THE CORRESPONDENCE PRINCIPLE IN (1+1)-DIMENSIONAL FIELD THEORY AND THE COLEMAN THEOREM

The correspondence relations between a fermion field and a boson field in (1+1)-dimensional quantum field theory is discussed in general. Emphases have been laid on the renorinalization with respect.to an arbitrary mass parameter in boson version as well as the nonlocal property of currents in fermion version. After establishing the equivalence between the continuous chiral transformation in fermion version and the translational transformation in boson version, we are able to prove the Coleman theorem correspondingly.     

On the character of chiral symmetry breaking and fermion vacuum structure in QED<Subscript>3</Subscript>

Equation for the Bethe-Salpeter wave function of the Goldstone boson in QED₃ is considered in the ladder approximation with the use of the Landau gauge for the photon propagator. With the help of standard simplifications, the existence of nonzero solutions for this equation is demonstrated, which testifies to the production of the above-described boson in the process of chiral symmetry breaking. At the same time, it is demonstrated that only one of the entire set of solutions describing the Goldstone boson corresponds to the stable ground state; this solution has the greatest fermion mass. In the remaining cases, the compound boson state with zero mass is excited, and all other states having smaller energies appear tachyon states and hence are unstable. The fermion condensate is calculated; it is demonstrated that in the examined case, it is finite. Based on the foregoing, conclusions are drawn about spontaneous rather than dynamic character of chiral symmetry breaking in QED₃, complex structure of fermion vacuum for the examined model, and at the same time, simple structure of the massive phase vacuum.     

Anomalous Vector-Boson Mass Generation on a Lattice

We show the vector boson mass generation on a lattice with the Wilson's fermion formulation. By calculating explicitly the change of the effective action under chiral transformation, it is also found an arbitrariness in the solution of the chiral Schwinger model, which depends on a lattice regularization in continuum theory.     

Dynamical mass generation in QED_3 beyond the instantaneous approximation

In this paper, we investigate dynamical mass generation in(2+1)-dimensional quantum electrodynamics at finite temperature. Many studies are carried out within the instantaneous-exchange approximation, which ignores all but the zero-frequency component of the boson propagator and fermion self-energy function. We extend these studies by taking the retardation effects into consideration. In this paper, we get the explicit frequency n and momentum p dependence of the fermion self-energy function and identify the critical temperature for different fermion flavors in the chiral limit. Also, the phase diagram for spontaneous symmetry breaking in the theory is presented in T_c-N_f space. The results show that the chiral condensate is just one-tenth of the scale of previous results, and the chiral symmetry is restored at a smaller critical temperature.     

Fermion propagators on a four-dimensional random-block lattice

Fermion propagators, composite boson propagators and the fermion condensate are calculated numerically on the four-dimensional random-block lattice, respectively. The ensemble-averaged fermion propagator agrees with the continuum propagator for distances greater than three average lattice spacings. The results on the fermion condensate show that the chiral symmetry of the doubled modes is broken in the continuum limit. The Goldstone boson arising from the broken symmetry is revealed by examining the composite pseudo-scalar propagator. The doubled fermion and the Goldstone boson both acquire masses of the order of inverse lattice spacing and thus decouple from the theory in the continuum limit.     

Effect of Fermion Velocity on Phase Structure of QED3

Dynamical chiral symmetry breaking (DCSB) in thermal QED₃ with fermion velocity is studied in the framework of Dyson-Schwinger equations. By adopting instantaneous approximation and neglecting the transverse component of gauge boson propagator at finite temperature, we numerically solve the fermion self-energy equation in the rainbow approximation. It is found that both DCSB and fermion chiral condensate are suppressed by fermion velocity. Moreover, the critical temperature decreases as fermion velocity increases.     

Interacting fermions on a random lattice

We extend previous work on the properties of the Dirac lagrangian on two-dimensional random lattices to the case where interaction terms are included. Although for free fermions the chiral symmetry of the doubles is spontaneously broken by their interaction with the lattice and they decouple from long-distance physics, our results in this paper show that all is undone by quantum corrections in an interacting field theory and that the end result is very similar to what is found with Wilson fermions. Two field-theoretical models with interacting fermions are studied by perturbation expansion in the field theory coupling constant. These are a model with one fermion and one boson species interacting via a scalar Yukawa coupling and the massive Thirring model. It is shown that on the random lattice ultraviolet finite diagrams and finite parts of ultraviolet divergent diagrams have the correct continuum limit. Ultraviolet divergent parts can be removed by the same renormalisation procedure as in the continuum, but do not exhibit the same dependence on the lagrangian mass. In the case of the massive Thirring model this causes a fermion mass correction of order the cut-off scale, which breaks the chiral symmetry of the remaining light fermion; there is consequently a fine-tuning problem. In the context of the same model we discuss the effect of the Goldstone boson associated with the spontaneous breakdown of the chiral symmetry of the doubles on two-dimensional models with vector couplings.     

Finite-size effects on a lattice calculation

We study in this Letter the finite-size effects of a non-periodic lattice on a lattice calculation. To this end we use a finite lattice equipped with a central difference derivative with homogeneous boundary conditions to calculate the bosonic mass associated to the Schwinger model. We found that the homogeneous boundary conditions produce absence of fermion doubling and chiral invariance, but we also found that in the continuum limit this lattice model does not yield the correct value of the boson mass as other models do. We discuss the reasons for this and, as a result, the matrix which cause the fermion doubling problem is identified.     

