相关论文: Remarks on a Nonlinear Quantum Theory
A recently proposed definition of a linear connection in non-commutative geometry, based on a generalized permutation, is used to construct linear connections on GL_q(n). Restrictions on the generalized permutation arising from the…
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the…
Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…
We consider a wide class of nonlinear canonical quantum systems described by a one-particle Schroedinger equation containing a complex nonlinearity. We introduce a nonlinear unitary transformation which permits us to linearize the…
The following lectures are an introduction to the phenomena of partonic saturation and nonlinear evolution equations in Quantum Chromodynamics. After a short introduction to the linear evolution, the problems of unitarity bound and parton…
Discussions of quantum mechanics often loosely claim that time evolution logically must be unitary, in order for the probabilistic interpretation of the amplitudes of the state vector to make sense at all times. We discuss from first…
The work presents two examples of simple mathematical formulas which are natural nonlinear modifications (one being a generalization) of Gielis' formula. These formulas involve a comparable number of parameters and provide non-Platonic…
We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is…
The possibility of deforming the (associative or Lie) product to obtain alternative descriptions for a given classical or quantum system has been considered in many papers. Here we discuss the possibility of obtaining some novel alternative…
Utilizing the general theory of open quantum systems to investigate the exact dynamical evolution of simple bilinear systems, we discover a mechanism of the dynamical genesis of quantum entanglement. We focus in detail on the exact quantum…
We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically…
The time development of equal-time correlation functions in quantum mechanics and quantum field theory is described by an exact evolution equation for generating functionals. This permits a comparison between classical and quantum evolution…
Quantum dynamics is linear. How do we know? From theory or experiment? The history of this question is reviewed. Nonlinear generalizations of quantum mechanics have been proposed. They predict small but clear nonlinear effects, which very…
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 explore and clarify the connections between two different forms of the renormalisation group equations describing the quantum evolution of hadronic structure functions at small $x$. This connection is established via a Langevin…
This dissertation explores various nonlinear responses that arise from the rich interplay between quantum geometry, disorder, magnetism and topology in quantum materials. In addition to presenting generalizations of quantum kinetic theory,…
Using the Madelung transformation on a generalized scalar Gross-Pitaevski equation, a nonlinear continuum fluid equations are derived for a classical fluid. A unitary quantum lattice algorithm is then determined as a second order discrete…
We describe several recent results obtained in collaboration with P. Gravejat, C. Hainzl, E. S\'er\'e and J.P. Solovej, concerning a nonlinear model for the relativistic quantum vacuum in interaction with a classical electromagnetic field.
Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signalling. As…
In this and a companion paper, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the dynamics extracted from the path integral or…