Related papers: Higher order topological actions
An analysis of the path-integral approach to quantum theory motivates the hypothesis that two experiments with the same classical action should have dual ontological descriptions. If correct, this hypothesis would not only constrain…
The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge…
Two-dimensional superintegrable systems with one third order and one lower order integral of motion are reviewed. The fact that Hamiltonian systems with higher order integrals of motion are not the same in classical and quantum mechanics is…
We present an action principle formulation for the study of motion of an extended body in General Relativity in the limit of weak gravitational field. This gives the classical equations of motion for multipole moments of arbitrary order…
We show that several interpretations of quantum mechanics admit an ontology of objects and events. This ontology reduces the breach between mind and matter. When humans act, their actions do not appear explainable in mechanical terms but…
The analytic physics, when it is development from aprioristic form, constructs all the laws from the Hamilton principle, also called action principle. According to this principle all systems are characterized by a magnitude called action…
The action principle is frequently used to derive the classical equations of motion. The action may also be used to associate group elements with curves in the space-time manifold, similar to the gauge transformations. The action principle…
In the framework of the topos approach to quantum mechanics we give a representation of physical properties in terms of modal operators on Heyting algebras. It allows us to introduce a classical type study of the mentioned properties.
We present a class of mappings between models with topological mass mechanism and purely topological models in arbitrary dimensions. These mappings are established by directly mapping the fields of one model in terms of the fields of the…
It is common knowledge that atoms can form molecules if they attract each other. Here, we show that it is possible to create molecules where bound states of the atoms are not the result of attractive interactions but have the topological…
The quantum walk was originally proposed as a quantum mechanical analogue of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete time quantum walks provide a…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
The relation that exists in quantum mechanics among action variables, angle variables and the phases of quantum states is clarified, by referring to the system of a generalized oscillator. As a by-product, quantum-mechanical meaning of the…
Characterising causal structure is an activity that is ubiquitous across the sciences. Causal models are representational devices that can be used as oracles for future interventions, to predict how values of some variables will change in…
Quantum mechanics and classical mechanics are two very different theories, but the correspondence principle states that quantum particles behave classically in the limit of high quantum number. In recent years much research has been done on…
Here I explore a novel no-collapse interpretation of quantum mechanics which combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical…
Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results on the $\h \to 0$ asymptotics, it is not yet clear how to explain within standard quantum…
To understand the foundations of quantum mechanics, we have to think carefully about how theoretical concepts are rooted in -- and limited by -- the nature of experience, as Bohr attempted to show. Geometrical pictures of physical phenomena…
Semigroups generated by topological operations such as closure, interior or boundary are considered. It is noted that some of these semigroups are in general finite and noncommutative. The problem is formulated whether they are always…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…