Related papers: Categorical quantum mechanics
Conventional approach to quantum mechanics in phase space, (q,p), is to take the operator based quantum mechanics of Schrodinger, or and equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher…
In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also…
It has become increasingly apparent that a number of perplexing issues associated with the interpretation of quantum mechanics are more easily resolved once the notion of retrocausality is introduced. The aim here is to list and discuss…
In the previous paper (quant-ph/0204037) we proved that the quantum mechanics not only has statistic interpretation, but also the specific electromagnetic form. Here, from this point of view we show that all the formal particularities of…
Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and…
Directed Algebraic Topology studies spaces equipped with a form of direction, to include models of non-reversible processes. In the present extension we also want to cover critical processes, indecomposable and unstoppable. The first part…
This is a systematic review of the concept of indistinguishability in both classical and quantum mechanics, with particular attention to Gibbs' paradox. Section 1 is on the Gibbs paradox; section 2 is a defense of the concept of classical…
These notes give an introduction to the quantization procedure called geometric quantization. It gives a definition of the mathematical background for its understanding and introductions to classical and quantum mechanics, to differentiable…
Efforts to give an improved mathematical meaning to Feynman's path integral formulation of quantum mechanics started soon after its introduction and continue to this day. In the present paper, one common thread of development is followed…
We look at the fundamental use of complex numbers in Quantum Mechanics (QM). A review of some of the most popular reasons given in the literature to support the necessity of the complex formalism, We add some insight by invoking others.…
The field of classical stochastic processes forms a major branch of mathematics. They are, of course, also very well studied in biology, chemistry, ecology, geology, finance, physics, and many more fields of natural and social sciences.…
A new version of NLQM is formulated in terms of the generalized Nambu dynamics. The generalization is free from the difficulties of earlier approaches. The paper is a second part of "Elements of NLQM (I): NL Schrodinger equation and…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
There is compelling theoretical evidence that quantum physics will change the face of information science. Exciting progress has been made during the last two decades towards the building of a large scale quantum computer. A quantum group…
We consider categorical logic on the category of Hilbert spaces. More generally, in fact, any pre-Hilbert category suffices. We characterise closed subobjects, and prove that they form orthomodular lattices. This shows that quantum logic is…
We review recent developments and open questions for the description of nonequilibrium quantum fields, continuing hep-ph/0302210 and hep-ph/0410330.
Underlying any theory of physics is a layer of conceptual frames. They connect the mathematical structures used in theoretical models with physical phenomena, but they also constitute our fundamental assumptions about reality. Many of the…
The ontology emerging from quantum field theory and the results following from Bell's theorems allowed the development of an intuitive picture of the microscopic world described by quantum mechanics, that is, we can say that we understand…
This paper unites two research lines. The first involves finding categorical models of quantum programming languages and their type systems. The second line concerns the program of quantization of mathematical structures, which amounts to…
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of classical…