Broken conformal ward identities in non-abelian gauge theories

Integrated broken conformal Ward identities for non-abelian gauge theories are derived. There exist anomalous terms linked to the ones in the Callan-Symanzik equations. Also there is a gauge dependent term that can be predicted classically and a new term involving Faddeev-Popov ghosts. These two terms cannot be neglected asymptotically relative to the other terms for gauge variant Greens functions.     

Gauge transformation between retarded and multipolar gauges

The gauge function, expressed in terms of the sources, required for a gauge transformation between the retarded electromagnetic gauge and the three-vector version of the multipolar gauge is obtained.     

On the Definition of Gauge Transformations in Gauge Theory

The different types of gauge transformations in gauge theory are discerned and defined in fiber bundle terms. The gauge gravitation case is analysed in order to examine various versions of the gauge gravitation theory.     

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.     

Invariance of fermion determinant under large gauge transformations

We argue that in the perturbative framework the natural symmetry of the fermionic determinant is the perturbative gauge transformation (p.g.t.) which differs from the usual gauge transformation of the effective action through the absence of terms independent of the coupling constant. Calculated in a non-perturbative framework appropriate for large gauge function, the sum of these latter terms vanish. In three dimensions the invariance of the full fermion determinant under large gauge transformations is thus ensured due to the invariance under p.g.t. of the Chern-Simons term arising in some perturbative regularisations.     

On Schwinger terms in nonabelian chiral gauge theories

Chiral fermionic currents, coupled with nonabelian background gauge fields, are known to have Schwinger terms in their commutators. It is shown that if the gauge group is semisimple, the anomaly is completely determined by these Schwinger terms. Violation of Jacobi identities can also be demonstrated using them.     

SU(2) Lattice Gauge Theory Formulation of the (2+1)-Dimensional Antiferromagnetic Heisenberg Model

The equivalence of 2+1 antiferromagnetic Heisenberg model and the SU(2) Kogut Susskind lattice gauge theory is recapitulated and the naive Euclidean lattice action of the threedimensional an tiferromagnetic Heisen berg model is derived. The three-dimensional lattice gauge fermion theory is formulated to give the consistent lattice gauge theory of antiferromagnetic Heisenberg model. In continu um limit the two copies of two flavor fermions are resulted, which give the negative results of the microscopic derivation of the Chern-Simons terms. The Chern-Simons terms, the gauge invariant problem of effective action and the '%hiralityn are discussed.     

The question of gauge dependence of transition probabilities in quantum mechanics: Facts,myths and misunderstandings

We show that, in terms of physical observables, transition probabilities in quantum mechanics can be calculated in a truly gauge invariant way, i.e., independent of the choice of gauge and that recent arguments for the preference of a particular gauge are due to misconceptions.     

The free energy of lattice gauge theories at large β

An upper and a lower bound for the free energy density of a lattice gauge teory with compact gauge group are derived, valid for all values of β. For large β the first two terms of the asymptotic expansions of these bounds coincide, thus determining the corresponding terms of the free energy density. Moreover the gauge groups U(N) and SU(N) are treated explicitly.     

Non-collinearity in high energy processes

We discuss the treatment of intrinsic transverse momenta in high energy scattering processes. Within the field theoretical framework of QCD, the process is described in terms of correlators containing quark and gluon fields. The correlators, parametrized in terms of distribution and fragmentation functions, contain matrix elements of nonlocal field configurations requiring a careful treatment to assure colour gauge invariance. It leads to nontrivial gauge links connecting the parton fields. For the transverse momentum-dependent correlators the gauge links give rise to time reversal odd phenomena, showing up as single spin and azimuthal asymmetries. The gauge links, arising from multi-gluon initial and final state interactions, depend on the colour flow in the process, challenging universality.      

Superalgebras in N = 1 gauge theories

N = 1 supersymmetric gauge theories with global flavor symmetries contain a gauge invariant W-superalgebra which acts on its moduli space of gauge invariants. With adjoint matter, this superalgebra reduces to a graded Lie algebra. When the gauge group is SO(n_c), with vector matter, it is a W-algebra, and the primary invariants form one of its representation. The same superalgebra exists in the dual theory, but its construction in terms of the dual fields suggests that duality may be understood in terms of a charge conjugation within the algebra. We extend the analysis to the gauge group E₆.     

CFT adapted gauge invariant formulation of arbitrary spin fields in AdS and modified de Donder gauge

Using Poincaré parametrization of AdS space, we study totally symmetric arbitrary spin massless fields in AdS space of dimension greater than or equal to four. CFT adapted gauge invariant formulation for such fields is developed. Gauge symmetries are realized similarly to the ones of Stueckelberg formulation of massive fields. We demonstrate that the curvature and radial coordinate contributions to the gauge transformation and Lagrangian of the AdS fields can be expressed in terms of ladder operators. Realization of the global AdS symmetries in the conformal algebra basis is obtained. Modified de Donder gauge leading to simple gauge fixed Lagrangian is found. The modified de Donder gauge leads to decoupled equations of motion which can easily be solved in terms of the Bessel function. Interrelations between our approach to the massless AdS fields and the Stueckelberg approach to massive fields in flat space are discussed.     

On the Gauge and BRST Invariance of the Chiral QED with Faddeevian Anomaly

Chiral Schwinger model with the Faddeevian anomaly is considered. It is found that imposing a chiral constraint this model can be expressed in terms of chiral boson. The model when expressed in terms of chiral boson remains anomalous and the Gauss law of which gives anomalous Poisson brackets between itself. In spite of that a systematic BRST quantization is possible. The Wess-Zumino term corresponding to this theory appears automatically during the process of quantization. A gauge invariant reformulation of this model is also constructed. Unlike the former one gauge invariance is done here without any extension of phase space. This gauge invariant version maps onto the vector Schwinger model. The gauge invariant version of the chiral Schwinger model for a=2 has a massive field with identical mass however gauge invariant version obtained here does not map on to that.     

Soft gauge algebras

Gauge transformations whose algebra closes only modulo field dependent terms (soft gauge algebras) are studied in detail. The results are explicitly applied to a supersymmetric gauge theory, to gravity and to conformal gravity, all seen as gauge theories overx-space; the obvious applications to supergravity are pointed out. A consistency requirement for the gauge transformations of those fields which appear in the algebra is seen to rule out “local translations” as independent gauge transformations.     

Gauge potential formulations of the spin Hall effect in graphene

Two different gauge potential methods are engaged to calculate explicitly the spin Hall conductivity in graphene. The graphene Hamiltonian with spin-orbit interaction is expressed in terms of kinematic momenta by introducing a gauge potential. A formulation of the spin Hall conductivity is established by requiring that the time evolution of this kinematic momentum vector vanishes. We then calculated the conductivity employing the Berry gauge fields. We show that both of the gauge fields can be deduced from the pure gauge field arising from the Foldy-Wouthuysen transformations.     

Study of renormalization counter terms in gauge theories

Theories with spontaneous broken gauge symmetry will have pseudo-Goldstone bosons, if the scalar multiplets are unlocked. Locking or unlocking of representations is best studied by the renormalization counter terms for general group representations. Renormalizability of the theory with less than complete terms (of dimension ? 4) allowed by gauge symmetry in the scalar polynomial is also studied.     

SO(n)规范势的可分解理论

使用几何代数方法,研究了n维紧致黎曼流形上SO(n)规范势(自旋联络)的一般分解理论,建立了SO(n)规范场用球丛上单位矢量场n分解的一般表达式.由此,分别得到了U(1)规范场和U(2)规范场用单位矢量场n分解的一般形式.