Some comments about a static-localized solution for the massive Thirring model

We derive the stability equation for a static-localized solution of the two-dimensional massive Thirring model. The corresponding eigenvalue spectrum is determined and compared with the eigenvalue spectrum of the stability equation for the soliton solution of the sine-Gordon theory.Facultad de Ciencias Exacta

Some comments about a static-localized solution for the massive Thirring model

We derive the stability equation for a static-localized solution of the two-dimensional massive Thirring model. The corresponding eigenvalue spectrum is determined and compared with the eigenvalue spectrum of the stability equation for the soliton solution of the sine-Gordon theory.Facultad de Ciencias Exacta

The low energy limit of the non-commutative Wess-Zumino model

The non-commutative Wess-Zumino model is used as a prototype for studying the low energy behaviour of a renormalizable non-commutative field theory. We start by deriving the potential mediating the fermion-fermion and boson-boson interactions in the non-relativistic regime. The quantum counterparts of these potentials are afflicted by irdering ambiguities but we show that there exists an ordering prescription which makes them hermitean. For space/space noncommutativity it turns out that Majorana fermions may be pictured as rods oriented perpendicularly to the direction of motion showing a lack of localituy, while bosons remain insensitive to the effects of noncommutativity. For time/space noncommutativity bosopns and fermions can be regarded as rods oriented along the direction of motion. For both cases of noncommutativity the scattering state described scattered waves, with at least one wave having negative time delay signalizing the underlying nonlocality. The superfield formulation of the model is used to compute the corresponding effective action in the one- and two-loop approximations. In the case of time/space noncommutativity, unitarity is violated in the relativistic regime. However, this does not preclude the existence of the unitary low energy limit.Comment: 14 pages, 2 figures, minor correction

Self-dual fields and causality

Causality aspects of two-dimensional self-dual fields are considered. We prove that there is no causal propagation for dimensionless self-dual fields whose Lagrangian does not contain dimensional parameters. It is shown that causal self-dual bosons are possible in the chiral Schwinger model which contains a dimensional charge

Self-dual fields and causality

Causality aspects of two-dimensional self-dual fields are considered. We prove that there is no causal propagation for dimensionless self-dual fields whose Lagrangian does not contain dimensional parameters. It is shown that causal self-dual bosons are possible in the chiral Schwinger model which contains a dimensional charge

Chiral bosonization

We show that the Dirac-bracket quantization of a single self-dual field leads naturally to the bosonization formulas. We find a numerical parameter describing the soliton charge and unveiling hidden soliton sectors

Chiral bosonization

We show that the Dirac-bracket quantization of a single self-dual field leads naturally to the bosonization formulas. We find a numerical parameter describing the soliton charge and unveiling hidden soliton sectors

Spontaneous symmetry breaking in noncommutative field theories

The spontaneous symmetry breaking of rotational O(N) symmetry in noncommutative field theory is investigated in a 2+1 dimensional model of scalar fields coupled through a combination of quartic and sextuple self-interactions. There are five possible orderings of the fields in the sextuple interaction and two for the quartic interaction. At one loop, we prove that for some choices of these orderings there is the absence of IR-UV mixing and the appearance of massless excitations. A supersymmetric extension of the model is also studied. Supersymmetry puts additional constraints on the couplings but for any given N there is a Moyal ordering of the superfields for which the requirement for the existence of Goldstone bosons is satisfied. For some ordering and when N→∞ we find evidence that the model is renormalizable to all orders in perturbation theory. We also consider a generic chiral model in 3+1 dimensions whose superpotential is invariant under local gauge transformations. We find that for any value of N there is no one loop correction to the pion mass and that, at two loops, there are no pion mass corrections for slowly varying superfields so that the Goldstone theorem holds true. We also find a new purely noncommutative coupling which gives contributions starting at order N — 2 loops

The low energy limit of the non-commutative Wess-Zumino model

The non-commutative Wess-Zumino model is used as a prototype for studying the low energy behavior of a renormalizable non-commutative field theory. We start by deriving the potentials mediating the fermion-fermion and boson-boson interactions in the non-relativistic regime. The quantum counterparts of these potentials are afflicted by ordering ambiguities but we show that there exists an ordering prescription which makes them hermitean. For space/space noncommutativity it turns out that Majorana fermions may be pictured as rods oriented perpendicularly to the direction of motion showing a lack of locality, while bosons remain insensitive to the efects of the non commutativity. For time/space noncommutativity bosons and fermions can be regarded as rods oriented along the direction of motion. For both cases of noncommutativity the scattering state describes scattered waves, with at least one wave having negative time delay signalizing the underlying nonlocality. The super field formulation of the model is used to compute the corresponding effective action in the one- and two-loop approximations. In the case of time/space noncommutativity, unitarity is violated in the relativistic regime. However, this does not preclude the existence of a unitary low energy limit

Spontaneous symmetry breaking in noncommutative field theories

The spontaneous symmetry breaking of rotational O(N) symmetry in noncommutative field theory is investigated in a 2+1 dimensional model of scalar fields coupled through a combination of quartic and sextuple self-interactions. There are five possible orderings of the fields in the sextuple interaction and two for the quartic interaction. At one loop, we prove that for some choices of these orderings there is the absence of IR-UV mixing and the appearance of massless excitations. A supersymmetric extension of the model is also studied. Supersymmetry puts additional constraints on the couplings but for any given N there is a Moyal ordering of the superfields for which the requirement for the existence of Goldstone bosons is satisfied. For some ordering and when N→∞ we find evidence that the model is renormalizable to all orders in perturbation theory. We also consider a generic chiral model in 3+1 dimensions whose superpotential is invariant under local gauge transformations. We find that for any value of N there is no one loop correction to the pion mass and that, at two loops, there are no pion mass corrections for slowly varying superfields so that the Goldstone theorem holds true. We also find a new purely noncommutative coupling which gives contributions starting at order N — 2 loops