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 equivalence between sine-Gordon model and Thirring model in the chirally broken phase of the Thirring model

We investigate the equivalence between Thirring model and sine-Gordon model in the chirally broken phase of the Thirring model. This is unlike all other available approaches where the fermion fields of the Thirring model were quantized in the chiral symmetric phase. In the path integral approach we show that the bosonized version of the massless Thirring model is described by a quantum field theory of a massless scalar field and exactly solvable, and the massive Thirring model bosonizes to the sine-Gordon model with a new relation between the coupling constants. We show that the non-perturbative vacuum of the chirally broken phase in the massless Thirring model can be described in complete analogy with the BCS ground state of superconductivity. The Mermin–Wagner theorem and Coleman's statement concerning the absence of Goldstone bosons in the 1+1-dimensional quantum field theories are discussed. We investigate the current algebra in the massless Thirring model and give a new value of the Schwinger term. We show that the topological current in the sine-Gordon model coincides with the Noether current responsible for the conservation of the fermion number in the Thirring model. This allows one to identify the topological charge in the sine-Gordon model with the fermion number. Received: 16 December 2000 / Revised version: 23 April 2001 / Published online: 13 June 2001     

Index theorem for the zero modes of Majorana fermion vortices in chiral p-wave superconductors

We show that the Majorana fermion zero modes in the cores of odd winding number vortices of a 2D (p(x)+ip(y))-paired superconductor is due to an index theorem. This theorem is analogous to that proven by Jackiw and Rebbi for the existence of localized Dirac fermion zero modes on the mass domain walls of a 1D Dirac theory. The important difference is that, in our case, the theorem is proven for a two component fermion field theory where the first and second components are related by parity reversal and Hermitian conjugation.     

Resonances of Spin-1/2 Fermions in Eddington-Inspired Born-Infeld Gravity

We investigate the fermionic resonances for both chiralities in five-dimensional Eddington-inspired BornInfeld(EiBI)theory.In order to localize fermion on the brane,it needs to be considered the Yukawa coupling between the fermion and the background scalar field.In our models,since the background scalar field has kink,double kink,or anti-kink solution,the system has rich resonant Kaluza-Klein(KK)modes structure.The massive KK fermionic modes feel a volcano potential,which result in a fermionic zero mode and a set of continuous massive KK modes.The inner structure of the branes and a free parameter in background scalar field influence the resonant behaviors of the massive KK fermions.     

Topological charge from thermodynamics in two dimensions

It is shown that in the weak coupling limit the partition function of massless (QED)₂ in a finite volume is identical to that of a bose field if the boson topological charge is identified with the fermion number. Generalizations to theories with U(N) gauge symmetry, fractional fermion number, and the Schwinger model for any coupling are also discussed.     

Lorentz Violation and Topologically Trapped Fermions in 2+1 Dimensions

The full spectrum of two‐dimensional fermion states in a scalar soliton trap with a Lorentz breaking background is investigated in the context of graphene, where the Lorentz symmetry should not be strictly valid. The field theoretical model with Lorentz breaking terms represents Dirac electrons in one valley and in a scalar field background. The Lorentz violation comes from the difference between the Dirac electron and scalar mode velocities, which should be expected when modelling the electronic and lattice excitations in graphene. Here, only one Lorentz‐violating parameter is considered, belonging to the scalar sector. The analytical methods developed in the context of 1+1 field theories are extended to explore the effect of the Lorentz symmetry breaking in the charge carrier density of two‐dimensional materials in the presence of a domain wall with a kink profile. The width and the depth of the trapping potential from the kink is controlled by the Lorentz violating term, which is reflected analytically in the band structure and properties of the trapped states. These findings enlarge previous studies of the edge states obtained with domain wall and in strained graphene nanoribbon in a chiral gauge theory.     

Nontopological finite temperature induced fermion number

We show that while the zero temperature induced fermion number in a chiral sigma model background depends only on the asymptotic values of the chiral field, at finite temperature the induced fermion number depends also on the detailed shape of the chiral background. We resum the leading low temperature terms to all orders in the derivative expansion, producing a simple result that can be interpreted physically as the different effect of the chiral background on virtual pairs of the Dirac sea and on the real particles of the thermal plasma. By contrast, for a kink background, not of sigma model form, the finite T induced fermion number is temperature dependent but topological.     

Induced fermion current in the σ model in (2 + 1) dimensions

The topological current in the (2 + 1)-dimensional O(3) nonlinear σ model is shown to be identical to the fermionic current induced by a Yukawa-type interaction with the classical field of the σ model. Alternatively, the system can be described in terms of two species of fermions interacting with an abelian gauge field, and hence related to the recently discovered three-dimensional anomaly. The role of fermion zone modes is also discussed.     

Localization of matters on the bent brane in bulk

We investigate the possibility of localizing various matter fields on a bent AdS₄ (dS₄) thick brane in AdS₅. For spin 0 scalar field, we find a massless zero mode and an excited state which can be localized on the bent brane. For spin 1 vector field, there is only a massless zero mode on the bent brane. For spin 1/2 fermion field, it is shown that, in the case of no Yukawa coupling of scalar-fermion, there is no existence of localized massless zero mode for both left and right chiral fermions. In order to localize massless fermions, some kind of Yukawa coupling must be included. We study two types of Yukawa couplings as examples. Localization property of chiral fermions is related to the parameters of the brane model, the Yukawa coupling constant and the cosmological constant of the 4-dimensional space–time.     

