We give simple formulas for the canonical metric, gradient, Lie derivative, Riemannian connection, parallel translation, geodesics and distance on the Grassmann manifold of p-planes in Rn. In these formulas, p-planes are represented as the column space of n £ p matrices. The Newton method on abstract Riemannian manifolds proposed by S. T. Smith is made explicit on the Grassmann manifold. Two ap...

We address the issue of recovering the time-dependent Schrödinger equation from quantum gravity in a natural way. To reach this aim it is necessary to understand the nonoccurrence of certain superpositions in quantum gravity. We explore various possible explanations and their relation. These are the delocalisation of interference terms through interaction with irrelevant degrees of freedom (dec...

We analyse in three space-time dimensions, the connection between abelian self dual vector doublets and their counterparts containing both an explicit mass and a topological mass. Their correspondence is established in the lagrangian formalism using an operator approach as well as a path integral approach. A canonical hamiltonian analysis is presented, which also shows the equivalence with the ...

We describe mechanisms to emulate properties of prime numbers by connecting them to computationally simpler representations involving bijections from natural numbers to sequences and multisets of natural numbers. Through a generic framework, implemented as a Haskell type class, we model interesting properties of canonical representation of factorization and its simpler equivalents, like informa...

When performing statistics on elements of sets that possess a particular geometric structure, it is desirable to respect this structure. For instance in a Lie group, it would be judicious to have a notion of a mean which is stable by the group operations (composition and inversion). Such a property is ensured for Riemannian center of mass in Lie groups endowed with a bi-invariant Riemannian met...

We exhibit equivalent conditions for subspaces of an inner product space to be isoclinic, including a characterization based on the classical notion canonical angles. identify connection with quantum error correction, showing that every correcting code is associated family isoclinic subspaces, and we prove converse pairs such subspaces. also show how angles arise in structure higher rank numeri...

We consider the semiclassical equations of motion of a particle when both an external electromagnetic field and the Berry gauge field in the momentum space are present. It is shown that these equations are Hamiltonian and relations between the canonical and covariant variables are determined through a consistent account of all components of the Berry connection. The Jacobian of the canonical-to...

Cylinders in projective varieties play an important role connection with unipotent group actions on certain affine algebraic varieties. The previous work due to Dubouloz and Kishimoto deals the condition for a del Pezzo fibration contain vertical cylinder. In present work, as generalization sense of singularities, we shall determine under which canonical singularities admits cylinder by means d...

In teleparallel geometries, symmetries are represented by affine frame which constrain both the (co)frame basis and spin-connection (which primary geometric objects). this paper we shall study geometries with a single symmetry, utilizing locally Lorentz covariant approach adopting complex null gauge. We first introduce an algorithm to consists of choosing coordinates adapted constructing canoni...