Ladder operators for subtle hidden shape-invariant potentials

Ladder operators can be constructed for all potentials that present the integrability condition known as shape invariance, satisfied by most of the exactly solvable potentials. Using the superalgebra of supersymmetric quantum mechanics, we construct the ladder operators for two exactly solvable potentials that present a subtle hidden shape invariance.

Comments on spin operators and spin-polarization states of 2+1 fermions

In this brief article we discuss spin-polarization operators and spin-polarization states of 2 + 1 massive Dirac fermions and find a convenient representation by the help of 4-spinors for their description. We stress that in particular the use of such a representation allows us to introduce the conserved covariant spin operator in the 2 + 1 field theory. Another advantage of this representation is related to the pseudoclassical limit of the theory. Indeed, quantization of the pseudoclassical model of a spinning particle in 2 + 1 dimensions leads to the 4-spinor representation as the adequate realization of the operator algebra, where the corresponding operator of a first-class constraint, which cannot be gauged out by imposing the gauge condition, is just the covariant operator previously introduced in the quantum theory.

Dynamics in discrete phase spaces and time interval operators

The von Neumann-Liouville time evolution equation is represented in a discrete quantum phase space. The mapped Liouville operator and the corresponding Wigner function are explicitly written for the problem of a magnetic moment interacting with a magnetic field and the precessing solution is found. The propagator is also discussed and a time interval operator, associated to a unitary operator which shifts the energy levels in the Zeeman spectrum, is introduced. This operator is associated to the particular dynamical process and is not the continuous parameter describing the time evolution. The pair of unitary operators which shifts the time and energy is shown to obey the Weyl-Schwinger algebra. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Vertex operators and Jordan fields

The construction of Lie algebras in terms of Jordan algebra generators is discussed. The key to the construction is the triality relation already incorporated into matrix products. A generalisation to Kac-Moody algebras in terms of vertex operators is proposed and may provide a clue for the construction of new representations of Kac-Moody algebras in terms of Jordan fields. © 1988.

On discrete symmetries of the multi-boson KP hierarchies

We show that the multi-boson KP hierarchies possess a class of discrete symmetries linking them to discrete Toda systems. These discrete symmetries are generated by the similarity transformation of the corresponding Lax operator. This establishes a canonical nature of the discrete transformations. The spectral equation, which defines both the lattice system and the corresponding Lax operator, plays a key role in determining pertinent symmetry structure. We also introduce the concept of the square root lattice leading to a family of new pseudo-differential operators with covariance under additional Bäcklund transformations.

Second quantization approach to composite hadron interactions in quark models

Starting from the Fock space representation of hadron bound states in a quark model, a change of representation is implemented by a unitary transformation such that the composite hadrons are redescribed by elementary-particle field operators. Application of the unitary transformation to the microscopic quark Hamiltonian gives rise to effective hadron-hadron, hadron-quark, and quark-quark Hamiltonians. An effective baryon Hamiltonian is derived using a simple quark model. The baryon Hamiltonian is free of the post-prior discrepancy which usually plagues composite-particle effective interactions.

Field-theoretic approach for systems of composite hadrons

Systems containing simultaneously hadrons and their constituents are most easily described by treating composite hadron field operators on the same kinematical footing as the constituent ones. Introduction of a unitary transformation allows redescription of hadrons by elementary-particle field operators. Transformation of the microscopic Hamiltonian leads to effective Hamiltonians describing all possible processes involving hadrons and their constituents.

Infrared finite solutions for the gluon propagator and the QCD vacuum energy

Nonperturbative infrared finite solutions for the gluon polarization tensor have been found, and the possibility that gluons may have a dynamically generated mass is supported by recent Monte Carlo simulation on the lattice. These solutions differ among themselves, due to different approximations performed when solving the Schwinger-Dyson equations for the gluon polarization tensor. Only approximations that minimize energy are meaningful, and, according to this, we compute an effective potential for composite operators as a function of these solutions in order to distinguish which one is selected by the vacuum. © 1997 Elsevier Science B.V.

Limits on anomalous top couplings from Z pole physics

We obtain constraints on possible anomalous interactions of the top quark with the electroweak vector bosons arising from the precision measurements at the Z pole. In the framework of SU(2)L ⊕ U(1)Y chiral Lagrangians, we examine all effective CP-conserving operators of dimension five which induce fermionic currents involving the top quark. We constrain the magnitudes of these anomalous interactions by evaluating their one-loop contributions to the Z pole physics. Our analysis shows that the operators that contribute to the LEP observables get bounds close to the theoretical expectation for their anomalous couplings. We also show that those which break the SU(2)C custodial symmetry are more strongly bounded. © 1997 Elsevier Science B.V.

Bounds on Higgs and gauge-boson interactions from LEP2 data

We derive bounds on Higgs and gauge-boson anomalous interactions using the LEP2 data on the production of three photons and photon pairs in association with hadrons. In the framework of SU(2)L ⊗ U(1)Y effective Lagrangians, we examine all dimension-six operators that lead to anomalous Higgs interactions involving γ and Z. The search for Higgs boson decaying to γγ pairs allow us to obtain constrains on these anomalous couplings that are comparable with the ones originating from the analysis of pp̄ collisions at the Tevatron. Our results also show that if the coefficients of all blind operators are assumed to have the same magnitude, the indirect constraints on the anomalous couplings obtained from this analysis, for Higgs masses MH ≲ 140 GeV, are more restrictive than the ones coming from the W+W- production. © 1998 Elsevier Science B.V. All rights reserved.

Testing anomalous Higgs couplings in triple photon production at the Tevatron collider

We derive bounds on Higgs and gauge-boson anomalous interactions using the CDF data for the process pp̄ → γγγ + X. We use a linearly realized SU L(2) X U Y(1) invariant effective Lagrangian to describe the bosonic sector of the Standard Model, keeping the fermionic couplings unchanged. All dimension-six operators that lead to anomalous Higgs interactions involving γ and Z are considered. We also show the sensitivity that can be achieved for these couplings at Fermilab Tevatron upgrades. © 1998 Published by Elsevier Science B.V. All rights reserved.

Three jet events and new strong couplings at LEP and NLC

We study the effects of new dimension-6 operators, resulting from a general SU(3)C ⊗ SU(2)L ⊗ U(1)Y invariant effective Lagrangian, on three jet production at LEP and at the Next Linear Collider. Contributions to the total event rate and to some event shape variables are analysed in order to establish bounds on these operators. © 1999 Elsevier Science B.V. All rights reserved.

Conservation laws for non-potential operators

A study was developed in order to build a function M invariant in time, by means of Hamiltonian's formulation, taking into account the equation associated to the problem, showing that starting from this function the equation of motion of the system with the contour conditions for non-conservative considered problems can be obtained. The Hamiltonian method is extended for these kind of systems in order to validate for non-potential operators through variational approach.