Related papers: A Poincare lemma in Geometric Quantisation
We give criteria for finite dimensionality or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative invariants of the group. In the finite dimensional scenario…
We propose a cosmological model in the framework of the Poincar\'e gauge theory of gravity (PG). The gravitational Lagrangian is quadratic in curvature and torsion. In our specific model, the Lagrangian contains (i) the curvature scalar $R$…
In this paper a generalisation of the notion of polarity is exhibited which allows to completely describe, in an incidence-geometric way, the linear complexes of $h$-subspaces. A generalised polarity is defined to be a partial map which…
By using classical invariant theory approach a formulas for computation of the Poincare series of the kernel of linear locally nilpotent derivations is found.
The path integral formulation of singular systems with second order Lagrangian is studied by using the canonical path integral method. The path integral of Podolsky electrodynamics is studied.
Development of quantum engineering put forward new theoretical problems. Behavior of a single mesoscopic cell (device) we may usually describe by equations of quantum mechanics. However if experimentators gather hundreds of thousands of…
The Poincare Equivalence Theorem states that any optical element which contains no absorbing components can be replaced by an equivalent optical model which consists of one linear retarder and one rotator only, both of which are uniquely…
Let a finite group $G$ act on the complex plane $({\Bbb C}^2, 0)$. We consider multi-index filtrations on the spaces of germs of holomorphic functions of two variables equivariant with respect to 1-dimensional representations of the group…
Started from our work "Fields on the Poincare Group and Quantum Description of Orientable Objects" (EPJC,2009), we consider here a classification of orientable relativistic quantum objects in 3+1 dimensions. In such a classification, one…
We discuss the choice of the Lagrangian in the Poincar\'e gauge theory of gravity. Drawing analogies to earlier de Sitter gauge models, we point out the possibility of deriving the Einstein-Cartan Lagrangian {\it without} cosmological term…
We have systematically computed the generators of the symmetries arising in Poincare gauge theory formulation of gravity, both in 2+1 and 3+1 dimensions. This was done using a completely Lagrangian approach. The results are expected to be…
Geometric phase has historically been defined using closed cycles of polarization states, often derived using differential geometry on the Poincare sphere. Using the recently-developed wave model of geometric phase, we show that it is…
We take as a starting point an expression for the quantum geometric tensor recently derived in the context of the gauge/gravity duality. We proceed to generalize this formalism in such way it is possible to compute the geometrical phases of…
We present the method for finding of the nonlinear Poisson-Lie groups structures on the vector spaces and for their quantization. For arbitrary central extension of Lie algebra explicit formulas of quantization are proposed.
We define prequantization for Dirac manifolds to generalize known procedures for Poisson and (pre) symplectic manifolds by using characteristic distributions obtained from 2-cocycles associated to Dirac structures. Given a Dirac manifold…
In this article we define a Poincare series on a subspace of a complex analytic germ, induced by a multi-index filtration on the ambient space. We compute this Poincare series for subspaces defined by principal ideals. For plane curve…
To a plane curve singularity one associates a multi-index filtration on the ring of germs of functions of two variables defined by the orders of a function on irreducible components of the curve. The Poincare series of this filtration…
We show that the partition function of the Ponzano-Regge quantum gravity model can be written as a sum over surfaces in a $(2+1)$ dimensional space-time. We suggest a geometrical meaning, in terms of surfaces, for the (regulated)…
It is well known that objects can oscillate around the Lagrangian point L4. In this manuscript we compute the period of these oscillations by computing the exact expression of the characteristic polynomial of the matrix that determined the…
The FORTRAN code POLRAD 2.0 for radiative correction calculation in inclusive and semi-inclusive deep inelastic scattering of polarized leptons by polarized nucleons and nuclei is described. Its theoretical basis, structure and algorithms…