相关论文: Fuzzy Spacetime Issues
Quantum transition amplitudes are formulated for a model system with local internal time, using path integrals. The amplitudes are shown to be more regular near a turning point of internal time than could be expected based on existing…
Path integration is a respected form of quantization that all theoretical quantum physicists should welcome. This elaboration begins with simple examples of three different versions of path integration. After an important clarification of…
For distinguishable particles it is well known that Brownian motion and a Feynman-Kac functional can be used to calculate the path integral (for imaginary times) for a general class of scalar potentials. In order to treat identical…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
The concepts of Feynman integrals in white noise analysis are used to construct the Feynman integrand for the harmonic oscillator in momentum space representation as a Hida distribution. Moreover it is shown that in a limit sense, the…
Spin foam models are the path integral counterparts to loop quantized canonical theories. In the last few years several spin foam models of gravity have been proposed, most of which live on finite simplicial lattice spacetime. The lattice…
The spacetime short-distance structure at the Planck scale is governed by the Planck length, usually interpreted as a three-dimensional Euclidian length. As such, it is not Lorentz invariant and clashes with Einstein's special relativity,…
By investigating the Feynman Path Integral we prove that elementary quantum particle dynamics are directly associated to single compact (cyclic) world-line parameters, playing the role of the particles' internal clock, implicit in ordinary…
We calculate the Feynman formula for the harmonic oscillator beyond and at caustics by the discrete formulation of path integral. The extension has been made by some authors, however, it is not obtained by the method which we consider the…
We study the path integral formulation of Friedmann universe filled with a massless scalar field in loop quantum cosmology. All the isotropic models of $k=0,+1,-1$ are considered. To construct the path integrals in the timeless framework, a…
In this Essay we construct a concrete, non-perturbative realization of metric reconstruction using quantum-optical model of particle detectors in relativistic quantum information. The non-perturbative approach allows us to realize a version…
Feynman's path integral is herein generalized to the nonextensive canonical density matrix based on Tsallis entropy. This generalization is done in two ways by using unnormalized and normalized constraints. Firstly, we consider the path…
We propose a simple criterion of compactness in the space of fuzzy number on the space of finite dimension and apply to deal with a class of fuzzy intergral equations in the best condition.
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…
The logical consistency of a description of Quantum Theory in the context of General Relativity, which includes Minimal Coupling Principle, is analyzed from the point of view of Feynman's formulation in terms of path integrals. We will…
Effective 4-dimensional theories are investigated which were obtained under dimensional reduction of multidimensional cosmological models with a minimal coupled scalar field as matter source. Conditions for the internal space stabilization…
Feynman's path integral formulation arose from his attempt to incorporate the Lagrangian framework into quantum mechanics, offering what he regarded as a more fundamental perspective than the Hamiltonian approach, particularly in the…
Quantum mechanical phase space path integrals are re-examined with regard to the physical interpretation of the phase space variables involved. It is demonstrated that the traditional phase space path integral implies a meaning for the…
We investigate properties of the fuzzy Henstock-Kurzweil delta integral (shortly, FHK $\Delta$-integral) on time scales, and obtain two necessary and sufficient conditions for FHK $\Delta$-integrability. The concept of uniformly FHK…
Feynman's laws of quantum dynamics are concisely stated, discussed in comparison with other formulations of quantum mechanics and applied to selected problems in the physical optics of photons and massive particles as well as flavour…