Jose Francisco Gomes - Academia.edu (original) (raw)
Papers by Jose Francisco Gomes
arXiv (Cornell University), Apr 4, 2023
The KdV hierarchy is a paradigmatic example of the rich mathematical structure underlying integra... more The KdV hierarchy is a paradigmatic example of the rich mathematical structure underlying integrable systems and has far-reaching connections in several areas of theoretical physics. While the positive part of the KdV hierarchy is well known, in this paper we consider an affine Lie algebraic construction for its negative part. We show that the original Miura transformation can be extended to a gauge transformation that implies several new types of relations among the negative flows of the KdV and mKdV hierarchies. Contrary to the positive flows, such a "gauge-Miura" correspondence becomes degenerate whereby more than one negative mKdV model is mapped into a single negative KdV model. For instance, the sine-Gordon and another negative mKdV flow are mapped into a single negative KdV flow which inherits solutions of both former models. The gauge-Miura correspondence implies a rich degeneracy regarding solutions of these hierarchies. We obtain similar results for the generalized KdV and mKdV hierachies constructed with the affine Lie algebra sℓ(r + 1). In this case the first negative mKdV flow corresponds to an affine Toda field theory and the gauge-Miura correspondence yields its KdV counterpart. In particular, we show explicitly a KdV analog of the Tzitzéica-Bullough-Dodd model. In short, we uncover a rich mathematical structure for the negative flows of integrable hierarchies obtaining novel relations and integrable systems.
Physics Letters B, 1994
The relation between the spin and the mass of an infinite number of particles in a q-deformed dua... more The relation between the spin and the mass of an infinite number of particles in a q-deformed dual string theory is studied. For the deformation parameter q a root of unity, in addition to the relation of such values of q with the rational conformal field theory, the Fock space of each oscillator mode in the Fubini-Veneziano operator formulation becomes truncated. Thus, based on general physical grounds, the resulting spin-(mass) 2 relation is expected to be below the usual linear trajectory. For such specific values of q, we find that the linear Regge trajectory turns into a square-root trajectory as the mass increases.
Journal of Physics A: Mathematical and General, 1998
In this paper we employ the construction of Dirac bracket for the remaining current of sl(2) q de... more In this paper we employ the construction of Dirac bracket for the remaining current of sl(2) q deformed Kac-Moody algebra when constraints similar to those connecting the sl(2)-WZW model and the Liouville theory are imposed and show that it satisfy the q-Virasoro algebra proposed by Frenkel and Reshetikhin. The crucial assumption considered in our calculation is the existence of a classical Poisson bracket algebra induced, in a consistent manner by the correspondence principle, mapping the quantum generators into commuting objects of classical nature preserving their algebra. 1 Supported by FAPESP 2 Work partially supported by CNPq 3 Supported by CNPq
Journal of Physics A: Mathematical and Theoretical, 2020
We extend Painlevé IV model by adding quadratic terms to its Hamiltonian obtaining two classes of... more We extend Painlevé IV model by adding quadratic terms to its Hamiltonian obtaining two classes of models (coalescence and deformation) that interpolate between Painlevé IV and II equations for special limits of the underlying parameters. We derive the underlying Bäcklund transformations, symmetry structure and requirements to satisfy Painlevé property.
Proceedings of 5th International School on Field Theory and Gravitation — PoS(ISFTG), 2009
Physics Letters B, 1992
As recently shown the conformal affinc Toda models can be obtained via hamiltonian reduction from... more As recently shown the conformal affinc Toda models can be obtained via hamiltonian reduction from a two-loop Kac-Moody algebra. In this paper we propose a systematic procedure to analyze the higher spin symmetries of the conformal affine Toda models. The method is based on an explicit construction of infinite towers of extended conformal symmetry generators. Two fundamental building blocks of this construction are special spin-one and-two primary fields characterizing the conformal structure of these models. The connection to the algebra of area preserving diffeomorphisms on a two-manifold (woo algebra) is established.
