Effective Gauge Theories of Composite W,Z and Massless Fermions

We have attempted to identify the circumstances under which a weakly coupled massive gauge theory such as the standard Glashow-Salam-Weinberg model, can emerge as a low energy effective Lagrangian of an ASF preon gauge theory. This involves many issues including the interplay between global and local symmetries and sum rules connecting long and short distance physics. The article puts together these issues and demonstrates that ASF preon models can be very tight and predictive frameworks. We make a systematic search of a minimal extension of the standard electro-weak theory, which could emerge as a low energy effective Lagrangian of an ASF preon gauge theory, in which the left-right symmetry is spontaneously broken by vacuum condensation.     

Magnetic Field Instability Driven by Anomalous Magnetic Moments of Massive Fermions and the Electroweak Interaction with Background Matter

A reversible thermotropic phase transition in an adsorption melissic acid film at the interface between n-hexane and an aqueous solution of potassium hydroxide (pH ≈ 10) is investigated by X-ray reflectometry and diffuse scattering using synchrotron radiation. The experimental data indicate that the interface “freezing” transition is accompanied not only by the crystallization of the Gibbs monolayer but also by the formation of a planar smectic structure in the ~300-Å-thick adsorption film; this structure is formed by ~50-Å-thick layers.     

Elliptic Genera of Two-Dimensional {\mathcal{N} = 2} Gauge Theories with Rank-One Gauge Groups

We compute the elliptic genera of two-dimensional ${\mathcal{N} = (2, 2)}$ and ${\mathcal{N} = (0, 2)}$ -gauged linear sigma models via supersymmetric localization, for rank-one gauge groups. The elliptic genus is expressed as a sum over residues of a meromorphic function whose argument is the holonomy of the gauge field along both the spatial and the temporal directions of the torus. We illustrate our formulas by a few examples including the quintic Calabi–Yau, ${\mathcal{N} = (2, 2)}$ SU(2) and O(2) gauge theories coupled to N fundamental chiral multiplets, and a geometric ${\mathcal{N} = (0, 2)}$ model.     

2维SU(NC)格点规范理论中夸克真空凝聚

用改进的Wilson夸克格点哈密顿量和变分法研究2维SU(N_C)规范场中夸克真空凝聚〈ψψ〉与夸克质量m_q和Wilson参数r的依赖关系. 结果表明: 对于给定的r, 当N_C=2,3,4,5,6,7,时, 〈ψψ〉_suba/(gN_C^3/2)的值随m_q的增大而减小. 对于较大的N_C(如N_C>3), 当m_q很小时, 〈ψψ〉_suba(gN_C^3/2)对r的依赖性很小, 但随着m_q的增大, 〈ψψ〉_suba/(gN_C^3/2)对r的依赖性增大, 且〈ψψ〉_suba/(gN_C^3/2)的值随r的增大而增大; 特别是, 当m_q→0时, 本文的格点结果与Zhitnitsky的连续理论分析结果(在弱耦合相中)很好地一致, 这意味着本文在m_q≠0时所得到的结果是可靠的.     

Quark Condensate in Two-Dimensional SU(NC) Lattice Gauge Theory with Massive Wilson Quarks

Using the improved lattice Hamiltonian with massive Wilson quark and the variational method, we study the quark mass m_q and the Wilson parameter r dependences of the quark condensate 〈ψψ〉in the two-dimensional SU(N_C) lattice gauge theory. The numerical results show that when r is given, for N_C=2,3,4,5,6,7, the value of 〈ψψ〉_suba/(gN_C^3/2) decreases as m_q increases. For N_C>3, when m_q is small, 〈ψψ〉_suba/(gN_C^3/2) is almost independent of r; when m_q is large, 〈ψψ〉_suba/(gN_C^3/2)increases with increasing r. Particularly, when m_q→0, our numerical results agree very well with Zhitnitsky's analytical weak coupling result in the continuum, which implys that our numerical results in the case of m_q≠0 are reliable.     

Gauge Symmetry and Transverse Symmetry Transformations in Gauge Theories

The transverse symmetry transformations associated with the normal symmetry transformations are proposed to build the transverse constraints on the basic vertices in gauge theories. I show that, while the BRST symmetry in non-Abelian gauge theory QCD (Quantum Chromodynamics) leads to the Slavnov-Taylor identity for the quark-gluon vertex which constrains the longitudinal part of thevertex, the transverse symmetry transformation associated with the BRST symmetry enables to derive the transverse Slavnov-Taylor identity for the quark-gluon vertex, which constrains the transverse part of the quark-gluon vertex from the gauge symmetry of QCD.     

Gauge Symmetry and Transverse Symmetry Transformations in Gauge Theories

The transverse symmetry transformations associated with the normal symmetry transformations are proposed to build the transverse constraints on the basic vertices in gauge theories. I show that, while the BRST symmetry in non-Abelian gauge theory QCD （Quantum Chromodynamics） leads to the Slavnov-Taylor identity for the quark-gluon vertex which constrains the longitudinal part of the vertex, the transverse symmetry transformation associated with the BRST symmetry enables to derive the transverse Slavnov-Taylor identity for the quark-gluon vertex, which constrains the transverse part of the quark-gluon vertex from the gauge symmetry of QCD.     

