Exact calculation of the Fermion determinant in chiral QCD2 reflecting the full regularization dependence

The fermion determinant of non-abelian anomalous gauge theory in two space-time dimensions is computed using the path-integral approach. The regularization dependence of the fermion determinant is worked out. Apart from a regularization dependentA ² term, the fermion determinant contains a Wess-Zumino-Witten anomaly functional.     

Anomalous Dimensions of Quark Masses in the Three-Loop Approximation

Physics of Particles and Nuclei Letters - The results of calculation of the three-loop radiative correction to the renormalization constant of fermion masses for non-abelian gauge theory...     

Renormalization and asymptotic behavior in a finite quantum field theory with shadow states

In this paper we present a study of the renormalization problem in a finite quantum field theory with shadow states for a system of a physical scalar field interacting with a physical fermion field. In order to make the theory finite, two fermion shadow fields are introduced. We observe that the stability criterion of renormalization can not be satisfied simultaneously by both physical fields and shadow fields, if the finiteness of the theory is to be maintained. A physical interpretation of this result is given. Furthermore, we find that the effective complete propagators for large space-like momenta behave like free field propagators without the logarithmic factors observed in the non-abelian gauge theory.     

手征QCD2模型的有效拉氏量和质量生成

利用路径积分方法,研究了(1+1)维带γ₅耦合的规范理论。通过进行一非阿贝耳手征变量变换和选择更一般的正规化算子,精确解出了费密子行列式,证明了理论中可以存在玻色子的质量生成机制。除了一质量项外,得到的解也包含有一规范化的Wess-Zumino-Witten反常作用量泛函和一些别的非定域项。 关键词：     

Gauging of chiral bosonized actions

We present bosonic actions which are equivalent to various chiral fermion theories. For the case of one chiral fermion coupled to an abelian gauge field, we present two bosonized actions, one corresponding to regularizing in the vector conserving scheme and the other in the left-right scheme. We then propose an action for the non-abelian bosonization of Weyl fermions which is a WZW action coupled to a fixed curved background. The chiral WZW action is then coupled to non-abelian gauge fields. We derive the anomalies of the axial current (in the vector conserving scheme) and the left-right currents (in the left-right regularization scheme), both for the abelian and non-abelian bosonized actions. The expressions for the anomalies are identical to those derived in the corresponding fermionic theories.     

An explicit example of a tumbling gauge theory

We present a class of two-dimensional models with a non-abelian gauge symmetry. In one model with gauge symmetry is dynamically broken by a fermion bilinear condensate in a $\text{1}\text{n}$ expansion. We discuss the differences between a dynamical and elementary Higgs mechanism due to the presence of a non-abelian axial anomaly.     

Instantons and the U(1) problem

If instantons spontaneously break the chiral SU(N) × SU(N) symmetry of a non-abelian gauge theory, they break U(1) symmetry in a manner consistent with the chiral Ward identities of the theory. Excitations of the fermion vacuum play a crucial role in this process. A model calculation of the symmetry breaking effect shows a phenomenological structure which differs from that provided by models with many color degrees of freedom.     

Composite vector fields and tumbling gauge theories

In non-abelian gauge theories with a non-real fermion content it is possible that vector channels become more attractive than the most attractive scalar channel. It is speculated that the appearance of a vector condensate may signal the presence of massless composite vector fields which gauge a flavour symmetry of the underlying model, as is suggested by earlier work on non-linear spinor models.     

Approaches to a non-abelian antisymmetric tensor gauge field theory

Two distinct attempts at constructing a theory of non-abelian antisymmetric tensor gauge fields (ATGF's) are considered. First, a recently proposed geometry of abelian ATGF's is reviewed and then generalized to the non-abelian case. The resulting geometric action is non-local and is invariant under non-local gauge transformations; in the local limit the action describes free fields. Lattice actions for both the abelian and non-abelian ATGF theories are also presented. In the second approach, a lattice action for non-abelian ATGF's is constructed using a plaquette variables that carry four internal indices. The continuum limit is also a non-interacting theory.     

Non-abelian Gauge Symmetry for Fields in Phase Space: a Realization of the Seiberg-Witten Non-abelian Gauge Theory

The Seiberg-Witten formalism has been realized as an electrodynamics in phase space (associated to the Dirac equation written in phase space) and this fact is explored here with non-abelian gauge group. First, a physically heuristic presentation of the Seiberg-Witten approach is carried out for non-abelian gauge in order to guide the calculation procedures. These results are realized by starting with the Lagrangian density for the free Dirac field in phase space. Then a field strength is derived, where the non-abelian gauge group is the SU(2), corresponding to an isospin (non-abelian) field theory in phase space. An application to nucleon is then discussed.

