Related papers: Non-standard phase space variables, quantization, …
Despite the current concentration on phase control in few-cycle pulses, it emerges that there exists a wide class of nonlinear optical interactions in which the carrier phase is essentially irrelevant, even for the shortest pulse profiles.…
See hep-th/9907179.
Phase spaces with nontrivial geometry appear in different approaches to quantum gravity and can also play a role in e.g. condensed matter physics. However, so far such phase spaces have only been considered for particles or strings. We…
We further elaborate on a phase-space picture for a system of $N$ qubits and explore the structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves satisfying certain additional properties and…
The relation between a recently proposed path integral for minisuperspaces and different canonical quantizations is established. The step of the procedure where a choice between non equivalent theories is made is identified. Coordinates…
We develop a mathematically well-defined path integral formalism for general symplectic manifolds. We argue that in order to make a path integral quantization covariant under general coordinate transformations on the phase space and involve…
The Feynman path integral does not allow a "one real path" interpretation, because amplitudes contribute to probabilities in a non-separable manner. The opposite extreme, "all paths happen", is not a useful or informative account. In this…
A sketch of a recent approach to quantum gravity is presented which involves several unconventional aspects. The basic ingredients include: (1) Affine kinematical variables; (2) Affine coherent states; (3) Projection operator approach for…
These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.
We use path integrals to calculate perturbative corrections to the correlation function of a particle under the action of nonlinear optical tweezers, both in the overdamped and underdamped regimes. In both cases, it is found that to leading…
The path integral is not typically utilized for analyzing entanglement experiments, in part because there is no standard toolbox for converting an arbitrary experiment into a form allowing a simple sum-over-history calculation. After…
Mathematical method of quantum phase space is very useful in physical applications like quantum optics and non-relativistic quantum mechanics. However, attempts to generalize it for the relativistic case lead to some difficulties. One of…
We make use of point transformations to introduce new canonical variables for systems defined on a finite interval and on the half-line so that new position variables should take all real values from $-\infty$ to $\infty$. The completeness…
This paper describes a path integral formulation of the free energy principle. The ensuing account expresses the paths or trajectories that a particle takes as it evolves over time. The main results are a method or principle of least action…
We give a mathematical definition of some path integrals, emphasizing those relevant to the quantization of symplectic manifolds (and more generally, Poisson manifolds) $\unicode{x2013}$ in particular, the coherent state path integral. We…
Path integrals appear to offer natural and intuitively appealing methods for defining quantum-mechanical amplitudes for questions involving spacetime regions. For example, the amplitude for entering a spatial region during a given time…
Semigroup algebras admit certain `coherent' deformations which, in the special case of a path algebra, may associate a periodic function to an evolving path; for a particle moving freely on a straight line after an initial impulse, the wave…
Using the fact that the nonintegrable phase factor can reformulate the gauge theory in terms of path dependent vector potentials, the quantization condition for the nonintegrable phase is investigated. It is shown that the path-dependent…
Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence (eg, quantum…
The path integral formulation of constrained systems leads to obtain the equations of motion as total differential equations in many variables. If these equations are integrable then one can constuct a valid and a canonical phase space…