A Condensed Matter Interpretation of SM Fermions and Gauge Fields

We present the bundle (Aff(3)⊗ℂ⊗Λ)(ℝ³), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each (ℂ⊗Λ)(ℝ³) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice space (Aff(3)⊗ℂ)(ℤ³). This space allows a simple physical interpretation as a phase space of a lattice of cells. We find the SM SU(3) _c ×SU(2) _L ×U(1) _Y action on (Aff(3)⊗ℂ⊗Λ)(ℝ³) to be a maximal anomaly-free gauge action preserving E(3) symmetry and symplectic structure, which can be constructed using two simple types of gauge-like lattice fields: Wilson gauge fields and correction terms for lattice deformations. The lattice fermion fields we propose to quantize as low energy states of a canonical quantum theory with ℤ₂-degenerated vacuum state. We construct anticommuting fermion operators for the resulting ℤ₂-valued (spin) field theory. A metric theory of gravity compatible with this model is presented too.     

Massive Gauge Fields and the Planck Scale

No Heading The present work is devoted to massive gauge fields in special relativity with two fundamental constants- the velocity of light, and the Planck length, so called doubly special relativity (DSR). The two invariant scales are accounted for by properly modified boost parameters. Within above framework we construct the vector potential as the (1/2, 0) (0, 1/2) direct product, build the associated field strength tensor together with the Dirac spinors and use them to calculate various observables as functions of the Planck length.     

Refined Spinor Technique for Calculation of the Amplitudes of Processes with Massive Fermions

A technique for reducing the matrix elements of the reactions of the interaction of elementary particles with the participation of massive fermions to spinor products is considered. For bispinors describing massive fermions, "spinor" Chisholm identities have been obtained.     

SU(2) Gauge System with Dynamical Fermions in Cumulant Expansion Treatment

The SU(2) lattice gauge system with dynamical Wilson fermions is investigated by the variational cumulant expansion method with the novel criterion to determine the variational parameters. The agreement of calculated order parameter Ep of the pure gauge sector with Monte Carlo data is much improved, especially, in the intermediate coupling region. The fermionic contributions are small to k⁶ hopping parameter expansion, but the general feature is in accordance with the Monte Carlo data qualitatively. The necessity of higher order calculations in the intermediate coupling region is discussed.     

带有质量的Wilson费米子的格点Schwinger模型中M_V对m的变化率的计算

用变分法计算带有质量的Ｗｉｌｓｏｎ费米子的格点Ｓｃｈｗｉｎｇｅｒ模型中矢量介子的质量Ｍ，从而求出Ｍ、对费米子质量ｍ的变化率Ｍｖ／ｍ（ｍ＝０处），结果与连续理论的准确解十分接近．     

Action Principle and Algebraic Approach to Gauge Transformations in Gauge Theories

The action principle is used to derive, by an entirely algebraic approach, gauge transformations of the full vacuum-to-vacuum transition amplitude (generating functional) from the Coulomb gauge to arbitrary covariant gauges and in turn to the celebrated Fock–Schwinger (FS) gauge for the Abelian (QED) gauge theory without recourse to path integrals or to commutation rules and without making use of delta functionals. The interest in the FS gauge, in particular, is that it leads to Faddeev–Popov ghosts-free non-Abelian gauge theories. This method is expected to be applicable to non-Abelian gauge theories including supersymmetric ones.     

Massive Shell Models in the Gravitational Theories with Higher Derivatives

The model of a thin massive shell is investigated in the framework of gravitational theories with fourth-order derivatives. The corresponding jump conditions are derived, and their possible consequences for structure and motion of the matter sources are shortly discussed. The results are compared with the conditions obtained in General Relativity Theory.     

Thermodynamics of the System of Massive Dirac Fermions in a Uniform Magnetic Field

We construct the grand partition function of the system of massive Dirac fermions in a uniform magnetic field from Landau levels,through which all thermodynamic quantities can be obtained.Making use of the Abel-Plana formula,these thermodynamic quantities can be expanded as power series with respect to the dimensionless variable b=2eB/T~2.The zero-field magnetic susceptibility is expanded at zero mass,and the leading order term is logarithmic.We also calculate scalar,vector current,axial vector current and energy-momentum tensor of the system through ensemble average approach.Mass correction to chiral separation effect is discussed.For massless chiral fermions,our results recover the chiral magnetic effect for right-and left-handed fermions,as well as chiral separation effect.     

Nonperturbative Solution of Yukawa Theory and Gauge Theories

Recent progress in the nonperturbative solution of (3 + 1)-dimensional Yukawa theory and quantum electrodynamics and (1 + 1)-dimensional super Yang-Mills theory is summarized.