Unified Field Theoretical Models from Generalized Affine Geometries

New model of a non-dualistic Unified Theory is analyzed. This model is based in a manifold equipped with an underlying hypercomplex structure and zero non-metricity, that makes it geometricaly and physically consistent. Wormhole solution from this new model is presented and is explicitly compared with our previous one coming from the Einstein-Non Abelian Born-Infeld theory (in Class. Quantum Gravity 22:4987–5004, 2005). We find that the torsion plays in this unified theory similar role that Yang Mills type strength field coming from the non-Abelian Born-Infeld energy momentum tensor. The meaning of the Yang-Mills ansatz based in the alignment of the isospin with the frame geometry of the spacetime is discussed.     

Unified Field Theoretical Models from Generalized Affine Geometries II

The space-time structure of the new Unified Field Theory presented in previous reference (Int. J. Theor. Phys. 49:1288–1301, 2010) is analyzed from its SL(2C) underlying structure in order to make precise the notion of minimal coupling. To this end, the framework is the language of tensors and particularly differential forms and the condition a priory of the existence of a potential for the torsion is relaxed. We shown trough exact cosmological solutions from this model, where the geometry is Euclidean R⊗O ₃∼R⊗SU(2), the relation between the space-time geometry and the structure of the gauge group. Precisely this relation is directly connected with the relation of the spin and torsion fields. The solution of this model is explicitly compared with our previous ones and we find that: (i) the torsion is not identified directly with the Yang Mills type strength field, (ii) there exists a compatibility condition connected with the identification of the gauge group with the geometric structure of the space-time: this fact lead the identification between derivatives of the scale factor a(τ) with the components of the torsion in order to allows the Hosoya-Ogura ansatz (namely, the alignment of the isospin with the frame geometry of the space-time), (iii) this compatibility condition precisely mark the fact that local gauge covariance, coordinate independence and arbitrary space time geometries are harmonious concepts and (iv) of two possible structures of the torsion the “tratorial” form (the only one studied here) forbids wormhole configurations, leading only, cosmological instanton space-time in eternal expansion.     

Affine R-Matrix and the Generalized Elliptic Ruijsenaars Models

Commutative elliptic difference operators associated with the affine root systems are constructed in terms of affine R-matrices. These operators describe the Ruijsenaars models with elliptic potentials and reduce to the Macdonald operators in the trigonometric limit.     

Ermakov System and Plane Curve Motions in Affine Geometries

It is shown that the Pinney equation, Ermakov systems, and their higher-order generalizations describe self-similar solutions of plane curve motions in centro-affine and affine geometries.     

Generalized Ghost Pilgrim Scalar Field Models of Dark Energy

We assume generalized ghost Pilgrim dark energy(GGPDE) model in the presence of cold dark matter in flat FRW universe.With suitable choice of interaction term between GGPDE and cold dark matter,we investigate the nature of equation of state parameter for GGPDE.Also,we investigate the natures of dynamical scalar field models(such as quintessence,tachyon,k-essence,and dilaton dark energy) and concerned potentials through the correspondence phenomenon between GGPDE and these models.     

Some Generalized Scalar Field Models with Abundant Soliton-Like configurations

Some generahed scalar field models are presented. It is shown that there exist generally three types of soliton solutions for the extended models. The form of the first type of the soliton solutions is model-independent. An arbitrary constant can be included in the second type of the soliton excitations which is model-dependent. The third type of the soliton solutions is also modeldependent but with no arbitrary constant. The extended φ⁴ model and sine-Gordon model are studied in detail.     

Generalized Ghost Pilgrim Scalar Field Models of Dark Energy

We assume generalized ghost Pilgrim dark energy (GGPDE) model in the presence of cold dark matter in flat FRW universe. With suitable choice of interaction term between GGPDE and cold dark matter, we investigate the nature of equation of state parameter for GGPDE. Also, we investigate the natures of dynamical scalar field models (such as quintessence, tachyon, k-essence, and dilaton dark energy) and concerned potentials through the correspondence phenomenon between GGPDE and these models.     

Higher-Dimensional Integrable Systems Induced by Motions of Curves in Affine Geometries

We discuss the motions of curves by introducing an extra spatial variable or equivalently, moving surfaces in arffine geometries. It is shown that the 2 ＋1-dimensional breaking soliton equation and a 2 ＋ 1-dimensional nonlinear evolution equation regarded as a generalization to the 1 ＋ 1-dimensional KdV equation arise from such motions.     

