Related papers: Some Studies in Noncommutative Quantum Field Theor…
The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A…
Since the subject of noncommutative geometry is now entering maturity, we felt there is need for presentation of the material at an undergraduate course level. Our review is a zero order approximation to this project. Thus, the present…
Classical and quantum aspects of noncommutative field theories are discussed. In particular, noncommutative solitons and instantons are constructed and also d=2,3 noncommutative fermion and bosonic (Wess-Zumino-Witten and…
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum…
A geometric interpretation of quantum self-interacting string field theory is given. Relations between various approaches to the second quantization of an interacting string are described in terms of the geometric quantization. An algorithm…
We complete our previous recent review on noncommutative field theory, discussing in particular the constructive aproach to the Grosse-Wulkenhaar theory. We also suggest that by gluing together many Grosse-Wulkenhaar theories at high energy…
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…
Phase spaces with nontrivial geometry appear in different approaches to quantum gravity and can also play a role in e.g. condensed matter physics. However, so far such phase spaces have only been considered for particles or strings. We…
The existence of a fundamental length (or fundamental time) has been conjecture in many contexts. Here one discusses some consequences of a fundamental constant of this type, which emerges as a consequence of deformation-stability…
We review the present status of gauge theories built on various quantum space-times described by noncommutative space-times. The mathematical tools and notions underlying their construction are given. Different formulations of gauge theory…
We briefly review the derivation of a non-relativistic quantum mechanics description of a weakly bound non-relativistic system from the underlying quantum field theory. We highlight the main techniques used.
The foundations of non-linear quantum mechanics are based on six postulates and five propositions. On a first quantised level, these approaches are built on non-linear differential operators, non-linear eigenvalue equations, and the notion…
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.
In gauge theories, physical histories are represented by space-time connections modulo gauge transformations. The space of histories is thus intrinsically non-linear. The standard framework of constructive quantum field theory has to be…
We discuss the implications of a model of noncommutative Quantum Mechanics where noncommutativity is extended to the phase space. We analyze how this model affects the problem of the two-dimensional gravitational quantum well and use the…
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and…
The axiomatic approach based on Wightman functions is developed in noncommutative quantum field theory. We have proved that the main results of the axiomatic approach remain valid if the noncommutativity affects only the spatial variables.
We present some ideas for a possible Noncommutative Topological Quantum Field Theory (NCTQFT) and Noncommutative Floer Homology (NCFH). Our motivation is two-fold and it comes both from physics and mathematics: On the one hand we argue that…
The suggested theory is the new quantum mechanics (QM) interpretation.The research proves that QM represents the electrodynamics of the curvilinear closed (non-linear) waves. It is entirely according to the modern interpretation and…
A discussion of different criteria of consistency of quantum field theory from the point of view of physics and mathematics.