Conserved Noether Currents Research Articles

The quantized O(1,2)/O(2) x Z2 sigma model has no continuum limit in four dimensions. I. Theoretical framework.

The nonlinear sigma model for which the field takes its values in the coset space O(1,2)/O(2)\ifmmode\times\else\texttimes\fi{}${\mathit{Z}}_{2}$ is similar to quantum gravity in being perturbatively nonrenormalizable and having a noncompact curved configuration space. It is therefore a good model for testing nonperturbative methods that may be useful in quantum gravity, especially methods based on lattice field theory. In this paper we develop the theoretical framework for recognizing and studying a consistent nonperturbative quantum field theory of the O(1,2)/O(2)\ifmmode\times\else\texttimes\fi{}${\mathit{Z}}_{2}$ model. We describe the action, the geometry of the configuration space, the conserved Noether currents, and the current algebra, and we construct a version of the Ward-Slavnov identity that makes it easy to switch from a given field to a nonlinearly related one. Renormalization of the model is defined via the effective action and via current algebra. The two definitions are shown to be equivalent. In a companion paper we develop a lattice formulation of the theory that is particularly well suited to the sigma model, and we report the results of Monte Carlo simulations of this lattice model. These simulations indicate that as the lattice cutoff is removed the theory becomes that of a pair of massless free fields. Because the geometry and symmetries of these fields differ from those of the original model we conclude that a continuum limit of the O(1,2)/O(2)\ifmmode\times\else\texttimes\fi{}${\mathit{Z}}_{2}$ model which preserves these properties does not exist.

Conserved Noether currents in stochastic quantization

A general procedure for constructing Noether conserved currents in the stochastic quantization scheme corresponding to symmetries of the equilibrium theory is proposed. Two different regularizations — the Breit-Gupta-Zaks stochastic time regularization and a new supersymmetric regularization — are employed, and the origin of chiral anomalies is exhibited in this framework.

On the classical and quantum irrotational motions of a relativistic perfect fluid I. Classical theory

Some aspects of perfect-fluid general-relativistic hydrodynamics under the assumptions of irrotationality and isentropicity are analysed. A new derivation of the known fact that the Lagrangian for these fluids is just the pressure is given. Then we study the fluctuations around a given background field configuration, extracting a rule that connects the order at which a Taylor expansion of the action functional possibly stops with the fluid equation of state. From a classical invariance of the action we deduce the conserved Noether current. Because of the spontaneous breaking of such an invariance on the vacuum state Goldstone bosons arise, which turn out to be just phonons (quantized sound waves). Some useful results concerning the linear theory of sound waves are also given.

Internal symmetries of non-Abelian gauge field configurations.

In a topologically nontrivial gauge theory not all gauge transformations are symmetries (as defined by Forg\'acs and Manton and by Schwarz) of a given field configuration: first, there may be an obstruction to implement gauge transformations on the fields; next, even those transformations which can be implemented may fail to be symmetries. For a test particle in such a background field, those gauge transformations which are symmetries generate ordinarily conserved Noether currents, one of which is the usual electric current. These results shed a new light on the problem of ``global color'' in monopole theory and explain why the electric charge of a nucleon is not in general conserved in the non-Abelian Aharonov-Bohm experiment of Wu and Yang.

Conserved noether currents and path intergrals for dynamical groups

We consider path integrals for the dynamical group SU(1,1) based on its associated coherent states. For relevant systems the classical dynamics is oscillator-like in a curved phase space. The classical lagrangian exhibits an “internal” symmetry whose conserved Noether currents are in the SU(1,1) Lie algebra.

Noether currents and algebraic structure of the hidden symmetry for super chiral fields

The parametric conserved Noether currents and the Kac-Moody algebra in two-dimensional super chiral fields are derived. The relations for them and the parametric Bianchi-Baecklund transformation are explicitly shown.