Fixed-axis polarization states: covariance and comparisons

Addressing the recent criticisms of Kvinikhidze and Miller, we prove that the spectator wave functions and currents based on ``fixed-axis'' polarization states (previously introduced by us) are Lorentz covariant, and find an explicit connection between them and conventional direction-dependent polarization states. The discussion shows explicitly how it is possible to construct pure $S$-wave models of the nucleon.Comment: Changed title and introductory material to match accepted pape

A note on the Guerra and Talagrand theorems for Mean Field Spin Glasses: the simple case of spherical models

The aim of this paper is to discuss the main ideas of the Talagrand proof of the Parisi Ansatz for the free-energy of Mean Field Spin Glasses with a physicist's approach. We consider the case of the spherical $p$-spin model, which has the following advantages: 1) the Parisi Ansatz takes the simple ``one step replica symmetry breaking form'', 2) the replica free-energy as a function of the order parameters is simple enough to allow for numerical maximization with arbitrary precision. We present the essential ideas of the proof, we stress its connections with the theory of effective potentials for glassy systems, and we reduce the technically more difficult part of the Talagrand's analysis to an explicit evaluation of the solution of a variational problem.Comment: 20 pages, 5 figures. Added references and minor language correction

Covariant nucleon wave function with S, D, and P-state components

Expressions for the nucleon wave functions in the covariant spectator theory (CST) are derived. The nucleon is described as a system with a off-mass-shell constituent quark, free to interact with an external probe, and two spectator constituent quarks on their mass shell. Integrating over the internal momentum of the on-mass-shell quark pair allows us to derive an effective nucleon wave function that can be written only in terms of the quark and diquark (quark-pair) variables. The derived nucleon wave function includes contributions from S, P and D-waves.Comment: 13 pages and 1 figur

Spin and angular momentum in the nucleon

Using the covariant spectator theory (CST), we present the results of a valence quark-diquark model calculation of the nucleon structure function f(x) measured in unpolarized deep inelastic scattering (DIS), and the structure functions g1(x) and g2(x) measured in DIS using polarized beams and targets. Parameters of the wave functions are adjusted to fit all the data. The fit fixes both the shape of the wave functions and the relative strength of each component. Two solutions are found that fit f(x) and g1(x), but only one of these gives a good description of g2(x). This fit requires the nucleon CST wave functions contain a large D-wave component (about 35%) and a small P-wave component (about 0.6%). The significance of these results is discussed.Comment: 27 pages; 13 figure

Chaos in temperature in the Sherrington-Kirkpatrick model

We prove the existence of chaos in temperature in the Sherringhton-Kirkpatrick model. The effect is exceedingly small, namely of the ninth order in perturbation theory. The equations describing two systems at different temperatures constrained to have a fixed overlap are studied analytically and numerically, yielding information about the behaviour of the overlap distribution function $P_{T_1,T_2}(q)$ in finite-size systems.Comment: REVTEX, 6 pages, 2 figure

Confinement, quark mass functions, and spontaneous chiral symmetry breaking in Minkowski space

We formulate the covariant equations for quark-antiquark bound states in Minkowski space in the framework of the Covariant Spectator Theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. We show that these equations are charge-conjugation invariant, and that in the chiral limit of vanishing bare quark mass, a massless pseudoscalar bound state is produced in a Nambu-Jona-Lasinio (NJL) mechanism, which is associated with the Goldstone boson of spontaneous chiral symmetry breaking. In this introductory paper, we test the formalism by using a simplified kernel consisting of a momentum-space delta-function with a vector Lorentz structure, to which one adds a mixed scalar and vector confining interaction. The scalar part of the confining interaction is not chirally invariant by itself, but decouples from the equations in the chiral limit and therefore allows the NJL mechanism to work. With this model we calculate the quark mass function, and we compare our Minkowski-space results to lattice QCD data obtained in Euclidean space. In a companion paper, we apply this formalism to a calculation of the pion form factor.Comment: 17 pages, 12 figures, version published in Phys. Rev.

Pion electromagnetic form factor in the Covariant Spectator Theory

The pion electromagnetic form factor at spacelike momentum transfer is calculated in relativistic impulse approximation using the Covariant Spectator Theory. The same dressed quark mass function and the equation for the pion bound-state vertex function as discussed in the companion paper are used for the calculation, together with a dressed quark current that satisfies the Ward-Takahashi identity. The results obtained for the pion form factor are in agreement with experimental data, they exhibit the typical monopole behavior at high-momentum transfer, and they satisfy some remarkable scaling relations.Comment: 11 pages, 8 figures, version published in Phys. Rev.