Left-Right Symmetric Models in Noncommutative Geometries?

Left-right symmetric models are analyzed within the context of noncommutative geometry where we show that spontaneous parity violation is ruled out.     

T-duality in Affine NA Toda Models

The construction of non-Abelian affine Toda models is discussed in terms of its underlying Lie algebraic structure. It is shown that a subclass of such non-conformal two-dimensional integrable models naturally leads to the construction of a pair of actions, which share the same spectra and are related by canonical transformations.     

Lessons from Quantum Field Theory: Hopf Algebras and Spacetime Geometries

We discuss the prominence of Hopf algebras in recent progress in Quantum Field Theory. In particular, we will consider the Hopf algebra of renormalization, whose antipode turned out to be the key to a conceptual understanding of the subtraction procedure. We shall then describe several occurrences of this, or closely related Hopf algebras, in other mathematical domains, such as foliations, Runge-Kutta methods, iterated integrals and multiple zeta values. We emphasize the unifying role which the Butcher group, discovered in the study of numerical integration of ordinary differential equations, plays in QFT.     

Study for Unified Preen Models

Two grand unified preon models with light quarks and leptons are presented.All these models have natural family structure at the composite level.One of them can give very low metacolor scale,Λ_MC～10⁴GeV.It is argued that the best choice for metacolor group is SU(4) and for unification group is SU(9).     

Generalized Relativity: A Unified Field Theory Based on Free Geodesic Connections in Finsler Space

An equation of structure on space-time is developed using the methods of Finslergeometry with an essentially unrestricted connection function, corresponding toa specification of the geodesic curves in the manifold. This contrasts with theusual approach in which the connection is derived in an explicit and restrictivemanner from a metric. The equation of structure based on the free geodesicconnection is found to incorporate, as a special case, equations which are closelycomparable to both Einstein's equation of gravity in the presence ofelectromagnetic energy and Maxwell's equations for a chargeless electromagneticfield. Beyond this unification of electromagnetism and gravity, the theory appearsto offer a wide scope for consideration of additional implications which mayprovide insights into other observed phenomena.     

Unified Field Theory from Enlarged Transformation Group. The Consistent Hamiltonian

A theory has been presented previously in which the geometrical structure of a real four-dimensional space time manifold is expressed by a real orthonormal tetrad, and the group of diffeomorphisms is replaced by a larger group. The group enlargement was accomplished by including those transformations to anholonomic coordinates under which conservation laws are covariant statements. Field equations have been obtained from a variational principle which is invariant under the larger group. These field equations imply the validity of the Einstein equations of general relativity with a stress-energy tensor that is just what one expects for the electroweak field and associated currents. In this paper, as a first step toward quantization, a consistent Hamiltonian for the theory is obtained. Some concluding remarks are given concerning the need for further development of the theory. These remarks include discussion of a possible method for extending the theory to include the strong interaction.     

Generalized Calogero and Toda Models

JETP Letters - A Calogero–Sutherland system with two types of interacting spin variables has been described using the Hitchin approach and quasicompact structure. Complete integrability has...     

1,8-萘啶衍生物分子结构与理论电子光谱

采用密度泛函理论B3LYP/6-31G(d)方法优化计算4种2,4-二甲基-7-氨基-1,8-萘啶衍生物分子结构,探讨了其分子结构与前线分子轨道、能量的关系。运用含时密度泛函理论(TD-DFT)计算了它们的气相和溶液相电子光谱,研究了溶剂模型和计算方法对理论光谱的影响。计算结果表明,4种萘啶衍生物均含离域π键,HOMO与LUMO能级差ΔE较小,且大小顺序与它们的最大吸收波长实验值变化趋势一致。理论电子光谱证实,1,8-萘啶衍生物的吸收光谱随共轭性增强逐渐红移, 最大吸收源自于HOMO→LUMO的π→π*电子跃迁。PCM-B3LYP/6-31+G(d)计算结果与实验值相比,最大吸收波长分别相差2.6,10.3,5.3和6.9 nm,能量相差0.03,0.09,0.04和0.08 eV。因此,在考虑溶剂效应条件下,采用B3LYP/6-31(d) 方法优化分子构型和TD-DFT方法获得的电子光谱与实验光谱具有一致性。