Related papers: Feynman path integrals and Lebesgue-Feynman measur…
It is hypothesized that the Langevin time of stochastic quantum quantization is a physical time over which quantum fields at all values of space and coordinate time fluctuate. The average over paths becomes a time average as opposed to an…
It is shown that some convolution semigroups of infinitely divisible measures are invariant under the random integral mappings $I^{h,r}_{(a,b]}$ defined in $(\star)$ below. The converse implication is specified for the semigroups of…
The influence od space-time curvature on quantum matter which can be theoretically described by covariant wave equations has not been experimentally established yet. In this paper we analyse in detail the suitability of the Ramsey atom beam…
The restricted Feynman path integrals (RFPIs) have been proposed to study continuous quantum measurements in physics. The RFPIs are heuristically determined in terms of the usual probability amplitude multiplied by weight for each path,…
Factorization of the (formal) path integral measure in a Wiener path integrals for Yang--Mills diffusion is studied. Using the nonlinear filtering stochastic differential equation, we perform the transformation of the path integral defined…
The alternative dynamics of loop quantum cosmology is examined by the path integral formulation. We consider the spatially flat FRW models with a massless scalar field, where the alternative quantization inherit more features from full loop…
A quantum transition can be seen as a result of interference between various pathways(e.g. Feynman paths) which can be labelled by a variable $f$. An attempt to determine the value of f without destroying the coherence between the pathways…
In order to evaluate the Feynman path integral in noncommutative quantum mechanics, we consider properties of a Lagrangian related to a quadratic Hamiltonian with noncommutative spatial coordinates. A quantum-mechanical system with…
The transference theory for Lp spaces of Calderon, Coifman, and Weiss is a powerful tool with many applications to singular integrals, ergodic theory, and spectral theory of operators. Transference methods afford a unified approach to many…
We revisit the Bieberbach conjecture in the framework of SLE processes and, more generally, L\'evy processes. The study of their unbounded whole-plane versions leads to a discrete series of exact results for the expectations of coefficients…
Let $A$ be a Lebesgue measure space. We interpret measures on $A\times A\times R_+$ as 'maps' from $A$ to $A$, which spread $A$ along itself; their Radon-Nikodym derivatives also are spread. We discuss basic properties of the semigroup of…
These notes were inspired by the course ''Quantum Field Theory from a Functional Integral Point of View'' given at the University of Zurich in Spring 2017 by Santosh Kandel. We describe Feynman's path integral approach to quantum mechanics…
The paper puts together some loosely connected observations, old and new, on the concept of a quantum field and on the properties of Feynman amplitudes. We recall, in particular, the role of (exceptional) elementary induced representations…
In this paper we discuss the relation between the standard covariant quantum field theory and light-front field theory. We define covariant theory by its Feynman diagrams, whereas light-front field theory is defined in terms of light-cone…
Many recent researches have investigated the deviations from the Friedmannian cosmological model, as well as their consequences on unexplained cosmological phenomena, such as dark matter and the acceleration of the Universe. On the one…
Complexifying space time has many interesting applications, from the construction of higher dimensional unification, to provide a useful framework for quantum gravity and to better define some local symmetries that suffer singularities in…
We establish a previously unexplored conservation law for the Quantum Fisher Information Matrix (QFIM) expressed as follows; when the QFIM is constructed from a set of observables closed under commutation, i.e., a Lie algebra, the spectrum…
Quantum trajectories are Markov processes describing the evolution of a quantum system subject to indirect measurements. They can be viewed as place dependent iterated function systems or the result of products of dependent and non…
Using the Cartan formulation of General Relativity, we construct a well defined lattice-regularized theory capable to describe large non-perturbative quantum fluctuations of the frame field (or the metric) and of the spin connection. To…
The loop transform in quantum gauge field theory can be recognized as the Fourier transform (or characteristic functional) of a measure on the space of generalized connections modulo gauge transformations. Since this space is a compact…