Related papers: Equivalence between Schwinger and Dirac schemes of…
In this article we present a detailed description of an electron in a uniform magnetic field evolving under the Schr\"odinger equation using ladder operators. Based on this analysis, we describe the same physical system using the Dirac…
The Dirac equation, usually obtained by `quantizing' a classical stochastic model is here obtained directly within classical statistical mechanics. The special underlying space-time geometry of the random walk replaces the missing analytic…
For a recently proposed alternative to the traditional axion model, we study its long distance behavior, in particular the confinement versus screening issue, and show that a compactified version of this theory can be further mapped into…
So far, it is not well known how to deal with dissipative systems. There are many paths of investigation in the literature and none of them present a systematic and general procedure to tackle the problem. On the other hand, it is well…
In this work we apply Dirac's Constraint Analysis (DCA) to solve Superconducting Quantum Circuits (SQC). The Lagrangian of a SQC reveals the constraints, that are classified in a Hamiltonian framework, such that redundant variables can be…
The method of refined algebraic quantization of constrained systems which is based on modification of the inner product of the theory rather than on imposing constraints on the physical states is generalized to the case of constrained…
We present a pseudoclassical mechanics model which exhibits gauge symmetry and time-reparametrization invariance. As such, first- and second-class constraints restrict the phase space, and the Hamiltonian weakly vanishes. We show that the…
We study feedback control for discrete-time linear time-invariant systems in the presence of quantization both in the control action and in the measurement of the controlled variable. While in some application the quantization effects can…
The system of two-dimensional damped harmonic oscillator is revisited in the extended phase space. It is an old problem already addressed by many authors that we present here in some fresh points of view and carry on smoothly a whole…
There are several mathematical and physical reasons why Dirac's quantization must hold. How far one can go without it remains an open problem. The present work outlines a few steps in this direction.
The quantisation of gauge invariant systems usually proceeds through some gauge fixing procedure of one type or another. Typically for most cases, such gauge fixings are plagued by Gribov ambiguities, while it is only for an admissible…
A gauge invariant partition function is defined for gauge theories which leads to the standard quantization. It is shown that the descent equations and consequently the consistent anomalies and Schwinger terms can be extracted from this…
The generators of the Poincar\'{e} symmetry of scalar electrodynamics are quantized in the functional Schr\"{o}dinger representation. We show that the factor ordering which corresponds to (minimal) Dirac quantization preserves the…
A manifestly covariant treatment of the free quantum eletromagnetic field, in a linear covariant gauge, is implemented employing the Schwinger's Variational Principle and the B-field formalism. It is also discussed the abelian Proca's model…
In this work, we have extended the factorization method of scalar shape-invariant Schr\"o\-din\-ger Hamiltonians to a class of Dirac-like matrix Hamiltonians. The intertwining operators of the Schr\"odinger equations have been implemented…
Recently, it is shown that the extended phase space formulation of quantum mechanics is a suitable technique for studying the quantum dissipative systems. Here, as a further application of this formalism, we consider a dissipative system of…
A gauge independent method of obtaining the reduced space of constrained dynamical systems is discussed in a purely lagrangian formalism. Implications of gauge fixing are also considered.
Quantization of electromagnetic fields is investigated in the framework of stochastic variational method (SVM). Differently from the canonical quantization, this method does not require canonical form and quantization can be performed…
In this paper, we explain the reasons behind constraint interaction, which is the phenomenon that the results of testing equality constraints may depend heavily on the scaling method used. We find that the scaling methods interfere with the…
Some basic ideas of the Refined Algebraic Quantization scheme are outlined at an intuitive level, using a class of simple models with a single wave equation as quantum constraint. In addition, hints are given how the scheme is applied to…