Related papers: Noncommutativity as a mapping of paths
The non-individuals interpretation of quantum mechanics is presented with the aim of clarifying it and highflying some of its salient features. Alternative formulations of it are proposed and examined.
We argue that there should exist a "noncommutative Fourier transform" which should identify functions of noncommutative variables (say, of matrices of indeterminate size) and ordinary functions or measures on the space of paths. Some…
Application of the noncommutative geometry to several physical models is considered.
We discuss various descriptions of a quantum particle on noncommutative space in a (possibly non-constant) magnetic field. We have tried to present the basic facts in a unified and synthetic manner, and to clarify the relationship between…
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this…
A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its…
We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment…
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the…
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
We propose a phase-space path integral formulation of noncommutative quantum mechanics, and prove its equivalence to the operatorial formulation. As an illustration, the partition function of a noncommutative two-dimensional harmonic…
On the basis of a 5-dimensional form of space-time transformations non-relativistic quantum mechanics is reformulated in a manifestly covariant manner. The resulting covariance resembles that of the conventional relativistic quantum…
It is shown that quantum mechanics on noncommutative spaces (NQM) can be obtained by the canonical quantization of some underlying second class constrained system formulated in extended configuration space. It leads, in particular, to an…
The central theme of this thesis is to study some aspects of noncommutative quantum mechanics and noncommutative quantum field theory. We explore how noncommutative structures can emerge and study the consequences of such structures in…
We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge…
We investigate the transition from second to first order systems. This transforms configuration space into phase space and hence introduces noncommutativity in the former. Quantum mechanically, the transition may be described in terms of…
In this article the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is…
General non-commutative supersymmetric quantum mechanics models in two and three dimensions are constructed and some two and three dimensional examples are explicitly studied. The structure of the theory studied suggest other possible…
We briefly review ideas about ``noncommutativity of space-time'' and approaches toward a corresponding theory of gravity.
The book covers basics of noncommutative geometry and its applications in topology, algebraic geometry and number theory. A brief survey of main parts of noncommutative geometry with historical remarks, bibliography and a list of exercises…
Noncommutative coordinates are decomposed into a sum of geometrical ones and a universal quantum shift operator. With the help of this operator, the mapping of a commutative field theory into a noncommutative field theory (NCFT) is…