Related papers: Bohmian Trajectories For a Time Foliation with Kin…
Starting with a concise review of quaternionic geometry and quaternionic K{\"a}hler manifolds, we define a transversely quaternionic K{\"a}hler foliation. Then we formulate and prove the foliated versions of the now classical results of…
The fractional Fokker-Planck equation for subdiffusion in time-dependent force fields is derived from the underlying continuous time random walk. Its limitations are discussed and it is then applied to the study of subdiffusion under the…
Bohmian trajectories have been used for various purposes, including the numerical simulation of the time-dependent Schroedinger equation and the visualization of time-dependent wave functions. We review the purpose they were invented for:…
In this work we study the presence of kinks in models described by two real scalar fields in bi-dimensional space-time. We generate new two-field models, constructed from distinct but important one-field models, and we solve them with…
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…
We study longstanding problem of cosmological clock in the context of Brans-Dicke theory of gravitation. We present the Hamiltonian formulation of the theory for a class of spatially homogenous cosmological models. Then, we show that…
We consider a four dimensional space-time symmetry which is a non trivial extension of the Poincar\'e algebra, different from supersymmetry and not contradicting {\sl a priori} the well-known no-go theorems. We investigate some field…
We prove Wilking's Conjecture about the completeness of dual leaves for the case of Riemannian foliations on nonnegatively curved symmetric spaces. Moreover, we conclude that such foliations split as a product of trivial foliations and a…
We propose a polymer quantization scheme to derive the effective propagation of gravitational waves on a classical Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. These waves, which may originate from a high energy source, are a…
Riemann Poisson manifolds were introduced by the author in [1] and studied in more details in [2]. K\"ahler-Riemann foliations form an interesting subset of the Riemannian foliations with remarkable properties (see [3]). In this paper we…
In this paper we propose the time-dependent Hamiltonian form of human biomechanics, as a sequel to our previous work in time-dependent Lagrangian biomechanics [1]. Starting with the Covariant Force Law, we first develop autonomous…
In this paper, we study a linear convection-diffusion equation with time-dependent coefficients on a bounded interval. The problem includes inhomogeneous Dirichlet boundary conditions and is motivated by physical models where the…
Close to the Planck energy scale, the quantum nature of space-time reveals itself and all forces, including gravity, should be unified so that all interactions correspond to just one underlying symmetry. In the absence of a full quantum…
Roe's partitioned manifold index theorem applies when a complete Riemannian manifold $M$ is cut into two pieces along a compact hypersurface $N$. It states that a version of the index of a Dirac operator on $M$ localized to $N$ equals the…
We construct globally hyperbolic spacetimes such that each slice $\{t=t_0\}$ of the universal time $t$ is a model space of constant curvature $k(t_0)$ which may not only vary with $t_0\in\mathbb{R}$ but also change its sign. The metric is…
We present a variant of the classical Darboux-Jouanolou Theorem. Our main result provides a characterization of foliations which are pull-backs of foliations on surfaces by rational maps. As an application, we provide a structure theorem…
The supersymmetric Lagrangian compatible with the presence of torsion in the background spacetime requires, in addition to the minimal coupling, an interaction between the spin and the torsion of the form ${1/2}…
It is well known that orthodox quantum mechanics does not make unambiguous predictions for the statistics in arrival time (or time-of-flight) experiments. Bohmian mechanics (or de Broglie-Bohm theory) offers a distinct conceptual advantage…
How to compute the probability distribution of a detection time, i.e., of the time which a detector registers as the arrival time of a quantum particle, is a long-debated problem. In this regard, Bohmian mechanics provides in a…
When the bulk spacetime has a foliation structure, the collective dynamics of the hypersurfaces should reveal certain aspects of the bulk physics. The procedure of reducing the bulk to a hypersurface, called ADM reduction, was implemented…