Effective Action for Noncommutative U（1） Gauge Theory with Higher Dimensional Terms

In this paper we apply the assumption of our recent work in noncommutative scalar models to the noncommutative U（1） gauge theories. This assumption is that the noneommutative effects start to be visible continuously from a scale ANC and that below this scale the theory is a commutative one. Based on this assumption and using background field method and loop calculations, an effective action is derived for noncommutative U（1） gauge theory. It will be shown that the corresponding low energy effective theory is asymptotically free and that under this condition the noncommutative quadratic IR divergences will not appear. The effective theory contains higher dimensional terms, which become more important at high energies. These terms predict an elastic photon-photon scattering due to the noncommutativity of space. The coefficients of these higher dimensional terms also satisfy a positivity constraint indicating that in this theory the related diseases of superluminal signal propagating and bad analytic properties of S-matrix do not exist. In the last section, we will apply our method to the noncommutative extra dimension theories.     

Decomposition of Noncommutative U(1) Gauge Potential

We investigate the decomposition of noncommutative gauge potential Â_i, and find that it has inner structure, namely, Â_i can be decomposed in two parts, hat{b}_i and â_i, where hat{b}_i satisfies gauge transformations while â_i satisfies adjoint transformations, so dose the Seiberg-Witten mapping of noncommutative U(1) gauge potential. By means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U(1) gauge potential and its gauge field tensor can be expressed in terms of the unit vector field. When the unit vector field has no singularity point, noncommutative gauge potential and gauge field tensor will equal ordinary gauge potential and gauge field tensor     

用独立元格等效作用量研究三维U(1)格点规范理论的相结构

在格点规范理论中,应用变分累积展开方法,引入独立元格等效作用量,研究了三维U(1)格点规范理论的元格内能,得到连续的内能曲线,与Monte Carlo(MC)数据相符,表明理论是禁闭的.     

The Geometric Construction of WZW Effective Action in Noncommutative Manifold

By constructing close-one-cochain density Ω^12n in the gauge group space we get the Wess-Zumino-Witten (WZW) effective Lagrangian on high-dimensional noncommutative space.Especially consistent anomalies derived from this WZW effective action in noncommutative four-dimensional space coincide with those obtained by L.Bonora etc.(het-th/0002210).     

Gauge Theory on a Discrete Noncommutative Space

In this paper, we apply Connes' noncommutative geometry and the Seiberg—Witten map to a discrete noncommutative space consisting of n copies of a given noncommutative space R ^m . The explicit action functional of gauge fields on this discrete noncommutative space is obtained.     

SU(3) Local Gauge Field Theory as Effective Dynamics of Composite Gluons

The effective dynamics of quarks is described by a nonperturbatively regularized NJL model equation with canonical quantization and probability interpretation. The quantum theory of this model is formulated in functional space and the gluons are considered as relativistic bound states of colored quark-antiquark pairs. Their wave functions are calculated as eigenstates of hardcore equations, and their effective dynamics is derived by weak mapping in functional space. This leads to the phenomenological SU(3) gauge invariant gluon equations in functional formulation, i.e., the local gauge symmetry is a dynamical effect resulting from the dynamics of the quark model.     

One-loop renormalizability of noncommutative U(1) gaugetheory with scalar fields

This paper uses the background field method to calculate one-loop divergent corrections to the gauge field propagators in noncommutative U(1) gauge theory with scalar fields. It shows that for a massless scalar field, the gauge field propagators are renormalizable to θ²-order, but for a massive scalar field they are renormalizable only to θ-order.     

Quantum Field Theory with a Minimal Length Induced from Noncommutative Space

From the inspection of noncommutative quantum mechanics, we obtain an approximate equivalent relation for the energy dependence of the Planck constant in the noncommutative space, which means a minimal length of the space. We find that this relation is reasonable and it can inherit the main properties of the noncommutative space. Based on this relation, we derive the modified Klein-Gordon equation and Dirac equation. We investigate the scalar field and φ4 model and then quantum electrodynamics in our theory, and derive the corresponding Feynman rules. These results may be considered as reasonable approximations to those of noncommutative quantum field theory. Our theory also shows a connection between the space with a minimal length and the noncommutative space.     

Supersymmetric U(1) Gauge Field Theory with Massive Gauge Field

A new mechanism to introduce the mass of U(1) gauge field in supcrsymmctric U(1) gauge theory is discussed.The modelhas the strict local U(1) gauge symmetry and supersymmetry.Because we introduce two vector superfields simultaneously,the model contains a massive U(1) gauge field as well as a massless U(1) gauge field.     

Letter: Perturbative Evaluation of the Effective Action for a Self-Interacting Conformal Field on a Manifold with Boundary

In a series of three projects a new technique which allows for higher-loop renormalisation on a manifold with boundary has been developed and used in order to assess the effects of the boundary on the dynamical behaviour of the theory. Commencing with a conceptual approach to the theoretical underpinnings of the, underlying, spherical formulation of Euclidean Quantum Field Theory this overview presents an outline of the stated technique's conceptual development, mathematical formalism and physical significance.     

