On Odd Perturbations of Free Fermion Fields

We study the scattering theory of fermion systems subject to a smooth local perturbation with a non-vanishing odd part. We introduce a modified free fermion fields which have an appropriate commutation relations with the free Fock fermion fields. We construct the wave operators using the modified field and prove asymptotic completeness. Our work extends former results on Hilbert space asymptotic completeness.     

Lattice cut-off effects and their reduction in studies of QCD thermodynamics at non-zero temperature and chemical potential

We clarify the relation between the improvement of dispersion relations in the fermion sector of lattice regularized QCD and the improvement of bulk thermodynamic observables. We show that in the infinite temperature limit the cut-off dependence in dispersion relations can be eliminated up to (aⁿ) corrections, if the quark propagator is chosen to be rotationally invariant up to this order. In bulk thermodynamic observables this eliminates cut-off effects up to the same order at vanishing as well as non-vanishing chemical potential. We furthermore show that in the infinite temperature, ideal gas limit the dependence of finite cut-off corrections on the chemical potential is given by Bernoulli polynomials which are universal as they do not depend on a particular discretization scheme. We explicitly calculate leading and next-to-leading order cut-off corrections for some staggered and Wilson fermion type actions and compare these with exact evaluations of the free fermion partition functions. This also includes the chirally invariant overlap and domain wall fermion formulations. PACS  11.15.Ha; 11.10.Wx; 12.38.Gc; 12.38.Mh     

Ultralocal spinor field models

Ultralocal spinor (fermion) field theories are distinguished by the independent temporal development of the field at each spacial point. For a wide class of models explicit operator constructions are given, in a positive definite Hilbert space, for the interacting field, the Hamiltonian, and several other operators. Not only do the fermion field operators fail to fulfill canonical anticommutation relations but associated ultralocal boson fields are required for their realization giving rise to both fermion and boson type excitations. Construction of the Hamiltonian from the field, as well as the transition from the interacting to the noninteracting theories entails various infinite renormalizations that are made explicit. The formulation and solution of these models is based solely on symmetry arguments and general principles, and makes no use whatsoever of cutoffs or perturbation theory.     

CP violation,flavour violation and fermion mass relations in some horizontal gauge theories

Six-quark horizontal gauge models incorporating a natural suppression mechanism for diagonal flavour-changing currents are considered. Some interesting possibilities for CP violation, flavour violation, fermion mass and mixing angle relations in these models are studied.     

Finite element methods for low-dimensional fermion field theories

We examine lattice fermion models based on operator difference equations derived using the method of finite elements, motivated by the absence of species doubling in such formulations. Interacting fermion theories in (0+1) and (1+1) spacetime dimensions are constructed, and shown to be consistent in the sense that suitably defined equal time commutation relations are preserved from timeslice to timeslice. Using weak coupling perturbation theory to calculate the two-point function, we show that the non-locality inherent in the differencing scheme results in a violation of microcasuality in the continuum limit.     

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.     

Bosonization rules in 12 + 1 dimensions

We derive the bosonization rules for free fermions on a half-line with physically sensible boundary conditions for Luttinger fermions. We use path-integral methods to calculate the bosonized fermionic currents on the half-line and derive their commutation relations for a system with a boundary. We compute the fermion determinant of the fermionic fluctuations for a system with a boundary using Forman's approach. We find that the degrees of freedom induced at the boundary do not to modify the commutation relations of the bulk. We give an explicit derivation of the bosonization rules for the fermion operators for a system with boundaries. We derive a set of bosonization rules for the Fermi operators which include the explicit effect of the boundaries and of boundary degrees of freedom. As a byproduct, we calculate the one-particle Green function and determine the effects of the boundaries on its analytic structure.     

The electroweak mixing angle in unified gauge theories

We study in detail the factors that influence the unification relations among the coupling parameters of strong and electroweak interactions. We find that the factor that decides the unification relations in a theory is the fermion content of the theory. The specific ‘observed’ group of strong and electroweak interactions used and the specific unification group in which these interactions are embedded are largely irrelevant. In particular, we find that the unification value of the electroweak mixing angle is the same for almost all models of interest. We also explicitly illustrate that the canonical value 3/8 of the mixing angle is a characteristic result of the currently popular sequential doublets scheme of fermions. Addition of extra fermion singlets reduces the mixing angle to 1/4. We propose this sequential triplets scheme of fermions as an interesting alternative to the current scheme.     

