Related papers: Loop Amplitudes in Supergravity by Canonical Quant…
In this work we exploit Dirac's Constraint Analysis (DCA) in Hamiltonian formalism to study different types of Superconducting Quantum Circuits (SQC) in a {\it{unified}} way. The Lagrangian of a SQC reveals the constraints, that are…
In generic curved spacetimes, the unavailability of a natural choice of vacuum state introduces a serious ambiguity in the Fock quantization of fields. In this review, we study the case of fermions described by a Dirac field in several…
In this article the methods of canonical analysis and quantization that were reviewed in the first part of the series are applied to the case of the Dirac field in the presence of electromagnetic interaction. It is shown that the…
We present the complete set of Feynman rules producing the rational terms of kind R_2 needed to perform any 1-loop calculation in the Electroweak Standard Model. Our formulae are given both in the R_xi gauge and in the Unitary gauge,…
The quantization rules recently proposed by M. Navarro (and independently I.V. Kanatchikov) for a finite-dimensional formulation of quantum field theory are applied to the Klein-Gordon and the Dirac fields to obtain the quantum equations of…
The existing approaches to quantization of gravity aim at giving quantum description of 3-geometry following to the ideas of the Wheeler -- DeWitt geometrodynamics. In this description the role of gauge gravitational degrees of freedom is…
The $n$-point amplitudes of gauge and gravity theory are given as a series in the coupling. The recursive derivative expansion is used to find all of the coupling coefficients. Initial conditions to any bare Lagrangian, or of an improved…
In this work, our aim is to obtain a Hamiltonian formulation suitable for canonical quantization. Moreover, we assume that the early Universe can be described with fewer initial symmetries, thus we abandon the isotropy assumption and…
Loop quantum cosmology is a symmetry reduced quantization of cosmological spacetimes based on loop quantum gravity. While it has been successful in resolution of various cosmological singularities and connecting Planck scale physics to…
A covariant Hamiltonian description was introduced in the dynamics of charges and electromagnetic interaction. By a canonical transformation this Hamiltonian formalism was transformed to obtain the Dirac generators for any form of…
Connes' formula defines a distance in loop quantum gravity, via the spinfoam Dirac operator. A simple notion of spectral distance on a graph can be extended do the discrete Lorentzian context, providing a physically natural example of…
We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three dimensional (Riemannian) gravity with positive cosmological constant (Lambda>0). We show that the usual regularization techniques (successful…
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear…
We elaborate on the proposed general boundary formulation as an extension of standard quantum mechanics to arbitrary (or no) backgrounds. Temporal transition amplitudes are generalized to amplitudes for arbitrary spacetime regions. State…
Within a first-order framework, we comprehensively examine the role played by boundary conditions in the canonical formulation of a completely general two-dimensional gravity model. Our analysis particularly elucidates the perennial themes…
We investigate the semiclassical dynamics of massless Dirac fermions in 2+1 dimensions in the presence of external electromagnetic fields. By generalizing the $\alpha$ matrices to the spin-$S$ matrices and doing a certain scaling, we…
In a series of seminal papers, Laddha and Varadarajan have developed in depth the quantisation of Parametrised Field Theory (PFT) in the kind of discontinuous representations that are employed in Loop Quantum Gravity (LQG). In one spatial…
Exploiting singularities in Feynman integrals to get information about scattering amplitudes has been particularly useful at one-loop in theories where no triangles or bubbles appear. At higher loops the integrals possess subtle…
We study the on-shell scattering amplitudes in quantum gravity for high-energy collisions in the eikonal approximation. We first evaluate the $n$-loop 2-particle scattering amplitude in the high energy and low momentum transfer limit. We do…
We apply the cannonical quantization procedure to the Dirac field inside a spherical boundary with rotating coordinates. The rotating quantum states with two kinds of boundary conditions, namely, spectral and MIT boundary conditions, are…