有效拉氏量理论

按照现代场论观点,所有现在所用的描述现实相互作用的理论都是某种更基本的理论的有效理论,有效理论的一个主要特点是其相互作用项一般是无穷多项.它与通常的可重整场论有很大差别.这里主要讨论一类特殊的有效理论——强作用手征有效拉氏量的理论特点及研究现状.没有涉及强作用中重夸克有效场论理论,NRQCD理论及它们与手征有效拉氏量结合而形成的理论.     

Chiral models: Geometrical aspects

Two-dimensional classical chiral models of field theory are considered, the main attention being paid on geometrical aspects of such theories.A characteristic feature of these models is that the interaction is inserted not by adding the interaction Lagrangian to the free field Lagrangian, but has a purely geometrical origin and is related to the inner curvature of the manifold.These models are in many respects analogous to non-Abelian gauge theories and as became clear recently, they are also important for the superstring theory which nowadays is the most probable candidate for a truly unified theory of all interactions including gravitation.     

Derivation of an effective Lagrangian from a generalized scalar curvature

A spinor Lagrangian invariant under global coordinate, local Lorentz and local chiral SU(n) × SU(n) gauge transformations is presented. The invariance requirement necessitates the introduction of boson fields, and a theory for these fields is then developed by relating them to generalizations of the vector connections in general relativity and utilizing an expanded scalar curvature as a boson Lagrangian. In implementing this plan, the local Lorentz group is found to greatly facilitate the correlation of the boson fields occurring in the spinor Lagrangian with the generalized vector connections.The independent boson fields of the theory are assumed to be the inhomogeneously transforming irreducible parts of the connections. It turns out that no homogeneously transforming parts are necessary to reproduce the chiral Lagrangian usually used as a basis for phenomenological field theories. The Lagrangian in question appears when the gravitational interaction is turned off. It includes pseudoscalar, spinor, vector, and axial vector fields, and the vector fields carry mass in spite of the fact that the theory is locally gauge invariant.     

New Terms for Compact Form of Electroweak Chiral Lagrangian

The compact form of the electroweak chiral Lagrangian is a reformulation of its original form and is expressed in terms of chiral rotated electroweak gauge fields, which is crucial for relating the information of underlying theories to the coefficients of the low-energy effective Lagrangian. However the compact form obtained in previous works is not complete. In this letter we add several new chiral invariant terms to it and discuss the contributions of these terms to the original electroweak chiral Lagrangian.     

Derivation of Effective Chiral Lagrangian Involving PSGB and Vector Bosons from QCD

The effective chiral Lagrangian for a matter field content consisting of pseudo-scalar Goldstone bosons and vector bosons (with hidden symmetry) is derived from the underlying QCD theory. No approximations are made. All the free parameters of the effective chiral Lagrangian are expressed in terms of QCD-based Green's functions. These may be regarded as the QCD definitions of these Lagrangian coefficients.     

Derivation of the Bosonic Part of the Electroweak Chiral Lagrangian from a General Underlying Technicolor Theory

Bosonic part of SU(2)L U(1)Y effective chiral Lagrangian for electroweak symmetry breaking is derived from an underlying technicolor theory with no approximation. The underlying theory is assumed to be the most general gauge theory without fundamental scalars. A condensate is required to exist in the theory which breaks SU(2)L U(1)Y dynamically to U(1)em and the anomaly of the theory caused by gauge interaction must be cancelled. The formulation offers general definitions in terms of underlying theory for the low energy constants in effective chiral Lagrangian.``     

STRONG INTERACTION AND CHIRAL GAUGE FIELD

The concept of e^{iα（x）γ_s} local gauge transformation is introduced in this article. The chiral gauge invariant Lagrangian is given. The relationship between chiral gauge field and strong interaction is also discussed. In a special condition, we obtain the effective Lagrangian for V-A type strong interaction.     

Effective field theories, Landau-Migdal Fermi liquid theory, and effective chiral Lagrangians for nuclear matter

We reinterpret Landau-Migdal Fermi liquid theory of nuclear matter as an effective chiral field theory with a Fermi surface. The effective field theory is formulated in terms of a chiral Lagrangian with its mass and coupling parameters scaling à la Brown-Rho and with the Landau-Migdal parameters identified as the fixed points of the field theory. We show how this mapping works out for response functions to the EM vector current and, then using the same reasoning, make a prediction on nuclear axial current, in particular on the enhanced axial-charge transitions in heavy nuclei. We speculate on how to extrapolate the resulting theory, which appears to be sound both theoretically and empirically up to normal nuclear-matter density r₀, to hitherto unexplored higher density regime relevant to relativistic heavy-ion processes and to cold compact (neutron) stars.     

SOLUTION OF CHIRAL QCD2 IN 1+1 DIMENSIONAL CURVED SPACETIME

The effective Lagrangian of chiral QCD₂ in 1+1 dimensional curved spacetime is derived by using pathintegral approach.It is shown that vector bosons may have a mass generation and interaction of gravity with gauge field may exist.Besides,the effective Lagrangian contains a term corresponding to the analog of the gauged Wess-Zumino-Witten term in 2-dimensional flat space-time.     

