Anomalous Commutators Research Articles

ALGEBRAIC STRUCTURES OF ANOMALOUS COMMUTATORS IN GENERAL DIMENSIONS

We propose an algebraic method to determine anomalous commutators, which constitute Faddeev’s anomaly, for general dimensions. This method is verified explicitly in 1+5 dimensions.

Point-splitting analysis of commutator anomalies in non-abelian chiral gauge theories

A gauge covariant point-splitting regularisation is employed to calculate different anomalous commutators in four dimensional chiral gauge theories. For an external gauge field the fixed time anomalous commutator of the gauge group generators is seen to violate the Jacobi identity. The cohomological prediction can be confirmed provided the electric fields do not commute. Other commutators like the current-current and current-electric field are consistent with the Bjorken-Johnson-Low (BJL) derivation.

Berry's phase, commutators, and the Dirac sea

We discuss the connection between the Berry phase and the Schwinger term in generators of symmetry groups, and stress the relative minus sign between the anomalous commutator of the currents and the anomalous commutator of the full group generators.

Deformation of symplectic structure and anomalous commutators in field theories.

We study anomalous commutators for field theories from the viewpoint of deformation of the symplectic structure of phase space. This deformation is connected with a phase holonomy associated with an adiabatic change of the field variables. In particular, we consider a chiral gauge field for which we get a novel explanation for Faddeev's operator anomaly.

EXTENDED SUGAWARA MODEL WITH ANOMALY

Sugawara model is extended to contain the anomalous commutator. Also the energy-momentum tensor is generalized. From the various restrictions we obtain the constraints of this model. The normal ordering effect of the model is discussed. As a result, the extended Sugawara model does not contain the central term of the parity preserving contribution but involves that of the parity violating contribution.

Fujikawa Jacobian, modified symplectic structures, and the anomalous commutators of chiral Abelian gauge theories.

We defined, for the anomalous Abelian gauge theory, a new symplectic structure so as to accommodate for the Fujikawa Jacobian that will appear in the path-integral formalism of the theory. This symplectic structure will in turn induce the equal-time commutator anomalies that were obtained via other means.

Derivation of anomalous commutator in the functional integral formalism

A simple method is proposed for calculating the anomalous commutator in the theory of interacting chiral fermions and Yang-Mills field.

Anomalous commutators in two-dimensional chiral gauge theories

It is shown that in two-dimensional models of chiral fermions coupled with background gauge fields, anomalous commutators of currents as well as of generators of time-independent gauge transformations are completely determined by the anomaly if the gauge group is semisimple. The four-dimensional case is commented on.

Adiabatic theorem and anomalous commutators

Abstract We show that the geometrical phase factor recently found in the quantum adiabatic theorem modifies the canonical structure of the phase space. This gives rise to the anomalous terms in the quantum mechanical commutation relations.

Adiabatic phase, Topological Action and Anomalous Commutators

Adiabatic phase, Topological Action and Anomalous Commutators

The Gauss law constraint in anomalous gauge theories

Starting from the path integral formulation, it is shown how to derive the Gauss law constraint in gauge theories. It is then shown without referring to the anomalous commutators that the conventional form of the Gauss law constraint cannot be imposed on “physical” state vectors in anomalous gauge theories, regardless whether being non-abelian or abelian theories. It is also described how to derive the anomalous commutators in the present formulation.

Anomalous current commutators in the nonlinear sigma model.

We calculate the equal-time commutation relations of the chiral SU(3${)}_{L}$\ifmmode\times\else\texttimes\fi{}SU(3${)}_{R}$ charge densities in the nonlinear \ensuremath{\sigma} model and obtain operator-valued Schwinger-term modifications arising from the axial anomaly. We check the modified commutators by a current-algebra derivation of the anomalous matrix element 〈${\ensuremath{\pi}}^{+}$${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$${\ensuremath{\pi}}^{0}$\ensuremath{\Vert}${V}_{0}^{8}$\ensuremath{\Vert}0〉. The result agrees with that obtained directly from the Wess-Zumino effective Lagrangian.

Berry's phase in chiral gauge theories

Berry's phase in chiral gauge theories is computed. The result implies that the anomalous commutator of gauge transformations is the one previously obtained by Faddeev.

Non-abelian Cheshire cat bag models in 1+1 dimensions

Non-abelian Cheshire cat models are investigated in their lagrangian and hamiltonian formulations. The lagrangian bag boundary conditions are used to derive the form of non-abelian soliton operators, through which fermions are represented in bosonic language. These soliton operators are then used to construct the boundary interaction in the hamiltonian picture, wherein the bosonic sector is formulated by means of a current algebra involving anomalous commutators. The hamiltonian and the momentum operator are shown to commute, thus implying that the Cheshire cat criterion — the independence of the energy spectrum on the bag wall position — is fulfilled by the system.

Hadronic sum rules andK→2π decays

We derive upper bounds on the matrix elements of the ΔS=1 operators in theK−π transition using the techniques of the hadronic sum rules. The derived bounds show that quark model calculations overestimate the matrix elements of the operators with left-left helicities. The penguin operators turns out to give a destructive contribution, the reason for which is large cancelation with an anomalous commutator term. This fact questions the role of penguins as an explanation of the ΔI=1/2 rule. Furthermore, we use our constraints on penguins to set a lower bound onɛ′/ɛ.

Associativity of Representations and Cocycles of Gauge Groups

It is shown that the consistency of certain representations of group requires a mod Z-cocycle condition which leads to some topological quantization constants in corresponding anomalous algebraic relations, such as anomalous commutators and anomalous Jacobi identities. It should be pointed out that the mod Z-cocycles for gauge groups could be constructed by means of the generalized secondary characteristic classes.

The gravitational analogue of the Witten effect

In the presence of massive fermions, and assuming a non-vanishing θ-parameter as the only source of CP violation, the Witten effect (a shift in the electric charge of a magnetic monopole due to CP non-conservation) is shown to follow from an anomalous chiral commutator. Next, given the gravitational contribution to the chiral anomaly, the corresponding anomalous commutator for Dirac fermion currents in a gravitational background is derived. From that, we infer the equivalence of θ R ̃ R term in the lagrangian to a shift in the mass parameter of the NUT metric, in proportion to θ. This is interpreted as the gravitational analogue of the Witten effect. Its relevance to certain Kaluza-Klein monopoles is briefly discussed.

Fermions from bosons in 3+1 dimensions through anomalous commutators

A derivation in the canonical formulation of the Wess-Zumino anomaly is given. This leads naturally to a construction of half-integer-spin, anticommuting operators starting from spin-zero bosonic ones. This fermionic operator creates a state that is a superposition of all half-integer spins. This is related to the effective Lagrangian for QCD.

Fractional charge and anomalous commutators

Non-integer charges on topological objects in the presence of fermions are further investigated. The connections with anomalous commutators is discussed. The reason for the identical results in two dimensional solitons and four dimensional monopoles is pointed out.

On anomalous commutators associated with anomalies

It is shown that conformal as well as chiral anomalies in spinor electrodynamics lead to anomalous commutators in the canonical local-operator approach. This may support the association of anomalies with jacobian factors in the path integral approach, since the appearance of the jacobian suggests that certain classical symmetries are not compatible with the quantization procedure. Some subtle aspects in the renormalization of the conventional energy-momentum tensor are also clarified.