The embedding of General Relativity in five dimensions

We argue that General Relativistic solutions can always be locally embedded in Ricci-flat 5-dimensional spaces. This is a direct consequence of a theorem of Campbell (given here for both a timelike and spacelike extra dimension, together with a special case of this theorem) which guarantees that anyn-dimensional Riemannian manifold can be locally embedded in an (n+1)-dimensional Ricci-flat Riemannian manifold. This is of great importance in establishing local generality for a proposal recently put forward and developed by Wesson and others, whereby vacuum (4+1)-dimensional field equations give rise to (3+1)-dimensional equations with sources. An important feature of Campbell's procedure is that it automatically guarantees the compatibility of Gauss-Codazzi equations and therefore allows the construction of embeddings to be in principle always possible. We employ this procedure to construct such embeddings in a number of simple cases.     

Berry phase and induced fractional fermion number on vaccum

We show that, in four dimensional field-theoretical model containing fermion field and background isovector scalar field, an induced magnetic monopole field emerges as a result of adiabatical evolution of the scalar field. For the corresponding Dirac Hamiltonian the degenerate eigenmodes of the vacuum are known to exist. The effective system is then shown to give fractional fermion number on vacuum. In the present approach the magnetic monopole field is not quite essentially given as a topologically non-trivial external field but induced as the result of adiabatic evolution of a scalar field.     

Vertex Correction at Finite Temperature and Decoupling Transition in (2+1) Dimensional Chiral Gross-Neveu Model

With the aid of imaginary time temperature field theory and fermion mass spectrum derived from Ward-Takahashi identities with composite fields,the vertex correction among fermions and σ meson is calculated beyond the leading order in 1/N expansion,and the change of vertex function with temperature and decoupling transition are discussed in (2+1) dimensional chiral Gross-Neveu model.It turns out that the critical temperature of decoupling transitionarises with increasing fermion mass and π meson mass at zero temperature;the vertex correction resulting from thermal fluctuation will affect the fermion dynamical mass and cannot be ignored at finite temperature.     

Quantum corrections to instanton calculations in the Abelian Higgs model

In the (1+1)-dimensional Abelian Higgs model we calculate the final state quantum corrections to the fermion number violating cross-section in the background of the instanton. The arising determinants are treated in the Schwinger proper time formalism using some refined approximation techniques which are controlled in several ways and are also applied to the well known case of the quantum double well for comparison.     

Study of （2＋1）-Dimensional Higher-Order Broer-Kaup System

Painleve property and infinite symmetries of the （2＋1）-dimensional higher-order Broer-Kaup （HBK） system are studied in this paper. Using the modified direct method, we derive the theorem of general symmetry gro.ups to （2＋1）-dimensional HBK system. Based on our theorem, some new forms of solutions are obtained. We also find infinite number of conservation laws of the （2＋1）-dimensional HBK system.     

Bosonic zero modes in discretized light-cone field theory

It is shown that for theories with bosonic fields a constrained zero mode is a necessary ingredient for a consistent discretized light-cone quantization (DLCQ). Inclusion of this zero mode is shown to remove a non-covariant, quadratically divergent contribution to the fermion self-energy in 3+1 dimensional Yukawa theory which would otherwise be present. It is further shown to result in a fully consistent set of Heisenberg equations. The possibility of maintaining parity in DLCQ is discussed.     

Fractional charge and automatic U(1) symmetry without domain walls

All fermion representations compatible with fractional charge in asymptotically free SU(N) gauge theories are constructed. With a survival hypothesis argument it is shown that none of them have three light ordinary fermion families. Automatic U(1) symmetry is constructed for each case, but all of them are plagued with domain-wall problems, unresolvable by the Lazarides and Shafi method.     

Conservative Currents of Boundary Charges in AdS2+1 Gravity

The boundary charge which constitutes the Virasoro algebra in (2+1)-dimensional anti-de Sitter gravity is derived by Noether theorem and diffeomorphic invariance. It shows that the boundary charge under discussion recently exhausts all the available independent nontrivial charges. Therefore, for any specific spacetime, the state counting via the central charge of the Virasoro algebra is exact.     

QCD1+1 in the limit of a large number of colors and flavors

QCD in 1+1 dimensions is examined in the limit of a large number of colors and flavors. The Hamiltonian matrix is given in a Fock space spanned by 't Hooft meson states and, for the case of zero fermion mass, a submatrix is diagonalized numerically to give the low-lying spectrum as a function of N_F/N_C. Pair creation effects generate bound states which are complicated mixtures of components of different meson number. There are a number of nontrivial zero modes; in the massive part of the spectrum some states tend to a well-defined N_F N_C limit while others become unstable and disappear. The masses of most states remain remarkably constant over a large range of N_F/N_C.     

Magnetization and dynamically induced finite densities in three-dimensional Chern-Simons QED

In (2 + 1)-dimensional QED with a Chem-Simons term, we show that spontaneous magnetization occurs in the context of finite density vacua, which are the lowest Landau levels fully or half occupied by fermions. Charge condensation is shown to appear so as to complement the fermion anti-fermion condensate, which breaks the flavor U(2N) symmetry and causes fermion mass generation. The solutions to the Schwinger-Dyson gap equation show that the fermion self-energy contributes to the induction of a finite fermion density and/or fermion mass. The magnetization can be supported by charge condensation for theories with the Chem-Simons coefficient κ = Ne²2gp, and κ = Ne²/4π, under the Gauss law constraint. For κ = Ne²/4π, both the magnetic field and the fermion mass are simultaneously generated in the half-filled ground state, which breaks the U(2N) symmetry as well as the Lorentz symmetry.