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Title: Stability under dilations of nonlinear spinor fields

Abstract

The stability problem of the localized solutions for classical Dirac fields with scalar self-interactions is considered in the framework of the Shatah-Strauss formalism. We study the stability and instability under dilations and provide an application to the Soler model.

Authors:
;
Publication Date:
Research Org.:
Mathematics Department, Brown University, Providence, Rhode Island 02912
OSTI Identifier:
5411697
Resource Type:
Journal Article
Resource Relation:
Journal Name: Phys. Rev. D; (United States); Journal Volume: 34:2
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; SCALAR FIELDS; SPINORS; STABILITY; BOUND STATE; DIRAC EQUATION; EIGENVALUES; LAGRANGIAN FUNCTION; WAVE EQUATIONS; DIFFERENTIAL EQUATIONS; EQUATIONS; FUNCTIONS; PARTIAL DIFFERENTIAL EQUATIONS; 645400* - High Energy Physics- Field Theory

Citation Formats

Strauss, W.A., and Va-acute-accentzquez, L.. Stability under dilations of nonlinear spinor fields. United States: N. p., 1986. Web. doi:10.1103/PhysRevD.34.641.
Strauss, W.A., & Va-acute-accentzquez, L.. Stability under dilations of nonlinear spinor fields. United States. doi:10.1103/PhysRevD.34.641.
Strauss, W.A., and Va-acute-accentzquez, L.. Tue . "Stability under dilations of nonlinear spinor fields". United States. doi:10.1103/PhysRevD.34.641.
@article{osti_5411697,
title = {Stability under dilations of nonlinear spinor fields},
author = {Strauss, W.A. and Va-acute-accentzquez, L.},
abstractNote = {The stability problem of the localized solutions for classical Dirac fields with scalar self-interactions is considered in the framework of the Shatah-Strauss formalism. We study the stability and instability under dilations and provide an application to the Soler model.},
doi = {10.1103/PhysRevD.34.641},
journal = {Phys. Rev. D; (United States)},
number = ,
volume = 34:2,
place = {United States},
year = {Tue Jul 15 00:00:00 EDT 1986},
month = {Tue Jul 15 00:00:00 EDT 1986}
}
  • We consider the stability problem for the localized solutions of classical nonlinear spinor fields in space dimensions N = 1 and N = 3 within the framework of the Shatah-Strauss formalism. We show that the well-known relations existing between the different stability criteria for scalar field equations are no longer valid for spinor fields. We discuss the application of the Shatah-Strauss formalism to several models: e.g., the Gross-Neveu, Thirring, and the Soler models.
  • It is noted that by merely rewriting the Lagrangian in a different form, Duerr and Saller do not realize their aim of inducing an additional hypercharge degree of freedom. It is pointed out that such an increase in the dynamical degrees of freedom would indeed occur if the Weinberg-Salam model could be derived starting from a four-fermion interaction. Existing studies on nonlinear spinor theories indicate that it may be possible to induce such additional symmetries, perhaps only in an approximate sense.
  • Generalized spinor field equations transform into linear Fermi-field equations when fermions are fused into bosons. Studies were made of cubic equations with normalization to arbitrary nonlinearity. Linearized spinor field equations correspond to the Green function equivalence for nonlinear and ordinary theory. Various fermion fusions are analyzed, and sources of nonlinearity are discussed. (tr-auth)
  • Building on general formulas obtained from the approximate renormalized effective action, the stress-energy tensor of the quantized massive spinor and vector fields in the spacetime of the regular black hole is constructed. Such a black hole is the solution to the coupled system of nonlinear electrodynamics and general relativity. A detailed analytical and numerical analysis of the stress-energy tensor in the exterior region is presented. It is shown that for small values of the charge as well as large distances from the black hole the leading behavior of the stress-energy tensor is similar to that in the Reissner-Nordstroem geometry. Importantmore » differences appear when the inner horizon becomes close to the event horizon. A special emphasis is put on the extremal configuration and it is shown that the stress-energy tensor is regular inside the event horizon of the extremal black hole.« less