We propose a systematic treatment of symmetries of KP integrable systems, including constrained (... more We propose a systematic treatment of symmetries of KP integrable systems, including constrained (reduced) KP models slcKPR,M{\sl cKP}_{R,M}slcKPR,M, and their multi-component (matrix) generalizations. Any such integrable hierarchy is shown to possess an additional (hatU(1)oplushatSL(M))+oplus(hatSL(M+R))−({\hat U}(1)\oplus{\hat {SL}}(M))_{+} \oplus ({\hat {SL}}(M+R))_{-}(hatU(1)oplushatSL(M))+oplus(hatSL(M+R))− loop-algebra symmetry. Also we provide a systematic construction of the full algebra of Virasoro additional symmetries in the case of constrained KP models which requires a nontrivial modification of the known Orlov-Schulman construction for the general unconstrained KP hierarchy. Multi-component KP hierarchies are identified as ordinary (scalar) one-component KP hierarchies supplemented with the Cartan subalgebra of the additional symmetry algebra, which provides the basis of a new method for construction of soliton-like solutions. Davey-Stewartson and NNN-wave resonant systems arise as symmetry flows of ordinary slcKPR,M{\sl cKP}_{R,M}slcKPR,M hierarchies.
Physics Letters B, 1992
It is shown that the two-loop Kac-Moody algebra is equivalent to a two variable loop algebra and ... more It is shown that the two-loop Kac-Moody algebra is equivalent to a two variable loop algebra and a decoupled β-γ system. Similarly WZNW and CSW models having as algebraic structure the Kac-Moody algebra are equivalent to an infinity of versions of the corresponding ordinary models and decoupled abelian fields.
Physics Letters B, 1998
The classical and quantum algebras of a class of conformal NA-Toda models are studied.It is shown... more The classical and quantum algebras of a class of conformal NA-Toda models are studied.It is shown that the SL(2, R) q Poisson brackets algebra generated by certain chiral and antichiral charges of the nonlocal currents and the global U (1) charge appears as an algebra of the symmetries of these models.
Physics Letters B, 1992
We construct a centerless W-infinity type of algebra in terms of a generator of a centerless Vira... more We construct a centerless W-infinity type of algebra in terms of a generator of a centerless Virasoro algebra and an abelian spin-1 current. This algebra conventionally emerges in the study of pseudo-differential operators on a circle or alternatively within KP hierarchy with Watanabe's bracket. Construction used here is based on a special deformation of the algebra w ∞ of area preserving diffeomorphisms of a 2-manifold. We show that this deformation technique applies to the two-loop WZNW and conformal affine Toda models, establishing henceforth W ∞ invariance of these models.
Physics Letters B, 1991
Using the coadjoint orbit method we derive a geometric WZWN action based on the extended two-loop... more Using the coadjoint orbit method we derive a geometric WZWN action based on the extended two-loop Kac-Moody algebra. We show that under a hamiltonian reduction procedure, which respects conformal invariance, we obtain a hierarchy of Toda type field theories, which contain as submodels the Toda molecule and periodic Toda lattice theories. We also discuss the classical rmatrix and integrability properties.
Nuclear Physics B, 2009
A systematic construction for an action describing a class of supersymmetric integrable models as... more A systematic construction for an action describing a class of supersymmetric integrable models as well as for pure fermionic theories is discussed in terms of the gauged WZNW model associated to twisted affine Kac-Moody algebras. Explicit examples of the N = 1, 2 super sinh(sine)-Gordon models are discussed in detail. Pure fermionic theories arises for cosets sl(p, 1)/sl(p) ⊗ u(1) when a maximal kernel condition is fulfilled. The integrability condition for such models is discussed and it is shown that the simplest example when p = 2 leads to the constrained Bukhvostov-Lipatov, Thirring, scalar massive and pseudo-scalar massless Gross-Neveu models.
Journal of Physics A: Mathematical and Theoretical, 2011
A Kac-Moody algebra construction for the integrable hierarchy containing the Gardner equation is ... more A Kac-Moody algebra construction for the integrable hierarchy containing the Gardner equation is proposed. Solutions are systematically constructed employing the dressing method and deformed vertex operators which takes into account the nonvanishing boundary value problem for the mKdV hierarchy. Explicit examples are given and besides usual KdV like solitons, our solutions contemplate the large amplitude table-top solitons, kinks, dark solitons, breathers and wobbles.
Journal of Physics: Conference Series, 2012
We propose an approach to the nonvanishing boundary value problem for integrable hierarchies base... more We propose an approach to the nonvanishing boundary value problem for integrable hierarchies based on the dressing method. Then we apply the method to the AKNS hierarchy. The solutions are found by introducing appropriate vertex operators that takes into account the boundary conditions.
