Related papers: A unifying perspective on linear continuum equatio…
An implicit solution to the vanishing of the so-called Universal Field Equation, or Bordered Hessian, which dates at least as far back as 1935 \cite{chaundy} is revived, and derived from a much later form of the solution. A linear ansatz…
(3+1) (continuous time) Regge calculus is reduced to Hamiltonian form. The constraints are classified, classical and quantum consequences are discussed. As basic variables connection matrices and antisymmetric area tensors are used…
We survey a variety of cosmological problems where the issue of generality has arisen. This is aimed at providing a wider context for many claims and deductions made when philosophers of science choose cosmological problems for…
Quantum cosmology offers a unique stage to address questions of time related to its underlying (and perhaps truly quantum dynamical) meaning as well as its origin. Some of these issues can be analyzed with a general scheme of quantum…
An approximate relativistic two-component Hamiltonian for use in molecular electronic structure calculations is derived in the form of a sum of fixed atom-centered kinetic and spin-orbit operators added to the non-relativistic Hamiltonian.…
We present a systematic derivation of the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) momentum composition law, dispersion relation, and momentum transformation laws, at…
We relate the convergence of time-changed processes driven by fractional equations to the convergence of corresponding Dirichlet forms. The fractional equations we dealt with are obtained by considering a general fractional operator in…
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of…
Parametrized field theories, which are generally covariant versions of ordinary field theories, are studied from the point of view of the covariant phase space: the space of solutions of the field equations equipped with a canonical…
In this work, we present a consistent Hamiltonian analysis of cosmological perturbations for generalized non-canonical scalar fields. In order to do so, we introduce a new phase-space variable that is uniquely defined for different…
We show that a compact representation of a semisimple Lie group has an orthogonal decomposition into finite length representations. This generalises and simplifies a number of more special spectral theorems in the literature. We apply it to…
This paper presents a unifying theory of Linear second order systems that allows time-varying and time invariant systems to be treated in the same way for the first time. In the process, a transformation is given that diagonalizes an…
We introduce new times in the monodromy preserving equations. While the usual times related to the moduli of complex structures of Riemann curves such as coordinates of marked points, we consider the moduli of generalized complex structures…
The general uncertainty principle applied to gravity can be implemented as a set of modified Poisson brackets in the canonical formalism. As such, the theory is not canonical and the resulting equations of motion do not lead to a covariant…
Newtonian cosmological perturbation equations valid to full nonlinear order are well known in the literature. Assuming the absence of the transverse-tracefree part of the metric, we present the general relativistic counterpart valid to full…
We investigate quantum correlations in time in different approaches. We assume that temporal correlations should be treated in an even-handed manner with spatial correlations. We compare the pseudo-density matrix formalism with several…
This thesis proposes a combinatorial generalization of a nilpotent operator on a vector space. The resulting object is highly natural, with basic connections to a variety of fields in pure mathematics, engineering, and the sciences. For the…
We review an attempt to set a suitable foundational principle for consistent quantization of gravity based on the canonical formulation. It requires extending the spacetime description of the relativistic postulates to also encompass an…
We explore the mathematical consequences of the assumption of a discrete space-time. The fundamental laws of physics have to be translated into the language of discrete mathematics. We find integral transformations that leave the lattice of…
In this paper, we develop a new integral representation for the solution of the time harmonic Maxwell equations in media with piecewise constant dielectric permittivity and magnetic permeability in R^3. This representation leads to a…