in this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  we relate the cohomology of a normal subgroup $n$ of a topological group $g$ and the quotient $g/n$ to the cohomology of $g$. we get the inflation-restriction exact sequence. also, we obtain a seven-term exact cohomology sequence up to dimension 2. we give an interpretation of the first non-a...

In this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  We relate the cohomology of a normal subgroup $N$ of a topological group $G$ and the quotient $G/N$ to the cohomology of $G$. We get the inflation-restriction exact sequence. Also, we obtain a seven-term exact cohomology sequence up to dimension 2. We give an interpretation of the first non-a...

The quantum duality principle (QDP) for homogeneous spaces gives four recipes to obtain, from a quantum homogeneous space, a dual one, in the sense of Poisson duality. One of these recipes fails (for lack of the initial ingredient) when the homogeneous space we start from is not a quasi-affine variety. In this work we solve this problem for the quantum Grassmannian, a key example of quantum pro...

The path integral on a homogeneous space G/H is constructed, based on the guiding principle ‘first lift to G and then project to G/H ’. It is then shown that this principle admits inequivalent quantizations inducing a gauge field (the canonical connection) on the homogeneous space, and thereby reproduces the result obtained earlier by algebraic approaches. ∗E-mail: [email protected] ...

Abstract The homogeneous causal action principle on a compact domain of momentum space is introduced. connection to fermion systems worked out. Existence and compactness results are reviewed. Euler–Lagrange equations derived analyzed under suitable regularity assumptions.

D’Alembert’s and similar wave equations are not fundamental relations, but result from a continuity equation and internal dynamics. The continuity equation is considered to be an elementary persistent element in a ’permanently changing world’ (Heraclitus). Generalizing a reasoning by Euler, the principle of sufficient reason implies inertial motion in a homogeneous and isotropic space-time to b...

here, we have considered the husimi and wigner distribution functions. we have, inparticular, shown how the uncertainty principle works for the two cases of simple and damped harmonicoscillators when either of these two distributions are used. the conclusion shows that the husimidistribution function remains non-negative through the phase space but it does not always satisfies theuncertainty pr...

In this paper, we use the generalized differentiability concept tostudy the fuzzy transport equation. We consider transport equationin the homogeneous and non-homogeneous cases with fuzzy initialcondition. We also present the solution when speed parameter is a fuzzynumber. Our method is based on the construction of the solutionsby employing Zadeh's extension principle.