Related papers: Self-adjointness and boundedness in quadratic quan…
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…
In a configuration space whose boundary can be identified with a subset of its interior, a boundary condition can relate the behaviour of a function on the boundary and in the interior. Additionally, boundary values can appear as additive…
As quantum parallelism allows the effective co-representation of classical mutually exclusive states, the diagonalization method of classical recursion theory has to be modified. Quantum diagonalization involves unitary operators whose…
We revisit the treatment of identical particles in quantum mechanics. Two kinds of solutions of Schr\"{o}dinger equation are found and analyzed. First, the known symmetrized and antisymmetrized eigenfunctions. We examine how the very…
We study the entanglement of unitary operators on $d_1\times d_2$ quantum systems. This quantity is closely related to the entangling power of the associated quantum evolutions. The entanglement of a class of unitary operators is quantified…
The quantization of closed cosmologies makes it necessary to study squared Dirac operators on closed intervals and the corresponding quantum amplitudes. This paper proves self-adjointness of these second-order elliptic operators.
We consider the class of non-Hermitian operators represented by infinite tridiagonal matrices, selfadjoint in an indefinite inner product space with one negative square. We approximate them with their finite truncations. Both infinite and…
We continue our study of topological partial *algebras, focusing our attention to the interplay between the various partial multiplications. The special case of partial *-algebras of operators is examined first, in particular the link…
Distinguished selfadjoint extensions of operators which are not semibounded can be deduced from the positivity of the Schur Complement (as a quadratic form). In practical applications this amounts to proving a Hardy-like inequality.…
In this article, we prove and disprove several generalizations of unbounded versions of the Fuglede-Putnam theorem. As applications, we give conditions guaranteeing the commutativity of a bounded self-adjoint operator with an unbounded…
The combination of quantum theory and special relativity leads to structures that differ in several respects from non-relativistic quantum mechanics of particles. These differences are quite familiar to practitioners of Algebraic Quantum…
We show that any coboundary Lie bialgebra can be quantized. For this, we prove that: (a) Etingof-Kazhdan quantization functors are compatible with Lie bialgebra twists, and (b) if such a quantization functor corresponds to an even…
Some typical quantization ambiguities of quantum geometry are studied within isotropic models. Since this allows explicit computations of operators and their spectra, one can investigate the effects of ambiguities in a quantitative manner.…
Canonical quantization (CQ) is built around $[Q,P]=i\hbar1\!\!1$, while affine quantization (AQ) is built around $[Q,D]=i\hbar\,Q$, where $D\equiv(PQ+QP)/2$. The basic CQ operators must fit $-\infty< P, Q <\infty$, while the basic AQ…
A generalized quantization principle is considered, which incorporates nontrivial commutation relations of the components of the variables of the quantized theory with the components of the corresponding canonical conjugated momenta…
We consider one particle confined to a deformed one-dimensional wire. The quantum mechanical equivalent of the classical problem is not uniquely defined. We describe several possible hamiltonians and corresponding solutions for a finite…
Coupling any interacting quantum mechanical system to gravity in one dimension requires the cosmological constant to belong to the matter energy spectrum and thus to be quantized, even though the gravity sector is free of any quantum…
What does it mean to quantize a symplectic map $\chi$? In deformation quantization, it means to construct an automorphism of the $*$ algebra associated to $\chi$. In quantum chaos it means to construct unitary operators $U_{\chi}$ such that…
Incompatibility between conjugate variables and complementary pictures comes in two kinds, exclusive of one another. The first kind is unconditional, and the second conditional on quantum's indivisibility. We employ this distinction to…
Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is…