Related papers: Power law duality in classical and quantum mechani…
Recently we have obtained a non-perturbative but convergent series expression of the one loop effective action of QED, and discussed the renormalization of the effective action. In this paper we establish the electric-magnetic duality in…
This paper investigates the classical and quantum elementary systems with Newton-Hoooke symmetry. A complete classification is given by explicit computation. In addition, we present an application example of quantization using the Moyal…
The classical equations of motion of Maxwell and Born-Infeld theories are known to be invariant under a duality symmetry acting on the field strengths. We implement the SL(2,Z) duality in these theories as linear but non-local…
In this paper a new look on the electro-magnetic duality is presented and appropriately exploited. The duality analysis in the nonrelativistic and relativistic formulations is shown to lead to the idea the mathematical model field to be a…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases…
We establish a duality between the free massless relativistic particle in d dimensions, the non-relativistic hydrogen atom (1/r potential) in (d-1) space dimensions, and the harmonic oscillator in (d-2) space dimensions with its mass given…
We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original…
The classical mechanics of a finite number of degrees of freedom requires a symplectic structure on phase space C, but it is independent of any complex structure. On the contrary, the quantum theory is intimately linked with the choice of a…
We consider a nonstandard $D=2+1$ gravity described by a translational Chern--Simons action, and couple it to the nonrelativistic point particles. We fix the asymptotic coordinate transformations in such a way that the space part of the…
We extend the work of Mello et al. based in Cabbibo and Ferrari concerning the description of electromagnetism with two gauge fields from a variational principle, i.e. an action. We provide a systematic independent derivation of the allowed…
We consider Hamiltonian systems which can be described both classically and quantum mechanically. Trace formulas establish links between the energy spectra of the quantum description and the spectrum of actions of periodic orbits in the…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
This thesis is divided in two parts. The first part contains the study of some properties of the electromagnetic duality in 4 dimensions. An extended double potential formalism for linearized gravity is introduced which allows to write an…
We describe a systematic way of the generalization, to models with non-linear duality, of the space-time covariant and duality-invariant formulation of duality-symmetric theories in which the covariance of the action is ensured by the…
We develop a systematic method of obtaining duality symmetric actions in different dimensions. This technique is applied for the quantum mechanical harmonic oscillator, the scalar field theory in two dimensions and the Maxwell theory in…
It is known that an electric-magnetic duality transformation is a symmetry of the classical source-free Maxwell theory in generic spacetimes. This provides a conserved Noether charge, physically related to the polarization state of the…
It is well known that the source-free Maxwell equations are invariant under electric-magnetic duality rotations, F --> F cos {\theta} + *F sin {\theta}. These transformations are indeed a symmetry of the theory in Noether sense. The…
Duality symmetries of supergravity theories are powerful tools to restrict the number of possible actions, to link different dimensions and number of supersymmetries and might help to control quantisation. (Hodge-Dirac-)Dualisation of gauge…
Duality is an indispensable tool for describing the strong-coupling dynamics of gauge theories. However, its actual realization is often quite subtle: quantities such as the partition function can transform covariantly, with degrees of…