Spinor

Abstract: Continuing the program developed in a previous paper, a "superconductive" solution describing the protonneutron doublet is obtained from a nonlinear spinor field Lagrangian. The pions of finite mass are found as nucleonantinucleon bound states by introducing a small bare mass into the Lagrangian which otherwise possesses a certain type of the gamma /sub 5/ invariance. In addition, heavier mesons and two-nucleon bound states are obtained in the same approximation. On the basis of numerical mass relations, it is suggested that the bare nucleon field is similar to the electron-neutrino field, and further speculations are made concerning the complete description of the baryons and leptons. (auth)

Abstract: The representation of Fermi particles by two-component Pauli spinors satisfying a second order differential equation and the suggestion that in β decay these spinors act without gradient couplings leads to an essentially unique weak four-fermion coupling. It is equivalent to equal amounts of vector and axial vector coupling with two-component neutrinos and conservation of leptons. (The relative sign is not determined theoretically.) It is taken to be "universal"; the lifetime of the μ agrees to within the experimental errors of 2%. The vector part of the coupling is, by analogy with electric charge, assumed to be not renormalized by virtual mesons. This requires, for example, that pions are also "charged" in the sense that there is a direct interaction in which, say, a π0 goes to π- and an electron goes to a neutrino. The weak decays of strange particles will result qualitatively if the universality is extended to include a coupling involving a Λ or Σ fermion. Parity is then not conserved even for those decays like K→2π or 3π which involve no neutrinos. The theory is at variance with the measured angular correlation of electron and neutrino in He6, and with the fact that fewer than 10^-4 pion decay into electron and neutrino.

Abstract: Bose–Einstein condensates — a low-temperature form of matter in which a macroscopic population of bosons occupies the quantum-mechanical ground state — have been demonstrated for weakly interacting, dilute gases of alkali-metal1,2,3 and hydrogen25 atoms. Magnetic traps are usually employed to confine the condensates, but have the drawback that spin flips in the atoms lead to untrapped states. For this reason, the spin orientation of the trapped alkali atoms cannot be regarded as a degree of freedom. Such condensates are therefore described by a scalar order parameter, like the spinless superfluid 4He. In contrast, a recently realized optical trap4 for sodium condensates confines atoms independently of their spin orientations. This offers the possibility of studying ‘spinor’ condensates in which spin comprises a degree of freedom, so that the order parameter is a vector rather than scalar quantity. Here we report the observation of equilibrium states of sodium spinor condensates in an optical trap. The freedom of spin orientation leads to the formation of spin domains in an external magnetic field, which can be either miscible or immiscible with one another.

Abstract: We consider the model of a spinor field with arbitrary internal degrees of freedom having arbitrary nonderivative coupling to external scalar, pseudoscalar, vector, and axial-vector fields. By carefully defining the $S$ matrix in the interaction picture, the vector and axial-vector currents associated with the external vector and axial-vector fields are found to satisfy anomalous Ward identities. If we require that the vector currents satisfy the usual Ward identities, the divergence of the axial-vector current contains well-defined anomalous terms. These terms are explicitly calculated.