Related papers: Semi-Complex Analysis & Mathematical Physics (Corr…
An analytical approach for studying the cosmological scenario with a homogeneous tachyon field within the framework of loop quantum gravity is developed. Our study is based on the semi-classical regime where space time can be approximated…
We present some applications of general harmonic/wavelet analysis approach (generalized coherent states, wavelet packets) to numerical/analytical calculations in (nonlinear) quasiclassical/quantum beam dynamics problems. (Naive) deformation…
Recently, motivated by certain loop quantum gravity inspired corrections, it was shown that for spherically symmetric midisuperspace models infinitely many second derivative theories of gravity exist (as revealed by the presence of three…
A midi-superspace model is a field theory obtained by symmetry reduction of a parent gravitational theory. Such models have proven useful for exploring the classical and quantum dynamics of the gravitational field. I present 3 recent…
In this article the algebra and the basis of corresponding analysis in 4-dimensional spaces are constructed, in pseudoeuclidean with signature (1, -1, -1, -1) and pseudo-Riemannian corresponding to the real space-time. In both cases the…
Quantum field theory can be physically regularized by modularizing it on several levels of aggregation. Since computation is already thoroughly modularized, physical experiments are treated here as quantum relativistic cellular computations…
This thesis investigates how the metric and tetrad formulations of three gravitational field theories in manifolds with timelike boundaries within the covariant phase space program. With the recently developed relative bicomplex framework,…
We present an auxiliary space theory that provides a unified framework for analyzing various iterative methods for solving linear systems that may be semidefinite. By interpreting a given iterative method for the original system as an…
The paper concerns the fictitious entanglement of the so-called ``singularities'' in problems, pertaining to quantum gravity, due, in point of fact, to the way we try to employ, in that context, differential geometry, the latter being…
The operator algebraic framework plays an important role in mathematical physics. Many different operator algebras exist for example for a theory of quantum mechanics. In Loop Quantum Gravity only two algebras have been introduced until…
In the e-print is discussed a few steps to introducing of "vocabulary" of relativistic physics in quantum theory of information and computation (QTI&C). The behavior of a few simple quantum systems those are used as models in QTI&C is…
Various applications of quantum algebraic techniques in nuclear structure physics and in molecular physics are briefly reviewed and a recent application of these techniques to the structure of atomic clusters is discussed in more detail.
This monograph provides a largely self--contained and broadly accessible exposition of two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime: a fundamental analysis of the cosmological evolution according…
In this essay I begin to lay out a conceptual scheme for: (i) analysing dualities as cases of theoretical equivalence; (ii) assessing when cases of theoretical equivalence are also cases of physical equivalence. The scheme is applied to…
We prove a triangulation theorem for semi-algebraic sets over a p-adically closed field, quite similar to its real counterpart. We derive from it several applications like the existence of flexible retractions and splitting for…
Emergent gravity views spacetime as an entity emergent from a more complete theory of interacting fundamental constituents valid at much finer resolution or higher energies, usually assumed to be above the Planck energy. In this view…
The description of almost periodic or quasiperiodic structures has a long tradition in mathematical physics, in particular since the discovery of quasicrystals in the early 80's. Frequently, the modelling of such structures leads to…
Real algebraic geometry is the study of semi-algebraic sets, subsets of $\R^k$ defined by Boolean combinations of polynomial equalities and inequalities. The focus of this thesis is to study quantitative results in real algebraic geometry,…
We provide a quiver setting for quasi-Hopf algebras, generalizing the Hopf quiver theory. As applications we obtain some general structure theorems, in particular the quasi-Hopf analogue of the Cartier theorem and the Cartier-Gabriel…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…