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.

A complete perturbative expansion for the Hamiltonian describing the motion of a quantomechanical system constrained to move on an arbitrary submanifold of its configuration space R n is obtained.

We derive the effective Hamiltonian for a quantomechanical system constrained to move on a submanifold M of its configuration space Rn by a confining potential V. Besides potential terms proportional to the intrinsic and mean curvature of M the restriction to the constraint produce the minimal interaction with a geometry-induced Yang-Mills field.

A realistic analysis shows that constraining a quantum mechanical system produces the effective dynamics to be coupled with AbelianÂnon-Abelian gauge fields and quantum potentials induced by the intrinsic and 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. AcademicPress, Inc.

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.