相关论文: Higher order topological actions

An idealised experiment estimating the spacetime topology is considered in both classical and quantum frameworks. The latter is described in terms of histories approach to quantum theory. A procedure creating combinatorial models of…

An idealized experiment estimating the spacetime topology is considered in both classical and quantum frameworks. The latter is described in terms of histories approach to quantum theory. A procedure creating combinatorial models of…

We present a multi-modal action logic with first-order modalities, which contain terms which can be unified with the terms inside the subsequent formulas and which can be quantified. This makes it possible to handle simultaneously time and…

The gravitational action is not always additive in the usual sense. We provide a general prescription for the change in action that results when different portions of the boundary of a spacetime are topologically identified. We discuss…

The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…

We find a series of topological phase transitions of increasing order, beyond the more standard second-order phase transition in a one-dimensional topological superconductor. The jumps in the order of the transitions depend on the range of…

When quantum back-reaction by fluctuations, correlations and higher moments of a state becomes strong, semiclassical quantum mechanics resembles a dynamical system with a high-dimensional phase space. Here, systematic computational methods…

Exponential actions defined by vector configurations provide a universal framework for several constructions of holomorphic dynamics, non-Kaehler complex geometry, toric geometry and topology. These include leaf spaces of holomorphic…

Topological groupoids admit various types of morphisms. We push these notions to the level of continuous groupoid actions to obtain various types of groupoid action morphisms. Some dynamical properties and their relation to these morphisms…

Classical decision theory models behaviour in terms of utility maximisation where utilities represent rational preference relations over outcomes. However, empirical evidence and theoretical considerations suggest that we need to go beyond…

The theory of operads (May, cyclic, modular, PROPs, etc) is extended to include higher dimensional phenomena, i.e. operations between operations, mimicking the algebraic structure on varieties of arbitrary dimensions, having marked…

An extension of the classical action principle obtained in the framework of the gauge transformations, is used to describe the motion of a particle. This extension assigns many, but not all, paths to a particle. Properties of the particle…

A global action is an algebraic analogue of a topological space. It consists of group actions $G_\alpha\curvearrowright X_\alpha$, $(\alpha\in\Phi)$, which fulfill a certain compatibility condition. We investigate the homotopy theory of…

Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…

A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…

We discuss the concept of the quantum action with the purpose to characterize and quantitatively compute quantum chaos. As an example we consider in quantum mechanics a 2-D Hamiltonian system - harmonic oscillators with anharmonic coupling…

These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by…

Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand…

The correspondence of a new form of quantum mechanics based on a quantum version of the action principle, which was proposed earlier [arXiv:0807.3508], with the ordinary quantum mechanics is established. New potentialities of the quantum…

We present, for the first time, an action principle that gives the equations of motion of an extended body possessing multipole moments in an external gravitational field, in the weak field limit. From the action, the experimentally…