Related papers: Geometric quantization rules in QCPB theory
The Heisenberg uncertainty principle and its extensions are all still inequalities form which hold the superior approximate estimations. Based on quantum covariant Poisson bracket theory, we propose quantum geomertainty relation to modify…
Using geometric quantization procedure, the quantization of algebra of observables for physical system with Ricci-flat phase space is obtained. In the classical case the appointed physical system is reduced to harmonic oscillator when the…
A binary expression in terms of operators is given which satisfies all the quantum counterparts of the algebraic properties of the classical antibracket. This quantum antibracket has therefore the same relation to the classical antibracket…
Geometric Algebra and Calculus are mathematical languages encoding fundamental geometric relations that theories of physics seem to respect. We propose criteria given which statistics of expressions in geometric algebra are computable in…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
\noindent We briefly discuss some algebraic and geometric aspects of the generalized Poisson bracket and non--commutative phase space for generalized quantum dynamics, which are analogous to properties of the classical Poisson bracket and…
An analogue of geometric quantization of Poisson algebras obtained by algebraic reduction of symmetries is developed. Interpretation of the obtained results and their application to the problem of commutativity of quantization and reduction…
I present a method of performing geometric quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UTC). I also show that by using this method…
The unsatisfactory status of the search for a consistent and predictive quantization of gravity is taken as motivation to study the question whether geometrical laws could be more fundamental than quantization procedures. In such an…
These notes give an introduction to the quantization procedure called geometric quantization. It gives a definition of the mathematical background for its understanding and introductions to classical and quantum mechanics, to differentiable…
Classical mechanics has a natural mathematical setting in symplectic geometry and it may be asked if the same is true for quantum mechanics. More precisely, is it possible to capture certain quantum idiosyncrasies within the symplectic…
We introduce the Poisson bracket operator which is an alternative quantum counterpart of the Poisson bracket. This operator is defined using the operator derivative formulated in quantum analysis and is equivalent to the Poisson bracket in…
The formulation of Geometric Quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the…
Nambu's construction of multi-linear brackets for super-integrable systems can be thought of as degenerate Poisson brackets with a maximal set of Casimirs in their kernel. By introducing privileged coordinates in phase space these…
The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…
We introduce a new method to compute the Quantum Geometric Tensor, this procedure allows us to compute the Quantum Information Metric and the Berry curvature perturbatively for a theory with an arbitrary interaction Hamiltonian. The…
In a Generalised Probabilistic Theory (GPT) equipped additionally with some extra geometric structure we define the morphophoric measurements as those for which the measurement map sending states to distributions of the measurement results…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
A quantum theory in a finite-dimensional Hilbert space can be geometrically formulated as a proper Hamiltonian theory as explained in [2, 3, 7, 8]. From this point of view a quantum system can be described in a classical-like framework…
We introduce the Gaussian quantum operator representation, using the most general multi-mode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose…