Related papers: Operadic quantization
The subject of this paper is the consecutive procedure of discretization and quantization of two similar classical integrable systems in three-dimensional space-time: the standard three-wave equations and less known modified three-wave…
A variational equation of the third order in three-dimensional space is proposed which describes autoparallel curves of some connection.
We present a simple visual description of the topology of the space of three-dimensional rotations, requiring just intuition, imagination and no advanced math.
A class of exact membrane solutions is quantized.
Classical mechanics, in the operatorial formulation of Koopman and von Neumann, can be written also in a functional form. In this form two Grassmann partners of time make their natural appearance extending in this manner time to a three…
We consider an approach in which the usual wave function in the quadrature representation of mode j of the electromagnetic field is further quantized to produce a field operator. Since the electromagnetic field is already second quantized,…
We show an equivalence between Dirac quantization and the reduced phase space quantization. The equivalence of the both quantization methods determines the operator ordering of the Hamiltonian. Some examples of the operator ordering are…
We give a streamlined proof of the multiplicative ergodic theorem for quasi-compact operators on Banach spaces with a separable dual.
This is an example on the cohomology of threefolds.
The paper shows that under some conditions the totalization of a cosimplicial space obtained from a multiplicative operad is a double loop space of the space of derived morphisms from the associative operad to the operad itself.
We construct an analogue of the Livernet--Loday operad for two compatible brackets. The Livernet--Loday operad can be used to define $\star$-products and deformation quantization for Poisson structures. We make use of our operad in the same…
Ambiguities arising in different approaches (canonical, quasiclassical, path integration) to quantization are discussed by an example of the mechanics of a point-like particle in the Riemannian space (the geodesic dynamics). A way to select…
We derive expressions for three-body phase space that are explicitly symmetrical in the masses of the three particles, by three separate methods.
In this paper we give examples of applications of general methods of quantization by symmetrization of classical integrable systems, which have been illustrated in two previous works by the same authors. We consider two classes of systems…
We define computational atoms named "actions" equipped primarily with three operations: reduction, collection, and inspection. We show how actions can be used for decision-making algorithms from simple axioms. We describe the encodings of…
We propose in this paper an alternative method for the quantisation of systems with first-class constraints. This method is a combination of the coherent-state-path-integral quantisation developed by Klauder, with the ideas of reduced state…
We consider here kinematical quantization: a first and often overlooked step in quantization procedures. $\mathbb{R}$, $\mathbb{R}_+$ and the interval are considered, as well as direct (Cartesian) products thereof. Some simple…
After introducing the Vogel plane we give the quantisation. Then we extend the Vogel plane to include certain symmetric spaces and give the quantisation of this extension.
We characterise the embeddability of simply connected locally 3-connected 2-dimensional simplicial complexes in 3-space in a way analogous to Kuratowski's characterisation of graph planarity, by excluded minors. This answers questions of…
The recently proposed projection quantization, which is a method to quantize particular subspaces of systems with known quantum theory, is shown to yield a genuine quantization in several cases. This may be inferred from exact results…