Nuclear mean field from chirally symmetric effective theory

The mean-field theory of the nuclear many-body problem proposed recently by Furnstahl, Serot, and Tang (FST) is discussed. The FST chiral Lagrangian is derived in terms of an effective field theory. This new approach allows one to construct in a controlled manner the universal nuclear Lagrangian consistent with symmetries of QCD. The FST Lagrangian is constructed by using power counting, i.e., the expansion in powers of the lowest lying hadronic fields and their derivatives. Terms in the Lagrangian are organized by applying Georgi’s naive dimensional analysis and “naturalness” condition. The relevant degrees of freedom are nucleons, pions, an isoscalar-vector field ω meson), an isoscalar-scalar field (σ meson), and an isovector-vector field (ρ meson). The chiral symmetry is realized nonlinearly using a standard WCCWZ procedure.     

Derivation of the Bosonic Part of the Electroweak Chiral Lagrangian from a General Underlying Technicolor Theory

Bosonic part of SU(2)_L\otimes U(1)_Y effective chiral Lagrangian for electroweak symmetry breaking is derived from an underlying technicolor theory with no approximation. The underlying theory is assumed to be the most general gauge theory without fundamental scalars. A condensate is required to exist in the theory which breaks SU(2)_L\otimes U(1)_Y dynamically to U(1)_em and the anomaly of the theory caused by gauge interaction must be cancelled. The formulation offers general definitions in terms of underlying theory for the low energy constants in effective chiral Lagrangian.     

On the effective potential in higher-derivatives superfield theories

We study the one-loop quantum corrections for higher-derivative superfield theories, generalizing the approach for calculating the superfield effective potential. In particular, we calculate the effective potential for two versions of higher-derivative chiral superfield models. We point out that the equivalence of the higher-derivative theory for the chiral superfield and the one without higher derivatives but with an extended number of chiral superfields occurs only when the mass term is contained in the general Lagrangian. The presence of divergences can be taken as an indication of that equivalence.     

Universality of the rho meson coupling in effective field theory

It is shown that both the universal coupling of the rho meson and the Kawarabayashi-Suzuki-Riadzuddin-Fayyazuddin expression for the magnitude of its coupling constant follow from the requirement that chiral perturbation theory of pions, nucleons, and rho mesons is a consistent effective field theory. The prerequisite of the derivation is that all ultraviolet divergences can be absorbed in the redefinition of fields and the available parameters of the most general effective Lagrangian.     

Perturbation theory in terms of superfields and its application to gauge theories

We formulate a perturbation theory in terms of superfields for Lagrangian field theories which are expressable by chiral or general scalar superfields. Especially we consider the generalized QED model of Wess and Zumino where an additional local gauge symmetry is present. Our calculations are manifestly covariant with respect to supersymmetry and local gauge transformations.     

Bott periodicity and realizations of chiral symmetry in arbitrary dimensions

We compute the chiral symmetries of the Lagrangian for confining “vector-like” gauge theories with massless fermions in d-dimensional Minkowski space and, under a few reasonable assumptions, determine the form of the quadratic fermion condensates which arise through spontaneous breaking of these symmetries. We find that for each type (complex, real, or pseudoreal) of representation of the gauge group carried by the fermions, the chiral symmetries of the Lagrangian, as well as the residual symmetries after dynamical breaking, exactly follow the pattern of Bott periodicity as the dimension changes. The consequences of this for the topological features of the low-energy effective theory are considered.     

Holographic correspondence in topological superconductors

We analytically derive a compatible family of effective field theories that uniquely describe topological superconductors in 3D, their 2D boundary and their 1D defect lines. We start by deriving the topological field theory of a 3D topological superconductor in class DIII, which is consistent with its symmetries. Then we identify the effective theory of a 2D topological superconductor in class D living on the gapped boundary of the 3D system. By employing the holographic correspondence we derive the effective chiral conformal field theory that describes the gapless modes living on the defect lines or effective boundary of the class D topological superconductor. We demonstrate that the chiral central charge is given in terms of the 3D winding number of the bulk which by its turn is equal to the Chern number of its gapped boundary.     

Gauge invariant theories of the generalized chiral Schwinger model

The gauge invariant theories of the generalized chiral Schwinger model are constructed in terms of two schemes with and without Wess-Zumino terms, respectively. Following the former scheme, we calculate the Wess-Zumino term which cancels the gauge anomaly, and then constitute the gauge invariant theory by adding the Wess-Zumino term to the original Lagrangian of the model. According to the latter, we modify the original Hamiltonian by adding a term composed of constraints of the model. It is so designed that the theory described by the modified Hamiltonian and its corresponding first-order Lagrangian maintains gauge invariance. We show by the canonical Dirac method that each of the two gauge invariant theories has the same physical spectrum as that of the original gauge noninvariant formulation.     

Gauge invariant theories of the generalized chiral Schwinger model

The gauge invariant theories of the generalized chiral Schwinger model are constructed in terms of two schemes with and without Wess-Zumino terms, respectively. Following the former scheme, we calculate the Wess-Zumino term which cancels the gauge anomaly, and then constitute the gauge invariant theory by adding the Wess-Zumino term to the original Lagrangian of the model. According to the latter, we modify the original Hamiltonian by adding a term composed of constraints of the model. It is so designed that the theory described by the modified Hamiltonian and its corresponding first-order Lagrangian maintains gauge invariance. We show by the canonical Dirac method that each of the two gauge invariant theories has the same physical spectrum as that of the original gauge noninvariant formulation.     

The Lee–Wick fields out of gravity

We study the Maxwell–Einstein theory in the framework of effective field theories. We show that the modified one-loop renormalizable Lagrangian due to quantum gravitational effects contains a Lee–Wick vector field as an extra degree of freedom in the theory. Thus gravity provides a natural mechanism for the emergence of this exotic particle.