Related papers: The Symplectic Egg
The aim of this work is to show that particle mechanics, both classical and quantum, Hamiltonian and Lagrangian, can be derived from few simple physical assumptions. Assuming deterministic and reversible time evolution will give us a…
We extract the information of a quantum motion and decode it into a certain orbit via a single measurable quantity. Such that a quantum chaotic system can be reconstructed as a chaotic attractor. Two configurations for reconstructing this…
Classical and quantum mechanical descriptions of physical world are seamlessly abridged within the framework of Lagrangian formalism which, besides revealing the essence of nonlocally correlated dynamic evolution, helps understanding abrupt…
A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions…
We compute the quantum cohomology of symplectic flag manifolds. Symplectic flag manifolds can be described by non-abelian GLSMs with superpotential. Although the ring relations cannot be directly read off from the equations of motion on the…
An account of determinism and indeterminism in physics, addressed to non-physicist readers, leading up to proposals for how to understand statements about the future and single-event probability, motivated by quantum mechanics.
In this paper we survey several intersection and non-intersection phenomena appearing in the realm of symplectic topology. We discuss their implications and finally outline some new relations of the subject to algebraic geometry.
Quantum mechanics led to spectacular technological developments, discovery of new constituents of matter and new materials. However there is still no consensus on its interpretation and limitations. Some scientists and scientific writers…
We explain the mechanism leading to directed chaotic transport in Hamiltonian systems with spatial and temporal periodicity. We show that a mixed phase space comprising both regular and chaotic motion is required and derive a classical sum…
This is a graduate course on elementary quantum mechanics written for the benefit of undergraduate and graduate students. It is the English version of physics/0003106, which I did at the suggestion of several students from different…
We start from classical general relativity coupled to matter fields. Each configuration variable and its conjugate momentum, as also space-time points, are raised to the status of matrices [equivalently operators]. These matrices obey a…
** The primary topic of this dissertation is the study of the relationships between parts and wholes as described by particular physical theories, namely generalized probability theories in a quasi-classical physics framework and…
Frames provide redundant, stable representations of data which have important applications in signal processing. We introduce a connection between symplectic geometry and frame theory and show that many important classes of frames have…
The physical concept of quantum entanglement is brought to the biological domain. We simulate the cooperation of two insects by hypothesizing that they share a large number of quantum entangled spin-1/2 particles. Each of them makes…
A book, concerning the classical restricted three body problem, and the approach to this old conundrum coming from the modern methods of symplectic and contact geometry. It is split into Part I (theoretical aspects), and Part II (practical…
As has been known since the time of Gromov's Nonsqueezing Theorem, symplectic embedding questions lie at the heart of symplectic geometry. After surveying some of the most important ways of measuring the size of a symplectic set, these…
It is shown that the action for Hamiltonian equations of motion can be brought into invariant symplectic form. In other words, it can be formulated directly in terms of the symplectic structure $\omega$ without any need to choose some…
In light of G\"{o}del's undecidability results (incomplete theorems) for math, quantum indeterminism indicates that physics and the Universe may be indeterministic, incomplete, and open in nature, and therefore demand no single unification…
We survey the progress on the study of symplectic geometry past five decades. The survey focuses on the convexity properties of a moment map, the classification of symplectic actions, the symplectic embedding problems, and the theory of…
We present an analysis of quantum mechanics and its problems and paradoxes taking into account the results that have been obtained during the last two decades by investigations in the field of `quantum structures research'. We concentrate…