Related papers: Geometric formulation of quantum mechanics
This document contains a description of physics entirely based on a geometric presentation: all of the theory is described giving only a pseudo-riemannian manifold (M, g) of dimension n > 5 for which the g tensor is, in studied domains,…
Motivated by Quantum Bayesianism I give background for a general epistemic approach to quantum mechanics, where complementarity and symmetry are the only essential features. A general definition of a symmetric epistemic setting is…
We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques…
It is shown that the recently geometric formulation of quantum mechanics implies the use of Weyl geometry. It is discussed that the natural framework for both gravity and quantum is Weyl geometry. At the end a Weyl invariant theory is…
`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…
The purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues…
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory…
We present a geometric formulation of quantum mechanics based on the symplectic structure of the projective Hilbert space. Building upon the standard K\"ahler framework, we introduce an extension in which the symplectic structure is allowed…
In this paper, we discuss a geometrodynamical approach to particle physics, in which quantum mechanics is no more than an approximated model of nature in the microscopic scale. We derive quantum mechanics from the concept of non-local…
The main purpose of this paper is to present a new approach to logic or what we will call superlogic. This approach constitutes a new way of looking at the connection between quantum mechanics and logic. It is a {\it geometrisation} of the…
The formulation of Geometric Quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the…
A quantum version of the action principle in a simple covariant dynamical theory of two relativistic particles is formulated. The central object of this new formulation of quantum theory is a stationary eigenvalue of the quantum action.…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
A generalized Noether's theorem and the operational determination of a physical geometry in quantum physics are used to motivate a quantum geometry consisting of relations between quantum states that are defined by a universal group. Making…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
Proposals for nonlinear extenstions of quantum mechanics are discussed. Two different concepts of "mixed state" for any nonlinear version of quantum theory are introduced: (i) >genuine mixture< corresponds to operational "mixing" of…
It is shown that the equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of conformally "curved" space-time. This shows that it is possible to formulate quantum…
This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…