Monopole Gauge Fields and Quantum Potentials Induced by the Geometry in Simple Dynamical Systems

A realistic analysis shows that constraining a quantomechanical system produces the effective dynamics to be coupled with {\sl abelian/non-abelian gauge fields} and {\sl quantum potentials} induced by the {\sl intrinsic} and {\sl extrinsic geometrical properties} of the constraint's surface. This phenomenon is observable in the effective rotational motion of some simple polyatomic molecules. By considering specific examples it is shown that the effective Hamiltonians for the nuclear rotation of linear and symmetric top molecules are equivalent to that of a charged system moving in a background magnetic-monopole field. For spherical top molecules an explicit analytical expression of a non-abelian monopole-like field is found. Quantum potentials are also relevant for the description of rotovibrational interactions.Comment: 24, LaTex, UPRF-94-40

Elementary Particles and Spin Representations

We emphasize that the group-theoretical considerations leading to SO(10) unification of electro-weak and strong matter field components naturally extend to space-time components, providing a truly unified description of all generation degrees of freedoms in terms of a single chiral spin representation of one of the groups SO(13,1), SO(9,5), SO(7,7) or SO(3,11). The realization of these groups as higher dimensional space-time symmetries produces unification of all fundamental fermions is a single space-time spinor.Comment: 4 page

Conformally flat Kaluza-Klein spaces, pseudo-/para-complex space forms and generalized gravitational kinks

The equations describing the Kaluza-Klein reduction of conformally flat spaces are investigated in arbitrary dimensions. Special classes of solution related to pseudo-Kahler and para-Kahler structures are constructed and classified according to spacetime dimension, signature and gauge field rank. Remarkably, rank two solutions include gravitational kinks together with their centripetal and centrifugal deformations.Comment: 20 pages, 1 figur

Centrifugal deformations of the gravitational kink

The Kaluza-Klein reduction of 4d conformally flat spacetimes is reconsidered. The corresponding 3d equations are shown to be equivalent to 2d gravitational kink equations augmented by a centrifugal term. For space-like gauge fields and non-trivial values of the centrifugal term the gravitational kink solutions describe a spacetime that is divided in two disconnected regions.Comment: 8 pages, no figure

Cold atom simulation of interacting relativistic quantum field theories

We demonstrate that Dirac fermions self-interacting or coupled to dynamic scalar fields can emerge in the low energy sector of designed bosonic and fermionic cold atom systems. We illustrate this with two examples defined in two spacetime dimensions. The first one is the self-interacting Thirring model. The second one is a model of Dirac fermions coupled to a dynamic scalar field that gives rise to the Gross-Neveu model. The proposed cold atom experiments can be used to probe spectral or correlation properties of interacting quantum field theories thereby presenting an alternative to lattice gauge theory simulations.Comment: 5 pages, 3 figues, Phys. Rev. Lett. versio

Universal features of dimensional reduction schemes from general covariance breaking

Many features of dimensional reduction schemes are determined by the breaking of higher dimensional general covariance associated with the selection of a particular subset of coordinates. By investigating residual covariance we introduce lower dimensional tensors, that successfully generalize to one side Kaluza–Klein gauge fields and to the other side extrinsic curvature and torsion of embedded spaces, thus fully characterizing the geometry of dimensional reduction. We obtain general formulas for the reduction of the main tensors and operators of Riemannian geometry. In particular, we provide what is probably the maximal possible generalization of Gauss, Codazzi and Ricci equations and various other standard formulas in Kaluza–Klein and embedded spacetimes theories. After general covariance breaking, part of the residual covariance is perceived by effective lower dimensional observers as an infinite dimensional gauge group. This reduces to finite dimensions in Kaluza–Klein and other few remarkable backgrounds, all characterized by the vanishing of appropriate lower dimensional tensors