Unification of Non-Abelian SU(N) Gauge Theory and Gravitational Gauge Theory

In this paper, a general theory on unification of non-Abelian SU(N) gauge interactions and gravitationalinteractions is discussed. SU(N) gauge interactions and gravitational interactions are formulated on the similar basisand are unified in a semi-direct product group GSU(N). Based on this model, we can discuss unification of fundamentalinteractions of Nature.     

Variational Cumulant Expansion Study of Z(N) Lattice Gauge Theory with Symanzik's Improved Action

With the variational cumulant expansion (VCE) method, the internal energy and the specific heat of the Z(N) lattice gauge theory with Symanzik's improved action are calculated up to the third order. The variational parameter is determined by the main valued method and the result is compared with the VCE result for standard Wilson action. Furthermore, the changes are compared with those of the SU(2) case.     

Magnetic Monopoles in U(1)4 Lattice Gauge Theory with Wilson Action

We construct the Euclidean Green functions for the soliton (magnetic monopole) field in the U(1)₄ Lattice Gauge Theory with Wilson action. We show that in the strong coupling regime there is monopole condensation while in the QED phase the physical Hilbert space splits into orthogonal soliton sectors labeled by integer magnetic charge. Received: 2 July 1997 / Accepted: 20 July 1998     

Effective Field Theory for Fermi Systems in a Large N Expansion

A system of fermions with short-range interactions at finite density is studied using the framework of effective field theory. The effective action formalism for fermions with auxiliary fields leads to a loop expansion in which particle-hole bubbles are resummed to all orders. For spin-independent interactions, the loop expansion is equivalent to a systematic expansion in 1/N, where N is the spin-isospin degeneracy g. Numerical results at next-to-leading order are presented and the connection to the Bose limit of this system is elucidated.     

Cornwall-Jackiw-Tomboulis Effective Potential for Quark Propagator in Real-Time Thermal Field Theory and Landau Gauge

We complete the derivation of the Cornwall-Jackiw-Tomboulis effective potentiM for quark propagator at finite temperature and finite quark chemical potential in the real-time formalism of thermal field theory and in Landau gauge. In the approximation that the function A（p^2） in inverse quark propagator is replaced by unity, by means of the running gauge coupling and the quark mass function invariant under the renormalization group in zero temperature Quantum Chromadynamics （QCD）, we obtain a calculable expression for the thermal effective potential, which will be a useful means to research chiral phase transition in QCD in the real-time formalism.     

Cornwall-Jackiw-Tomboulis Effective Potential for Quark Propagator in Real-Time Thermal Field Theory and Landau Gauge

We complete the derivation of the Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperature and finite quark chemical potential in the real-time formalism of thermal field theory and in Landau gauge. In the approximation that the function A(p2) in inverse quark propagator is replaced by unity, by means of the running gauge coupling and the quark mass function invariant under the renormalization group in zero temperature Quantum Chromadynamics (QCD), we obtain a calculable expression for the thermal effective potential, which will be a useful means to research chiral phase transition in QCD in the real-time formalism.     

Two-Particle Irreducible Effective Action in Gauge Theories

The goal of this paper is to develop the formalism of the two-particle irreducible (2PI) (G. Baym (1962). Physical Review 127, 1391; H. D. Dahmen and G. Jona Lasino (1962). Nuovo Cimento A 52, 807; C. de Dominicis and P. Martin (1964). Journal of Mathematical Physics 5, 14; J. Luttinger and J. Ward (1960). Physical Review 118, 1417; B. Vanderheyden and G. Baym (1998). Journal of Statistical Physics 98, 843; B. Vanderheyden and G. Baym (2000). In Progress in Nonequilibrium Green's Functions, World Scientific, Singapore). (or Cornwall–Jackiw–Tomboulis (CJT) (J. Cornwall, R. Jackiw, and E. Tomboulis (1974). Physical Review D 10, 2428; U. Kraemmer and A. Rebhan (2004). Reports on Progress in Physics 67, 351; R. Norton and J. Cornwall (1975). Annals of Physics 91, 106) effective action (EA) in a way appropiate to its application to nonequilibrium gauge theories. We hope this review article will stimulate new work into this field.     

U(1)规范理论的定量分析

在Migdal及Migdal-Kadanoff交换方案基础上导出了重整化群方程、并将其应用到Wilson形式的U(1)格点规范理论,给出了强耦合区,弱耦合区及临界耦合点,中间耦合区的数值结果.这些结果与严格的强耦合展开,弱耦合展开及Monte Carlo模拟结果一致.从而说明:本文得到的重整化群方程在讨论规范理论的非微扰特性方面是可行而有效的.     

2+1维SU(3)格点纯规范场的真空态计算

用连续极限截断的格点本征值方法^[1],研究2+1维SU(3)的格点规范理论的真空态.在强耦合区,上述方法的结果与强耦合展开一致.在过渡区,上述方法的结果显示出较好的标度行为.     

有限温度格点U(1)及定模U(1)–Higgs模型Symanzik作用量的解析研究

用变分累积展开方法(VCE)解析研究了Symanzik作用量形式的有限温度格点U(1)及定模U(1)-Higgs规范模型,并计算了序参量Polyakov线及临界指数β.结果表明,采用Symanzik作用量的变分累积展开比Wilson作用量收敛快.