Annals of Physics, 1999
We investigate a class of conformal nonabelian-Toda models representing noncompact SL(2, R)/U(1) ... more We investigate a class of conformal nonabelian-Toda models representing noncompact SL(2, R)/U(1) parafermions (PF) interacting with specific abelian Toda theories and having a global U(1) symmetry. A systematic derivation of the conserved currents, their algebras, and the exact solution of these models are presented. An important property of this class of models is the affine SL(2, R)q algebra spanned by charges of
The gauge equivalence between basic KP hierarchies is discussed. The first two Hamiltonian struct... more The gauge equivalence between basic KP hierarchies is discussed. The first two Hamiltonian structures for KP hierarchies leading to the linear and non-linear W ∞ algebras are derived. The realization of the corresponding generators in terms of two boson currents is presented and it is shown to be related to many integrable models which are bi-Hamiltonian. We can also realize those generators by adding extra currents, coupled in a particular way, allowing for instance a description of multi-layered Benney equations or multi-component non-linear Schroedinger equation. In this case we can have a second Hamiltonian bracket structure which violates Jacobi identity. We consider the reduction to one-boson systems leading to KdV and mKdV hierarchies. A Miura transformation relating these two hierarchies is obtained by restricting gauge transformation between corresponding two-boson hierarchies. Connection to Drinfeld-Sokolov approach is also discussed in the SL(2, IR) gauge theory.
A class of non abelian affine Toda models is constructed in terms of the axial and vector gauged ... more A class of non abelian affine Toda models is constructed in terms of the axial and vector gauged WZW model. It is shown that the multivacua structure of the potential together with non abelian nature of the zero grade subalgebra allows soliton solutions with non trivial electric and topological charges. Their zero curvature representation and the classical r-matrix are also constructed in order to prove their classical integrability.
Journal of Mathematical Physics, 1995
Journal of Physics A: Mathematical and Theoretical, 2021
The construction of Miura and Bäcklund transformations for A n mKdV and KdV hierarchies are prese... more The construction of Miura and Bäcklund transformations for A n mKdV and KdV hierarchies are presented in terms of gauge transformations acting upon the zero curvature representation. As in the well known sl(2) case, we derive and relate the equations of motion for the two hierarchies. Moreover, the Miura-gauge transformation is not unique, instead, it is shown to be connected to a set of generators labeled by the exponents of A n The construction of generalized gauge-Bäcklund transformation for the A n-KdV hierarchy is obtained as a composition of Miura and Bäcklund-gauge transformations for A n-mKdV hierarchy. The zero curvature representation provide a framework which is universal within all flows and generate systematically Bäcklund transformations for the entirely hierarchy.
arXiv (Cornell University), Apr 4, 2023
The KdV hierarchy is a paradigmatic example of the rich mathematical structure underlying integra... more The KdV hierarchy is a paradigmatic example of the rich mathematical structure underlying integrable systems and has far-reaching connections in several areas of theoretical physics. While the positive part of the KdV hierarchy is well known, in this paper we consider an affine Lie algebraic construction for its negative part. We show that the original Miura transformation can be extended to a gauge transformation that implies several new types of relations among the negative flows of the KdV and mKdV hierarchies. Contrary to the positive flows, such a "gauge-Miura" correspondence becomes degenerate whereby more than one negative mKdV model is mapped into a single negative KdV model. For instance, the sine-Gordon and another negative mKdV flow are mapped into a single negative KdV flow which inherits solutions of both former models. The gauge-Miura correspondence implies a rich degeneracy regarding solutions of these hierarchies. We obtain similar results for the generalized KdV and mKdV hierachies constructed with the affine Lie algebra sℓ(r + 1). In this case the first negative mKdV flow corresponds to an affine Toda field theory and the gauge-Miura correspondence yields its KdV counterpart. In particular, we show explicitly a KdV analog of the Tzitzéica-Bullough-Dodd model. In short, we uncover a rich mathematical structure for the negative flows of integrable hierarchies obtaining novel relations and integrable systems.
Physics Letters B, 1994
The relation between the spin and the mass of an infinite number of particles in a q-deformed dua... more The relation between the spin and the mass of an infinite number of particles in a q-deformed dual string theory is studied. For the deformation parameter q a root of unity, in addition to the relation of such values of q with the rational conformal field theory, the Fock space of each oscillator mode in the Fubini-Veneziano operator formulation becomes truncated. Thus, based on general physical grounds, the resulting spin-(mass) 2 relation is expected to be below the usual linear trajectory. For such specific values of q, we find that the linear Regge trajectory turns into a square-root trajectory as the mass increases.
