Related papers: Particle on a torus knot: Symplectic analysis
We present the Dirac Hamiltonian formalism for a pair of $1$-form fields with a topological-like potential coupled to first-order gravity in three-dimensional spacetime. By considering the complete phase space, we derive the full structure…
It is well known that both the symplectic structure and the Poisson brackets of classical field theory can be constructed directly from the Lagrangian in a covariant way, without passing through the non-covariant canonical Hamiltonian…
The gauge fixed polygon model of 2+1 gravity with zero cosmological constant and arbitrary number of spinless point particles is reconstructed from the first order formalism of the theory in terms of the triad and the spin connection. The…
Classical knot theory deals with {\em diagrams} and {\em invariants}. By means of horizontal {\em trisecants}, we construct a new theory of classical braids with invariants valued in {\em pictures}. These pictures are closely related to…
We present a classical and quantum analysis of a particle confined in a three-dimensional paraboloidal cavity formed by two confocal paraboloids. Classically, the system is integrable and presents three independent constants of motion,…
Lie-Poisson electrodynamics describes the semi-classical limit of non-commutative $U(1)$ gauge theory, characterized by Lie-algebra-type non-commutativity. We focus on the mechanics of a charged point-like particle moving in a given gauge…
We examine the model of Two-Dimensional Quadratic Gravity as a consequence of symmetry breaking within the framework of background field (BF) theory. This theory is essentially an extension of BF theory, introducing an additional polynomial…
We discuss a general prototypical constrained Hamiltonian system with a broad application in quantum field theory and similar contexts where dynamics is defined through a functional action obeying a stationarity principle. The prototypical…
We develop a Thermodynamic Formalism for bounded continuous potentials defined on the sequence space $X\equiv E^{\mathbb{N}}$, where $E$ is a general Borel standard space. In particular, we introduce meaningful concepts of entropy and…
We consider several aspects of `confining strings', recently proposed to describe the confining phase of gauge field theories. We perform the exact duality transformation that leads to the confining string action and show that it reduces to…
A dynamical non-Abelian 2-form gauge theory (with B \wedge F term) is endowed with the "scalar" and "vector" gauge symmetry transformations. In our present endeavor, we exploit the latter gauge symmetry transformations and perform the…
We study the problem of test-particle motion in the Nonsymmetric Gravitational Theory (NGT) assuming the four-velocity of the particle is parallel-transported along the trajectory. The predicted motion is studied on a static, spherically…
As a preparation for its quantization in the loop formalism, the 2-dimensional gravitation model of Jackiw and Teitelboim is analysed in the classical canonical formalism. The dynamics is of pure constraints as it is well-known. A partial…
3D Loop Quantum Gravity with a vanishing cosmological constant can be related to the quantization of the $\textrm{SU}(2)$ BF theory discretized on a lattice. At the classical level, this discrete model characterizes discrete flat geometries…
Point particle may interact to traceless symmetric tensors of arbitrary rank. Free gauge theories of traceless symmetric tensors are constructed, that provides a possibility for a new type of interactions, when particles exchange by those…
Some recently proposed definitions of Jackiw-Teitelboim gravity and supergravities in terms of combinations of minimal string models are explored, with a focus on physics beyond the perturbative expansion in spacetime topology. While this…
We propose a modification of the Faddeev-Popov procedure to construct a path integral representation for the transition amplitude and the partition function for gauge theories whose orbit space has a non-Euclidean geometry. Our approach is…
Constrained symplectic quantization is a functional formulation of quantum field theory in which quantum fluctuations are sampled through a deterministic Hamiltonian flow in an auxiliary intrinsic time $\tau$. In this paper we extend the…
The aim of the present article is to describe the symmetry structure of a general gauge (singular) theory, and, in particular, to relate the structure of gauge transformations with the constraint structure of a theory in the Hamiltonian…
This paper brings a methodological character where we present a comprehensive formalism for constructing conserved quantities in the Teleparallel Equivalent of General Relativity (TEGR) and Symmetric Teleparallel Equivalent of General…