Multiflavor soldering

In two dimensions the simple addition of two chiral bosons of opposite chiralities does not lead to a full massless scalar field. Similarly, in three dimensions the addition of two Maxwell-Chern-Simons fields of opposite helicities +/- 1 will not produce a parity invariant Maxwell-Proca theory. An interference term between the opposite chiralities (helicities) states is required in order to obtain the expected result. The so-called soldering procedure provides the missing interference Lagrangian in both 2D and 3D cases. In two dimensions such interference term allows to fuse two chiral fermionic determinants into, a non-chiral one. In a recent work we have generalized this procedure by allowing the appearance of an extra parameter which takes two possible values and leads to two different soldered Lagrangians. Here we apply this generalized soldering in a bosonic theory which has appeared in a partial bosonization of the 3D gauged Thirring model with N flavors. The multiplicity of flavors allow new types of solderings and help us to understand the connection between different perturbative approaches to bosonization in 3D. In particular, we obtain an interference term which takes us from a multiflavor Niaxwell-Chern-Simons theory to a pair of self-dual and anti-self-dual theories when we combine together both fermionic determinants of +1/2 and -1/2 helicity fermions. An important role is played by a set of pure non-interacting Chern-Simons fields which amount to a normalization factor in the fermionic determinants and act like spectators in the original theory but play an active role in the soldering procedure. Our results suggest that the generalized soldering could be used to provide dual theories in both 2D and 3D cases. (c) 2007 Elsevier B.V. All rights reserved.

Relativistic effects of mixed vector-scalar-pseudoscalar potentials for fermions in 1+1 dimensions

The problem of fermions in the presence of a pseudoscalar plus a mixing of vector and scalar potentials which have equal or opposite signs is investigated. We explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. The cases of mixed vector and scalar Poschl-Teller-like and pseudoscalar kink-like potentials, already analyzed in previous works, are obtained as particular cases.

A fermion in a scalar inversely linear potential

The problem of a fermion subject to a a scalar inversely linear potential in a two-dimensional world is mapped into a Sturm-Liouville problem for nonzero eigenenergies. This mapping gives rise to an effective Kratzer potential and exact bounded solutions are found in closed form. The normalizable zero-eigenmode solution is also found. A few unusual results are revealed.

Klein-Gordon particles in mixed vector-scalar inversely linear potentials

The problem of a spinless particle subject to a general mixing of vector and scalar inversely linear potentials in a two-dimensional world is analyzed. Exact bounded solutions are found in closed form by imposing boundary conditions on the eigenfunctions which ensure that the effective Hamiltonian is Hermitian for all the points of the space. The nonrelativistic limit of our results adds a new support to the conclusion that even-parity solutions to the nonrelativistic one-dimensional hydrogen atom do not exist. (c) 2005 Elsevier B.V. All rights reserved.

Confinement of spin-0 and spin-1/2 particles in a mixed vector-scalar coupling with unequal shapes for the potentials

The Klein - Gordon and the Dirac equations with vector and scalar potentials are investigated under a more general condition, V-v = V-s + constant. These isospectral problems are solved in the case of squared trigonometric potential functions and bound states for either particles or antiparticles are found. The eigenvalues and eigenfunctions are discussed in some detail. It is revealed that a spin-0 particle is better localized than a spin-1/2 particle when they have the same mass and are subjected to the same potentials.

Confinement of fermions by mixed vector-scalar linear potentials in two-dimensional space-time

The problem of confinement of fermions in 1 + 1 dimensions is approached with a linear potential in the Dirac equation by considering a mixing of Lorentz vector and scalar couplings. Analytical bound-states solutions are obtained when the scalar coupling is of sufficient intensity compared to the vector coupling. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Exact closed-form solutions of the Dirac equation with a scalar exponential potential

The problem of a fermion subject to a general scalar potential in a two-dimensional world for nonzero eigenenergies is mapped into a Sturm-Liouville problem for the upper component of the Dirac spinor. In the specific circumstance of an exponential potential, we have an effective Morse potential which reveals itself as an essentially relativistic problem. Exact bound solutions are found in closed form for this problem. The behaviour of the upper and lower components of the Dirac spinor is discussed in detail, particularly the existence of zero modes. (c) 2005 Elsevier B.v. All rights reserved.