Related papers: An introduction to strict quantization
We first review the historical developments, both in physics and in mathematics, that preceded (and in some sense provided the background of) deformation quantization. Then we describe the birth of the latter theory and its evolution in the…
This work considers a formal deformation of the quantum disc (it is developed via an application of the Berezin method) and presents an explicit formula for this deformation.
This set of notes corresponds to a mini-course given in September 2018 in Bedlewo; it does not contain any new result; it complements -- with intersection -- the introduction to formal deformation quantization and group actions,…
The quantization of the gravitational field is discussed within the exact uncertainty approach. The method may be described as a Hamilton-Jacobi quantization of gravity. It differs from previous approaches that take the classical…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
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 study the Moyal quantization for the constrained system. One of the purposes is to give a proper definition of the Wigner-Weyl(WW) correspondence, which connects the Weyl symbols with the corresponding quantum operators. A Hamiltonian in…
A method for the deformation quantization of coadjoint orbits of semisimple Lie groups is proposed. It is based on the algebraic structure of the orbit. Its relation to geometric quantization and differentiable deformations is explored.
The idea of quantum relativity as a generalized, or rather deformed, version of Einstein (special) relativity has been taking shape in recent years. Following the perspective of deformations, while staying within the framework of Lie…
We uncover an inconsistency in the uniform WKB quantization of deformed quantum mechanics.
We discuss a recently developed formalism which describes the quantum evolution of a solid-state qubit due to its continuous measurement. In contrast to the conventional ensemble-averaged formalism, it takes into account the measurement…
In this paper, we will deform the second and third quantized theories by deforming the canonical commutation relations in such a way that they become consistent with the generalized uncertainty principle. Thus, we will first deform the…
We investigate the application of deformation quantization to the system of a free particle evolving within a universe described by a Friedmann-Lemaitre-Robertson-Walker (FLRW) geometry. This approach allows us to analyze the dynamics of…
We analyze the estimation of a finite ensemble of quantum bits which have been sent through a depolarizing channel. Instead of using the depolarized qubits directly, we first apply a purification step and show that this improves the…
We develop a general framework for studying relative weight representations for certain pairs consisting of an associative algebra and a commutative subalgebra. Using these tools we describe projective and simple weight modules for quantum…
We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is…
We discuss the procedure of Rieffel induction of representations in the framework of formal deformation quantization of Poisson manifolds. We focus on the central role played by algebraic notions of complete positivity.
We present a first attempt to apply the approach of deformation quantization to linearized Einstein's equations. We use the analogy with Maxwell equations to derive the field equations of linearized gravity from a modified Maxwell…
Second quantization of a classical nonrelativistic one-particle system as a deformation quantization of the Schrodinger spinless field is considered. Under the assumption that the phase space of the Schrodinger field is $C^{\infty}$, both,…
In this paper Quantum Mechanics with Fundamental Length is chosen as the theory for describing the early Universe. This is possible due to the presence in the theory of General Uncertainty Relations from which unavoidable it follows that in…