     

String Geometry and the Noncommutative Torus

We construct a new gauge theory on a pair of d-dimensional noncommutative tori. The latter comes from an intimate relationship between the noncommutative geometry associated with a lattice vertex operator algebra ? and the noncommutative torus. We show that the tachyon algebra of ? is naturally isomorphic to a class of twisted modules representing quantum deformations of the algebra of functions on the torus. We construct the corresponding real spectral triples and determine their Morita equivalence classes using string duality arguments. These constructions yield simple proofs of the O(d,d;ℤ) Morita equivalences between d-dimensional noncommutative tori and give a natural physical interpretation of them in terms of the target space duality group of toroidally compactified string theory. We classify the automorphisms of the twisted modules and construct the most general gauge theory which is invariant under the automorphism group. We compute bosonic and fermionic actions associated with these gauge theories and show that they are explicitly duality-symmetric. The duality-invariant gauge theory is manifestly covariant but contains highly non-local interactions. We show that it also admits a new sort of particle-antiparticle duality which enables the construction of instanton field configurations in any dimension. The duality non-symmetric on-shell projection of the field theory is shown to coincide with the standard non-abelian Yang–Mills gauge theory minimally coupled to massive Dirac fermion fields. Received: 26 October 1998/ Accepted: 9 April 1999     

Phase factors,point-splitting regularisation and chiral anomalies

A method is proposed to construct the path-independent form of phase factors pertaining to non-abelian gauge theories. It is found that the original form of the phase factor, as envisaged by Schwinger, is reproduced for a straight path. As an illustration of its use this work is applied, within the framework of point-splitting regularisation, to obtain the familiar axial anomaly in a pure vector gauge theory. Subtleties associated with the treatment of the vector gauge current are also discussed. Finally, the scheme of computations is employed to derive the covariant and consistent anomalies in a non-abelian chiral gauge theory in arbitrary even dimensions.     

Gauge Covariant Fermion Propagator in the Presence of Arbitrary External Gauge Field and Its Schwinger--Dyson Equation

Gauge covariance for Green＇s functions of a gauge theory through a fermion propagator in the presence of arbitrary external gauge field is proven and a formalism of gauge and Lorentz covariant Schwinger-Dyson equation for the fermion propagator with external gauge field is built up within ladder approximation.     

The fermion determinant in two dimensional Minkowski space: Zeros and related properties

We present a detailed analysis of the non-abelian determinant of massless fermions in two dimensional Minkowski space. In the framework of the external field problem, the determinant vanishes if the out- and ingoing vacua are orthogonal; the gauge potentials for which this happens are identified. Causality implies that the effective action obtained from the sum of fermion loops has the right singularity at a zero of the determinant. Such a zero can be reached by a continuous deformation of a potential with non-vanishing determinant. The set of zeros exhibits a rich structure.Work partially supported by the Swiss National Science Foundation     

Maximal symmetry and mass generation of Dirac fermions and gravitational gauge field theory in six-dimensional spacetime

The relativistic Dirac equation in four-dimensional spacetime reveals a coherent relation between the dimensions of spacetime and the degrees of freedom of fermionic spinors. A massless Dirac fermion generates new symmetries corresponding to chirality spin and charge spin as well as conformal scaling transformations. With the introduction of intrinsic W-parity, a massless Dirac fermion can be treated as a Majorana-type or Weyl-type spinor in a six-dimensional spacetime that reflects the intrinsic quantum numbers of chirality spin. A generalized Dirac equation is obtained in the six-dimensional spacetime with a maximal symmetry. Based on the framework of gravitational quantum field theory proposed in Ref. [1] with the postulate of gauge invariance and coordinate independence, we arrive at a maximally symmetric gravitational gauge field theory for the massless Dirac fermion in six-dimensional spacetime. Such a theory is governed by the local spin gauge symmetry SP(1,5) and the global Poincar′e symmetry P(1,5)= SO(1,5) P~(1,5) as well as the charge spin gauge symmetry SU(2). The theory leads to the prediction of doubly electrically charged bosons. A scalar field and conformal scaling gauge field are introduced to maintain both global and local conformal scaling symmetries. A generalized gravitational Dirac equation for the massless Dirac fermion is derived in the six-dimensional spacetime. The equations of motion for gauge fields are obtained with conserved currents in the presence of gravitational effects. The dynamics of the gauge-type gravifield as a Goldstone-like boson is shown to be governed by a conserved energy-momentum tensor, and its symmetric part provides a generalized Einstein equation of gravity. An alternative geometrical symmetry breaking mechanism for the mass generation of Dirac fermions is demonstrated.     

含外规范场和动力学费米子自能的狄拉克算符及费米子凝聚

将非阿贝尔规范理论中狄拉克算符行列式的计算从传统的只能含有硬费米子质量项的情况推广到可以含有动量相关的费米子自能的情况，并且行列式与费米子凝聚的计算都被推广到使之能够含有任意的外规范场. 关键词： 费米子自能 外规范场 狄拉克算符的行列式 费米子凝聚     

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.     

Renormalization of non-abelian gauge theories in curved space-time

We use indirect, renormalization group arguments to calculate the gravitational counterterms needed to renormalize an interacting non-abelian gauge theory in curved space-time. This method makes it straightforward to calculate terms in the trace anomaly which first appear at high order in the coupling constant, some of which would need a 4-loop calculation to find directly. The role of gauge invariance in the theory is considered, and we discuss briefly the effect of using coordinate-dependent gauge-fixing terms. We conclude by suggesting possible applications of this work to models of the very early universe.     

On spin three self interactions

In this paper we start the construction of a self interacting massless spin three field theory. The first order self interaction is constructed. The free field gauge invariance is modified by a term of first order in the coupling constant. Finally the abelian gauge transformation of the free Lagrangian is shown to become non-abelian.     

Quantization and unitary in antisymmetric tensor gauge theories

Following the procedure of Batalin and Vilkovisky we discuss the quantization of a non-abelian antisymmetric tensor gauge theory and describe the verification of one-loop unitarity for the quantized model, using the Ward identities and the procedure of 't Hooft and Veltman. The quantization of this system is similar to that of the Witten string field theory, requiring among other things the presence of three-ghost couplings.