Journal of Physics A: Mathematical and General, 1998
In this paper we employ the construction of Dirac bracket for the remaining current of sl(2) q de... more In this paper we employ the construction of Dirac bracket for the remaining current of sl(2) q deformed Kac-Moody algebra when constraints similar to those connecting the sl(2)-WZW model and the Liouville theory are imposed and show that it satisfy the q-Virasoro algebra proposed by Frenkel and Reshetikhin. The crucial assumption considered in our calculation is the existence of a classical Poisson bracket algebra induced, in a consistent manner by the correspondence principle, mapping the quantum generators into commuting objects of classical nature preserving their algebra. 1 Supported by FAPESP 2 Work partially supported by CNPq 3 Supported by CNPq
Journal of Physics A: Mathematical and Theoretical, 2020
We extend Painlevé IV model by adding quadratic terms to its Hamiltonian obtaining two classes of... more We extend Painlevé IV model by adding quadratic terms to its Hamiltonian obtaining two classes of models (coalescence and deformation) that interpolate between Painlevé IV and II equations for special limits of the underlying parameters. We derive the underlying Bäcklund transformations, symmetry structure and requirements to satisfy Painlevé property.
Proceedings of 5th International School on Field Theory and Gravitation — PoS(ISFTG), 2009
Physics Letters B, 1992
As recently shown the conformal affinc Toda models can be obtained via hamiltonian reduction from... more As recently shown the conformal affinc Toda models can be obtained via hamiltonian reduction from a two-loop Kac-Moody algebra. In this paper we propose a systematic procedure to analyze the higher spin symmetries of the conformal affine Toda models. The method is based on an explicit construction of infinite towers of extended conformal symmetry generators. Two fundamental building blocks of this construction are special spin-one and-two primary fields characterizing the conformal structure of these models. The connection to the algebra of area preserving diffeomorphisms on a two-manifold (woo algebra) is established.
We propose a systematic treatment of symmetries of KP integrable systems, including constrained (... more We propose a systematic treatment of symmetries of KP integrable systems, including constrained (reduced) KP models slcKPR,M{\sl cKP}_{R,M}slcKPR,M, and their multi-component (matrix) generalizations. Any such integrable hierarchy is shown to possess an additional (hatU(1)oplushatSL(M))+oplus(hatSL(M+R))−({\hat U}(1)\oplus{\hat {SL}}(M))_{+} \oplus ({\hat {SL}}(M+R))_{-}(hatU(1)oplushatSL(M))+oplus(hatSL(M+R))− loop-algebra symmetry. Also we provide a systematic construction of the full algebra of Virasoro additional symmetries in the case of constrained KP models which requires a nontrivial modification of the known Orlov-Schulman construction for the general unconstrained KP hierarchy. Multi-component KP hierarchies are identified as ordinary (scalar) one-component KP hierarchies supplemented with the Cartan subalgebra of the additional symmetry algebra, which provides the basis of a new method for construction of soliton-like solutions. Davey-Stewartson and NNN-wave resonant systems arise as symmetry flows of ordinary slcKPR,M{\sl cKP}_{R,M}slcKPR,M hierarchies.
Physics Letters B, 1992
It is shown that the two-loop Kac-Moody algebra is equivalent to a two variable loop algebra and ... more It is shown that the two-loop Kac-Moody algebra is equivalent to a two variable loop algebra and a decoupled β-γ system. Similarly WZNW and CSW models having as algebraic structure the Kac-Moody algebra are equivalent to an infinity of versions of the corresponding ordinary models and decoupled abelian fields.
Physics Letters B, 1998
The classical and quantum algebras of a class of conformal NA-Toda models are studied.It is shown... more The classical and quantum algebras of a class of conformal NA-Toda models are studied.It is shown that the SL(2, R) q Poisson brackets algebra generated by certain chiral and antichiral charges of the nonlocal currents and the global U (1) charge appears as an algebra of the symmetries of these models.
Physics Letters B, 1992
We construct a centerless W-infinity type of algebra in terms of a generator of a centerless Vira... more We construct a centerless W-infinity type of algebra in terms of a generator of a centerless Virasoro algebra and an abelian spin-1 current. This algebra conventionally emerges in the study of pseudo-differential operators on a circle or alternatively within KP hierarchy with Watanabe's bracket. Construction used here is based on a special deformation of the algebra w ∞ of area preserving diffeomorphisms of a 2-manifold. We show that this deformation technique applies to the two-loop WZNW and conformal affine Toda models, establishing henceforth W ∞ invariance of these models.
