Bare mass

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: It is shown how finite-temperature effects in a renormalizable quantum field theory can restore a symmetry which is broken at zero temperature. In general, for both gauge symmetries and ordinary symmetries, such effects occur only through a temperature-dependent change in the effective bare mass of the scalar bosons. The change in the boson bare mass is calculated for general field theories, and the results are used to derive the critical temperatures for a few special cases, including gauge and nongauge theories. In one case, it is found that a symmetry which is unbroken at low temperature can be broken by raising the temperature above a critical value. An appendix presents a general operator formalism for dealing with higher-order effects, and it is observed that the one-loop diagrams of field theory simply represent the contribution of zero-point energies to the free energy density. The cosmological implications of this work are briefly discussed.

Abstract: Any nonrelativistic theory may be rewritten by introducing fictitious elementary particles with arbitrary properties. No physical predictions are affected, provided that the interaction part of the Hamiltonian is correspondingly modified. The fictitious elementary particle provides a good representation of a real composite particle if the modified interaction is sufficiently weakened for perturbation theory to work. It corresponds to a truly elementary particle with infinite bare mass, and hence with $Z=0$. We show how the latter condition yields a sum rule for the coupling of a composite particle to its constituents as a function of energy. The sum rule can be used to evaluate such coupling constants as that for the proton-electron-hydrogen vertex. The mathematical method used is that developed by Schmidt for the study of the Fredholm equation, and corresponds to the extraction of a single factor from the full Fredholm determinant.