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Application of the standard canonical quantization rules of quantum field theory to macroscopic electromagnetism has encountered obstacles due to material dispersion and absorption. This has led to a phenomenological approach to macroscopic…

We present an approach to the canonical quantization of systems with equations of motion that are historically called non-Lagrangian equations. Our viewpoint of this problem is the following: despite the fact that a set of differential…

After the separation of the center-of-mass motion, a new privileged class of canonical Darboux bases is proposed for the non-relativistic N-body problem by exploiting a geometrical and group theoretical approach to the definition of {\it…

Previous analyses on the gauge invariance of the action for a generally covariant system are generalized. It is shown that if the action principle is properly improved, there is as much gauge freedom at the endpoints for an arbitrary gauge…

Building on the results of previous work, we demonstrate how matter fields are incorporated into the general linear frame approach to general relativity. When considering the Maxwell one-form field, we find that the system that leads…

We address the Hamiltonian formulation of classical gauge field theories while putting forward results some of which are not entirely new, though they do not appear to be well known. We refer in particular to the fact that neither the…

In classical mechanics, we can describe the dynamics of a given system using either the Lagrangian formalism or the Hamiltonian formalism, the choice of either one being determined by whether one wants to deal with a second degree…

Emergent modified gravity has shown that the canonical formulation of general relativity gives rise to a larger class of covariant modifications than action-based approaches, so far in symmetry-reduced models. This outcome is made possible…

The Lagrangians and Hamiltonians of classical field theory require to comprise gauge fields in order to be form-invariant under local gauge transformations. These gauge fields have turned out to correctly describe pertaining elementary…

An important representation of the general-type fundamental solutions of the canonical systems corresponding to matrix string equations is established using linear similarity of a certain class of Volterra operators to the squared…

We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the…

Variational principles for field theories where variations of fields are restricted along a parametrization are considered. In particular, gauge-natural parametrized variational problems are defined as those in which both the Lagrangian and…

We show that the material dependencies of macroscopically quantized fields in linear media are not consistent with the classical electromagnetic boundary conditions. We then phenomenologically construct macroscopic quantized fields that…

We reexamine the model of relativistic particle with higher-derivative term linear on the first extrinsic curvature (rigidity). The passage from classical to quantum theory requires a number of rather unexpected steps which we report here.…

We consider the problem of constrained motion along a conic path under a given external potential function. The model is described as a second-class system capturing the behavior of a certain class of specific quantum field theories. By…

The basic features of the complex canonical formulation of general relativity and the recent developments in the quantum gravity program based on it are reviewed. The exposition is intended to be complementary to the review articles…

Beginning with the work of Dirac and Arnowitt, Deser, Misner in the late fifties and early sixties, and then after subsequent development by Kucha\v r, the canonical dynamical structure of general relativity has often been viewed as that of…

We study canonical transformations of general relativity (GR) to provide a novel matter coupling to gravity. Although the transformed theory is equivalent to GR in vacuum, the equivalence no longer holds if a matter field minimally couples…

The problem of time in canonical quantum gravity is related to the fact that the canonical description is based on the prior choice of a spacelike foliation, hence making a reference to a spacetime metric. However, the metric is expected to…

I study the canonical formulation and quantization of some simple parametrized systems, including the non-relativistic parametrized particle and the relativistic parametrized particle. Using Dirac's formalism I construct for each case the…