Related papers: Operadic quantization

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…

The 4-dimensional space-time is extended to pseudo-complex coordinates. Proposing the standard quantization rules in this extended space, the ones for the 4-dimensional sub-space acquire, as one solution, the commutation relations with…

In this paper we consider successive iterations of the first-order differential operations in space ${\bf R}^3.$

The third quantization formalism of quantum cosmology adds simplicity and conceptual insight into the quantum description of the multiverse. Within such a formalism, the existence of squeezed and entangled states raises the question of…

The unique third-order invariant variational equation in three-dimensional (pseudo)Euclidean space is derived.

We consider the third quantization in quantum cosmology of a minisuperspace extended by the Eisenhart-Duval lift. We study the third quantization based on both Klein-Gordon type and Dirac-type equations in the extended minisuperspace.…

We give a simple proof of a pointwise decay estimate in 3+1 dimensions stated in two versions, making advantage of a particular simplicity of inverting the spherically symmetric part of the wave operator and of the comparison theorem. We…

In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over…

The concept of quantization consists in replacing commutative quantities by noncommutative ones. In mathematical language an algebra of continuous functions on a locally compact topological space is replaced with a noncommutative…

We determine what should correspond to the Dirac operator on certain quantized hermitian symmetric spaces and what its properties are. A new insight into the quantized wave operator is obtained.

Deformation quantization (sometimes called phase-space quantization) is a formulation of quantum mechanics that is not usually taught to undergraduates. It is formally quite similar to classical mechanics: ordinary functions on phase space…

For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.

The physical meaning of the operators is not reducible to the intrinsic relations of the quantum system, since unitary transformations can find other operators satisfying the exact same relations. The physical meaning is determined…

It is shown uniquely that quantized spaces are realised on four-dimensional compact manifolds. In the case of O(1,5) quantized space this are four independent parameters of O(5) unit vector; in the case of O(2,4) these are parameters of one…

This paper considers an extension of origami geometry to the case of "folding" a three dimensional (3D) space along a plane. First, all possible incidence constraints between given points, lines and planes are analyzed by using the geometry…

The basic ideas of second quantization and Fock space are extended to density operator states, used in treatments of open many-body systems. This can be done for fermions and bosons. While the former only requires the use of a…

We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple…

We obtain sufficient conditions for a densely defined operator on the Fock space to be bounded or compact. Under the boundedness condition we then characterize the compactness of the operator in terms of its Berezin transform.

The author has introduced in a recent paper a new class of operators, called co-Toeplitz operators, with symbols in a co-algebra. This is the categorical dual to Toeplitz operators which have symbols in an algebra. The mapping from a symbol…

The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The…