Small Bare Masses Research Articles

Radiative dynamical mass of planar charged fermion in a constant homogeneous magnetic field

The effective Lagrangian and mass operator are calculated for planar charged massive and massless fermions in a constant external homogeneous magnetic field in the one-loop approximation of the 2+1 dimensional quantum electrodynamics (QED_{2+1}). We obtain the renormalizable effective Lagrangian and the fermion mass operator for a charged fermion of mass m and then calculate these quantities for the massless case. The radiative corrections to the mass of charged massless fermion when it occupies the lowest Landau level are found for the cases of the pure QED_{2+1} as well as the so-called reduced QED_{3+1} on a 2-brane. The fermion masses were found can be generated dynamically in an external magnetic field in the pure QED_{2+1} if the charged fermion has small bare mass m_0 and in the reduced QED_{3+1} on a 2-brane even at m_0=0. The dynamical mass seems to be likely to be revealed in monolayer graphene in the presence of constant homogeneous magnetic field (normal to the graphene sample).

Chiral Symmetry Breaking in Quantum Field Theory

An analysis of the spontaneous breaking of chiral symmetry in three dimensional electrodynamics is described. It is argued that this model, when treated in a 1/ N expansion, does exhibit spontaneous chiral symmetry breaking. This is established by finding analytic and numer· ical solutions to the Dyson-Schwinger equation and then computing the composite-operator effective potential. During the fifty years since Y uka wa proposed the J[ meson as the intermediary of nuclear forces, our view of this particle has continued to evolve. We now know it to be a quark-antiquark composite, and in quantum chromodynamics, QCD, we have a strong interaction theory that may well describe its dynamics and that of the other hadrons. Among all the hadrons, however, the 1f meson is believed to play a special role. The underlying theory of strong interactions posseses a near chiral symmetry, SU(2h X SU(2) R, because of the approximate masslessness of the up and down quarks. This symmetry must then break spontaneously in order to explain the effective 300 MeV masses that these quarks appear to possess as the constituents of hadrons. The spontaneous breaking of any continuous symmetry necessarily leads to the existence of massless Goldstone bosons, and in the case of chiral symmetry, the 1f mesons approximately play this role. The small bare mass of the up and down quarks leads to a small mass for 1f mesons 1

Dynamical fermion mass generation and exciton spectra in graphene

The Coulomb interaction between massless Dirac fermions may induce dynamical chiral symmetry breaking by forming excitonic pairs in clean graphene, leading to semimetal-insulator transition. If the Dirac fermions have zero bare mass, an exact continuous chiral symmetry is dynamically broken and thus there are massless Goldstone excitons. If the Dirac fermions have a small bare mass, an approximate continuous chiral symmetry is dynamically broken and the resultant Goldstone type excitons become massive, which is analogous to what happens in QCD. In this paper, after solving Dyson-Schwinger gap equation in the presence of a small bare fermion mass, we found a remarkable reduction of the critical Coulomb interaction strength for excitonic pair formation and a strong enhancement of dynamical fermion mass. We then calculate the masses of Goldstone type excitons using the SVZ sum rule method and operator product expansion technique developed in QCD and find that the exciton masses are much larger than bare fermion mass but smaller than dynamical fermion mass gap. We also study the spin susceptibilities and estimate the masses of non-Goldstone type excitons using the same tools.

Chiral Symmetry Breaking in Quantum Field Theory

An analysis of the spontaneous breaking of chiral symmetry in three dimensional electrodynamics is described. It is argued that this model, when treated in a 1/ N expansion, does exhibit spontaneous chiral symmetry breaking. This is established by finding analytic and numer· ical solutions to the Dyson-Schwinger equation and then computing the composite-operator effective potential. During the fifty years since Y uka wa proposed the J[ meson as the intermediary of nuclear forces, our view of this particle has continued to evolve. We now know it to be a quark-antiquark composite, and in quantum chromodynamics, QCD, we have a strong interaction theory that may well describe its dynamics and that of the other hadrons. Among all the hadrons, however, the 1f meson is believed to play a special role. The underlying theory of strong interactions posseses a near chiral symmetry, SU(2h X SU(2) R, because of the approximate masslessness of the up and down quarks. This symmetry must then break spontaneously in order to explain the effective 300 MeV masses that these quarks appear to possess as the constituents of hadrons. The spontaneous breaking of any continuous symmetry necessarily leads to the existence of massless Goldstone bosons, and in the case of chiral symmetry, the 1f mesons approximately play this role. The small bare mass of the up and down quarks leads to a small mass for 1f mesons 1

Nonleptonic weak decays in two -dimensional quantum chromodynamics

The two-body nonleptonic decays of strange and charmed mesons are computed numerically in the framework of quantum chromodynamics in 2 dimensions using the 1/N/sub c/ expansion. It is shown that the amplitudes have no simple SU(4) algebraic properties. The decays of strange mesons are governed by the approximate ..delta..I = 1/2 rule which occurs as a consequence of the small bare masses of the s, u, and d quarks.

Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. II

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)