Pseudospin symmetry and the relativistic harmonic oscillator

A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U linear in r. Setting either or both combinations Σ=5+V and δ=V-S to zero, analytical solutions for bound states of the corresponding Dirac equations are found. The eigenenergies and wave functions are presented and particular cases are discussed, devoting a special attention to the nonrelativistic limit and the case Σ=0, for which pseudospin symmetry is exact. We also show that the case U=δ=0 is the most natural generalization of the nonrelativistic harmonic oscillator. The radial node structure of the Dirac spinor is studied for several combinations of harmonic-oscillator potentials, and that study allows us to explain why nuclear intruder levels cannot be described in the framework of the relativistic harmonic oscillator in the pseudospin limit.

Self-dual super-Yang-Mills as a string theory in (x, θ) space

Different string theories in twistor space have recently been proposed for describing N = 4 super-Yang-Mills. In this paper, a string theory in (x, θ) space is constructed for self-dual N = 4 super-Yang-Mills. It is hoped that these results will be useful for understanding the twistor-string proposals and their possible relation with the pure spinor formalism of the D = 10 superstring. © SISSA/ISAS 2004.

Higher-dimensional twistor transforms using pure spinors

Hughston has shown that projective pure spinors can be used to construct massless solutions in higher dimensions, generalizing the four-dimensional twistor transform of Penrose. In any even (euclidean) dimension d = 2n, projective pure spinors parameterize the coset space SO(2n)/U(n), which is the space of all complex structures on ℝ2n. For d = 4 and d = 6, these spaces are ℂℙ1 and ℂℙ3 and the appropriate twistor transforms can easily be constructed. In this paper, we show how to construct the twistor transform for d > 6 when the pure spinor satisfies nonlinear constraints, and present explicit formulas for solutions of the massless field equations. © SISSA/ISAS 2005.

BRST cohomology and nonlocal conserved charges

A relation is found between nonlocal conserved charges in string theory and certain ghost-number two states in the BRST cohomology. This provides a simple proof that the nonlocal conserved charges for the superstring in an AdS 5 × S5 background are BRST-invariant in the pure spinor formalism and are κ-symmetric in the Green-Schwarz formalism. © SISSA/ISAS 2005.

Quantum consistency of the superstring

Using arguments based on BRST cohomology, the pure spinor formalism for the superstring in an AdS 5×S 5 background is proven to be BRST invariant and conformally invariant at the quantum level to all orders in perturbation theory. Cohomology arguments are also used to prove the existence of an infinite set of non-local BRST-invariant charges at the quantum level. © SISSA 2005.

Relativistic particle dynamics in D = 2+1

We propose a SUSY variant of the action for a massless spinning particles via the inclusion of twistor variables. The action is constructed to be invariant under SUSY transformations and τ-reparametrizations even when an interaction field is including. The constraint analysis is achieved and the equations of motion are derived. The commutation relations obtained for the commuting spinor variables λα show that the particle states have fractional statistics and spin. At once we introduce a possible massive term for the non-interacting model. © SISSA 2006.

Spin and pseudospin symmetries and the equivalent spectra of relativistic spin-1/2 and spin-0 particles

We show that the conditions which originate the spin and pseudospin symmetries in the Dirac equation are the same that produce equivalent energy spectra of relativistic spin-1/2 and spin-0 particles in the presence of vector and scalar potentials. The conclusions do not depend on the particular shapes of the potentials and can be important in different fields of physics. When both scalar and vector potentials are spherical, these conditions for isospectrality imply that the spin-orbit and Darwin terms of either the upper component or the lower component of the Dirac spinor vanish, making it equivalent, as far as energy is concerned, to a spin-0 state. In this case, besides energy, a scalar particle will also have the same orbital angular momentum as the (conserved) orbital angular momentum of either the upper or lower component of the corresponding spin-1/2 particle. We point out a few possible applications of this result. © 2007 The American Physical Society.

The overall coefficient of the two-loop superstring amplitude using pure spinors

Using the results recently obtained for computing integrals over (non-minimal) pure spinor superspace, we compute the coefficient of the massless two-loop four-point amplitude from first principles. Contrasting with the mathematical difficulties in the RNS formalism where unknown normalizations of chiral determinant formulæ force the two-loop coefficient to be determined only indirectly through factorization, the computation in the pure spinor formalism can be smoothly carried out. © SISSA 2010.

Cohomology ring of the brst operator associated to the sum of two pure spinors

In the study of the Type II superstring, it is useful to consider the BRST complex associated to the sum of two pure spinors. The cohomology of this complex is an infinite-dimensional vector space. It is also a finite-dimensional algebra over the algebra of functions of a single pure spinor. In this paper we study the multiplicative structure. © 2013 World Scientific Publishing Company.

Sobre interações escalares e vetoriais na teoria de Duffin-Kemmer-Petiau

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Espalhamento e estados ligados de partículas de spin 1/2 em um potencial degrau suave com acoplamentos escalar e vetorial

Pós-graduação em Física - FEG

Soluções analíticas da equação de Duffin-Kemmer-Petiau

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Relação entre os formalismos de Green-Schwarz e espinores puros para a supercorda

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Anti-de Sitter holography in di?erent coordinates

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

N-point tree-level scattering amplitude in the new Berkovits' string

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)