Related papers: S'Darboux coordinates and WKB approximations in de…
Starting from a new principle inspired by quantum tomography rather than from Born's rule, this paper gives a self-contained deductive approach to quantum mechanics and quantum measurement. A suggestive notion for what constitutes a quantum…
We investigate noncommutative deformations of quantum field theories for different star products, particularly emphasizing the locality properties and the regularity of the deformed fields. Using functional analysis methods, we describe the…
A star-product formalism describing deformations of the standard quantum mechanical harmonic oscillator is introduced. A number of existing generalized oscillators occur as particular choises of star-products between the elements of the…
The quantum dynamics of an electron in a uniform magnetic field is studied for geometries corresponding to integrable cases. We obtain the uniform asymptotic approximation of the WKB energies and wavefunctions for the semi-infinite plane…
Quantum algebras (also called quantum groups) are deformed versions of the usual Lie algebras, to which they reduce when the deformation parameter q is set equal to unity. From the mathematical point of view they are Hopf algebras. Their…
The spectral curve is the key ingredient in the modern theory of classical integrable systems. We develop a construction of the ``quantum spectral curve'' and argue that it takes the analogous structural and unifying role on the quantum…
A class of decoherence schemes is described for implementing the principles of generalized quantum theory in reparametrization-invariant `hyperbolic' models such as minisuperspace quantum cosmology. The connection with sum-over-histories…
We introduce a family of operations in quantum mechanics that one can regard as "universal quantum measurements" (UQMs). These measurements are applicable to all finite-dimensional quantum systems and entail the specification of only a…
We formulate a ''minimal'' interpretational scheme for fairly general (minisuperspace) quantum cosmological models. Admitting as few exact mathematical structure as is reasonably possible at the fundamental level, we apply approximate…
In this paper we derive new two-component integrable differential difference and partial difference systems by applying a Lax-Darboux scheme to an operator formed from an ${\mathfrak{sl}}_3({\mathbb{C}})$-based automorphic Lie algebra. The…
We show that quantum measures and integrals appear naturally in any $L_2$-Hilbert space $H$. We begin by defining a decoherence operator $D(A,B)$ and it's associated $q$-measure operator $\mu (A)=D(A,A)$ on $H$. We show that these operators…
In this paper we introduce a measure of genuine quantum incompatibility in the estimation task of multiple parameters, that has a geometric character and is backed by a clear operational interpretation. This measure is then applied to some…
The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity…
We construct quantum circuits which exactly encode the spectra of correlated electron models up to errors from rotation synthesis. By invoking these circuits as oracles within the recently introduced "qubitization" framework, one can use…
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…
Integrable quantum field theories can be regularized on the lattice while preserving integrability. The resulting theory on the lattice are integrable lattice models. A prototype of such a regularization is the correspondence between…
We analyze a certain class of integral equations related to Marchenko equations and Gel'fand-Levitan equations associated with various systems of ordinary differential operators. When the integral operator is perturbed by a finite-rank…
Starting from deformation quantization (star-products), the quantization problem of Nambu Mechanics is investigated. After considering some impossibilities and pushing some analogies with field quantization, a solution to the quantization…
This paper introduces a novel boundary integral approach of shape uncertainty quantification for the Helmholtz scattering problem in the framework of the so-called parametric method. The key idea is to construct an integration grid whose…
Based on a closed formula for a star product of Wick type on $\CP^n$, which has been discovered in an earlier article of the authors, we explicitly construct a subalgebra of the formal star-algebra (with coefficients contained in the…