inequivalent irreducible charged representations, all of which are non-Fock. The representation vectors and their charges admit two interpretations besides those of spinors or states of quantum fields: as wavelets on the circle, with charge conjugations acting via ordinary complex conjugation; and as infinite-dimensional numbers, with charge conjugations acting by automorphisms. 相似文献
155.
For a finite dimensional semisimple Lie algebra
and a root q of unity in a field k, we associate to these data a double quiver
. It is shown that a restricted version of the quantized enveloping algebras
is a quotient of the double quiver algebra
.*The author is partially supported by the National Science Foundation of China (Grant. 10271014) and Natural Science Foundation of Beijing City (grant. 1042001) 相似文献
156.
In this paper, we paraquantize the spinning string theory in the Neveu-Shwarz model. Unlike the Ardalan and Mansouri work [Phys. Rev. D, Vol. 9, (1974) 3341], the paraquantum system is such that both the center of mass variables and the excitation modes of the string verify paracommutation relations. The commutators of the Poincaré algebra are satisfied, except the [p
,p
] one, since one can only write [p
,p
]= 0, for Q1. Because of the relation [x
,x
] =,0 and with the sole use of the trilinear relations, we find existence possibilities of spinning strings defined in a noncommutative space-time at space-time dimensions other than D=10. 相似文献
157.
Anatolij Dvurečenskij 《International Journal of Theoretical Physics》2004,43(11):2169-2185
Pseudo-effect algebras are partial algebras (E;+,0,1) with a partially defined addition + which is not necessarily commutative and therefore with two complements, left and right. If they satisfy a special kind of the Riesz decomposition property, they are intervals in unital po-groups. The general comparability property in unital po-groups with strong unit (G,u), allows to compare elements of G in some intervals with Boolean ends. Such a po-group is always an -group admitting a state. We prove that every such (G,u) is a subdirect product of linearly ordered unital po-groups. 相似文献
158.
Fukui Guo Yufeng Zhang Qingyou Yan 《International Journal of Theoretical Physics》2004,43(4):1139-1146
A new simple method for obtaining integrable hierarchies of soliton equations is proposed. First of all, a new loop algebra
is constructed, whose commutation operation is clear as that in loop algebra
. Second, by making use of the Tu scheme, many of integrable hierarchies with multicomponent potential functions can be produced. As a specific application of our method, a multicomponent AKNS hierarchy is obtained. Finally, an expanding loop algebra
of the loop algebra
is constructed. Taking advantage of
above, a type of integrable coupling system of the multicomponent AKNS hierarchy is worked out. 相似文献
159.
We consider a category of effect algebras and formulate an abstract-hidden variables problem for an object of this category. A notion of indeterministic object is introduced as of an object which induces a Kochen–Specker-type contradiction. A sufficient condition for an object to be indeterministic is derived. An abstract algebraic point of view on a no-hidden variables example constructed by Mermin is given. The notion of a passage to the semiclassical limit is analyzed and refined. 相似文献
160.