Critical Mass of Gauge Boson in Rainbow QED3

In three-dimensional quantum electrodynamics (QED₃) with a massive gauge boson, we investigate the coupled Dyson-Schwinger equations for the fermion and photon propagators in the rainbow approximation, and obtain the critical gauge boson mass for various numbers of the fermion flavors. A comparison with the previous results is presented.     

Chiral bosons

The local lagrangian formulation for chiral bosons recently suggested by Floreanini and Jackiw is analyzed. We quantize the system and explain how the unconventional Poincaré generators of left and right chiral bosons combine to form the standard generators. The left-U(1) Kac-Moody algebra and the left-Virasoro algebra are shown to be the same as for left Weyl fermions. We compare the partition functions, on the torus, of a chiral boson and a chiral fermion. The left-moving boson is coupled to gauge fields producing the same anomalies as in the fermionic formulation. It is pointed out that the unconventional Lorentz transformations are inapplicable for the coupled system and a set of different transformations is presented. A coupling to gravity is proposed. We present the theory of chiral bosons on a group manifold, the chiral WZW model. The (1,0) supersymmetric abelian and non-abelian chiral bosons are described.     

On the boson mapping of fermion collective pairs

We study the problem of the mapping of fermion collective pairs onto particle-particle bosons and of different fermion operators (hamiltonian, one- and two-particle transfer operators) onto corresponding boson ones and we test the consequences of the truncation to lowest orders of these boson operators. We find that, although the lowest-order terms in the expansion of the operators in boson space lead to matrix elements between boson states which display the qualitative behaviour of the corresponding ones between fermion states, higher-order terms are required to get a quantitative agreement when a large number of particles are involved, as a direct consequence of the increased role of the Pauli principle.     

Fermions and bosons in a two-dimensional world

We derive the formal equivalence of a free massless two-dimensional theory and a free massless two-dimensional boson theory constructed from the bilinear products of the self-same fermion theory. The sense of this equivalence is investigated. Using a box normalization, it is found that the fermion states are Glauber coherent states of bosons, where the boson vacuum is the ground state of the charge sector corresponding to the given fermion state. The massless boson is the Goldstone boson and the degenerate vacua are the ground states of the various charge sectors. A complete operator identity between fermion and boson operators can be obtained, but to do this an additional boson operator must be introduced which cannot be defined in terms of bilinear products of the fermion operators. Doing this makes the charge spectrum continuous.     

General electroweak mixing models and extended gauge theories

General electroweak mixing schemes containing an arbitrary number of weak bosons and agreeing with the predictions of the standard model for neutrino scattering and polarized electron scattering in the low energy approximation are analyzed using the propagator matrix formalism. The mean charged boson mass is bounded while the mean neutral boson mass is unbounded and determined as a function of the mean charged one. Under a special assumption on the electroweak mixing parameters the four fermion interaction agrees with the one of extended gauge theories and the mean boson masses agree with the boson masses of the standard model.     

Correlations in charged fermion–boson mixture in dimensionalities D=2 and D=3

We numerically study the correlation effects in a two-component charged fermion–boson mixture at zero temperature investigating the role played by the statistical effects and Coulomb correlations in a model with different fermion and boson mass ratios in two and three dimensions. The local-field factors describing the correlation effects and collective excitation modes are determined through the self-consistent scheme. We find that the effects of correlations and statistics are more pronounced in two-dimensional mixtures.     

含G对费米子动力学对称SP(10)模型的Dyson玻色子实现

将费米子动力学对称模型包含G费米子对能够构造出SP(10)或SO(12)动力学对称群.本文用GeneralizedDyson玻色子映射方法求出SP(10)对称群精确的玻色子映像,其子群SU(5)生成元的玻色子映像与sdg相互作用玻色子模型(IBM)SU(5)生成元相同,唯象sdgIBMSU(5)极限能谱公式可由费米子动力学对称模型的微观参数描述.     

Weight diagrams for superfields

A scheme for describing superfields by weight diagrams is proposed. The weights in such diagram are just the conventional boson and fermion fields contained in a supermultiplet. As in the case of SU(3), the weight diagrams produce no new results, but they afford an easy visualization of the standard operations of supersymmetry, such as infinitesimal transformations, chiral reductions, and decomposition of products.     

Rearrangements of interacting Fermi liquids

The stability condition of the Landau Fermi liquid theory may be broken when the interaction between particles is strong enough. In this case, the ground state is reconstructed to have a particle distribution different from the Fermi-step function. For specific instances, one case with the vector boson exchange and another with the relativistic heavy-ion collision are taken into consideration. With the vector boson exchange, we find that the relative weak interaction strength can lead to the ground-state rearrangement as long as the fermion mass is large enough. It is found that the relativistic heavy-ion collision may also cause the ground-state rearrangement, affecting the statistics of the collision system.     

On the correspondence between fermion and boson states and operators

Mapping of shell-model (fermion) Hamiltonians onto boson Hamiltonians which underly the interaction boson model ^1–5) is investigated. A simple correspondence is defined and a sufficient condition given for shell-model Hamiltonians to simply correspond to finite hermitian boson Hamiltonians. A special case is discussed where diagonalization of a shell-model Hamiltonian for valence protons and neutrons can be exactly carried out in an equivalent (but different) boson space. If, however, the proton Hamiltonian and neutron Hamiltonian are diagonal in the seniority scheme, mapping of fermion states onto orthogonal boson states cannot be a simple correspondence. In that case the boson quadrupole operators equivalent to fermion guadrupole operators cannot be single-boson operators but must be more complicated, ones.