A Groupoidification of the Fermion Algebra

In this paper, we consider the groupoidification of the fermion algebra. We construct a groupoid as the categorical analogues of the fermionic Fock space, and the creation and annihilation operators correspond to spans of groupoids. The categorical fermionic Fock states have some extra structures comparing with the normal forms. We also construct a 2-category of spans of groupoids corresponding to the fermion algebra. The relations of the morphisms in this 2-category are consistent with those in the graphical category which is represented by string diagrams. One may use these formalisms to describe the fermion systems more finely, and study some additional properties of the fermion systems.     

QCD类规范的南部模型中费米子与动力学产生的介子的密度效应

将两味(N_f=2)情况下的QCD类规范的南部模型应用到核物质中并得到了费米子的能隙方程.与四费米子相互作用部分相比,胶子部分对费米子质量约有1/4的贡献.手征序参量与QCD求和规则所预言的结果符合得很好.基于能隙方程,得到了标量与赝标量介子的一系列动力学性质,理论结果很好地符合了实验.     

Fermion theories on a 2d torus with Wilson action improved by Pauli – Villars regularization

Vectorial and anomaly free chiral U(1) fermion models on a 2d finite lattice are considered. It is demonstrated both numerically and analytically that introduction of Pauli – Villars type regularization suppresses the symmetry breaking effects caused by the Wilson term.     

The fermion density operator in the droplet bosonization picture

We derive the phase space particle density operator in the ‘droplet’ picture of bosonization in terms of the boundary operator. We demonstrate that it satisfies the correct algebra and acts on the proper Hilbert space describing the underlying fermion system, and therefore it can be used to bosonize any Hamiltonian or related operator. As a demonstration we show that it reproduces the correct excitation energies for a system of free fermions with arbitrary dispersion relations.     

Preons and SO(10)

Two composite models based on SO(10) are explored, the first containing a fermion and a scalar each in the 16 rep, the second containing two fermion reps 10 + 16. The second model contains a massless composite fermion in the confined picture with a Higgs picture interpretation.     

Conformal invariance,current algebra and modular invariance

A large class of conformally invariant models in two dimensions is realised by constraining free fermion theories. The Fock spaces of the constrained theories are described, using the representation theory of affine Kac-Moody algebras. The results are extended to superconformally invariant theories. Projections of the models, producing consistent two-dimensional field theories, are discussed.     

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.     

Unitarity and modular invariance as constraints on four-dimensional superstrings

It is shown that the requirements of space-time factorization for vertices and one-loop modular invariance guarantee higher-loop modular invariance (as it is presently understood) in the context of string models built out of free fermion fields, either twisted or untwisted. The general solution satisfying these requirements is derived and their relation to the conservation of quantum numbers at general fermionic vertices is discussed. A number of models are discussed using a diagrammatic notation. The natural occurrence in such models of spinor representations which have features in common with the observed quark-lepton multiplets is noted.     

Bosonization rules in dimensions

We derive the bosonization rules for free fermions on a half-line with physically sensible boundary conditions for Luttinger fermions. We use path-integral methods to calculate the bosonized fermionic currents on the half-line and derive their commutation relations for a system with a boundary. We compute the fermion determinant of the fermionic fluctuations for a system with a boundary using Forman's approach. We find that the degrees of freedom induced at the boundary do not to modify the commutation relations of the bulk. We give an explicit derivation of the bosonization rules for the fermion operators for a system with boundaries. We derive a set of bosonization rules for the Fermi operators which include the explicit effect of the boundaries and of boundary degrees of freedom. As a byproduct, we calculate the one-particle Green function and determine the effects of the boundaries on its analytic structure.     

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.     

Simplified test of universality in lattice QCD

A simplified test of universality in lattice QCD is performed by analytically evaluating the continuous Euclidean time limits of various lattice fermion determinants, both with and without a Wilson term to lift the fermion doubling on the Euclidean time axis, and comparing them with each other and with the zeta-regularized fermion determinant in the continuous time-lattice space setting. The determinant relations expected from universality considerations are found to be violated by a certain gauge field-dependent factor; i.e., we uncover a "universality anomaly." The physical significance, or lack thereof, of this factor is a delicate question that remains to be settled.     

The Critical Behavior of the Ising Model on Union Jack Lattice

In this paper, we have investigated the critical behavior of the ferromagnetic Ising model on union jack lattice. The model is equivalent to the eight-vertex model which can be solved as a free fermion model with the free fermion approximation. The critical exponents have been obtained as aα = α = 0, β = β'= 0.125, γ = γ' = 0.875 and δ = δ' = 8.