Physics Letters B, 1991
Using the coadjoint orbit method we derive a geometric WZWN action based on the extended two-loop... more Using the coadjoint orbit method we derive a geometric WZWN action based on the extended two-loop Kac-Moody algebra. We show that under a hamiltonian reduction procedure, which respects conformal invariance, we obtain a hierarchy of Toda type field theories, which contain as submodels the Toda molecule and periodic Toda lattice theories. We also discuss the classical rmatrix and integrability properties.
Nuclear Physics B, 2009
A systematic construction for an action describing a class of supersymmetric integrable models as... more A systematic construction for an action describing a class of supersymmetric integrable models as well as for pure fermionic theories is discussed in terms of the gauged WZNW model associated to twisted affine Kac-Moody algebras. Explicit examples of the N = 1, 2 super sinh(sine)-Gordon models are discussed in detail. Pure fermionic theories arises for cosets sl(p, 1)/sl(p) ⊗ u(1) when a maximal kernel condition is fulfilled. The integrability condition for such models is discussed and it is shown that the simplest example when p = 2 leads to the constrained Bukhvostov-Lipatov, Thirring, scalar massive and pseudo-scalar massless Gross-Neveu models.
Journal of Physics A: Mathematical and Theoretical, 2011
A Kac-Moody algebra construction for the integrable hierarchy containing the Gardner equation is ... more A Kac-Moody algebra construction for the integrable hierarchy containing the Gardner equation is proposed. Solutions are systematically constructed employing the dressing method and deformed vertex operators which takes into account the nonvanishing boundary value problem for the mKdV hierarchy. Explicit examples are given and besides usual KdV like solitons, our solutions contemplate the large amplitude table-top solitons, kinks, dark solitons, breathers and wobbles.
Journal of Physics: Conference Series, 2012
We propose an approach to the nonvanishing boundary value problem for integrable hierarchies base... more We propose an approach to the nonvanishing boundary value problem for integrable hierarchies based on the dressing method. Then we apply the method to the AKNS hierarchy. The solutions are found by introducing appropriate vertex operators that takes into account the boundary conditions.
Annals of Physics, 1999
We investigate a class of conformal nonabelian-Toda models representing noncompact SL(2, R)/U(1) ... more We investigate a class of conformal nonabelian-Toda models representing noncompact SL(2, R)/U(1) parafermions (PF) interacting with specific abelian Toda theories and having a global U(1) symmetry. A systematic derivation of the conserved currents, their algebras, and the exact solution of these models are presented. An important property of this class of models is the affine SL(2, R)q algebra spanned by charges of
The gauge equivalence between basic KP hierarchies is discussed. The first two Hamiltonian struct... more The gauge equivalence between basic KP hierarchies is discussed. The first two Hamiltonian structures for KP hierarchies leading to the linear and non-linear W ∞ algebras are derived. The realization of the corresponding generators in terms of two boson currents is presented and it is shown to be related to many integrable models which are bi-Hamiltonian. We can also realize those generators by adding extra currents, coupled in a particular way, allowing for instance a description of multi-layered Benney equations or multi-component non-linear Schroedinger equation. In this case we can have a second Hamiltonian bracket structure which violates Jacobi identity. We consider the reduction to one-boson systems leading to KdV and mKdV hierarchies. A Miura transformation relating these two hierarchies is obtained by restricting gauge transformation between corresponding two-boson hierarchies. Connection to Drinfeld-Sokolov approach is also discussed in the SL(2, IR) gauge theory.
A class of non abelian affine Toda models is constructed in terms of the axial and vector gauged ... more A class of non abelian affine Toda models is constructed in terms of the axial and vector gauged WZW model. It is shown that the multivacua structure of the potential together with non abelian nature of the zero grade subalgebra allows soliton solutions with non trivial electric and topological charges. Their zero curvature representation and the classical r-matrix are also constructed in order to prove their classical integrability.
Journal of Mathematical Physics, 1995
Journal of Physics A: Mathematical and Theoretical, 2021
The construction of Miura and Bäcklund transformations for A n mKdV and KdV hierarchies are prese... more The construction of Miura and Bäcklund transformations for A n mKdV and KdV hierarchies are presented in terms of gauge transformations acting upon the zero curvature representation. As in the well known sl(2) case, we derive and relate the equations of motion for the two hierarchies. Moreover, the Miura-gauge transformation is not unique, instead, it is shown to be connected to a set of generators labeled by the exponents of A n The construction of generalized gauge-Bäcklund transformation for the A n-KdV hierarchy is obtained as a composition of Miura and Bäcklund-gauge transformations for A n-mKdV hierarchy. The zero curvature representation provide a framework which is universal within all flows and generate systematically Bäcklund transformations for the entirely hierarchy.