Modern Physics Letters A

Following the symplectic approach we show how to embed the Abelian Proca model into a first-class system by extending the configuration space to include an additional pair of scalar fields, and compare it with the improved Dirac scheme. We obtain in this way the desired Wess–Zumino and gauge fixing terms of BRST-invariant Lagrangian. Furthermore, the integrability properties of the second-class system described by the Abelian Proca model are investigated using the Hamilton–Jacobi formalism, where we construct the closed Lie algebra by introducing operators associated with the generalized Poisson brackets.

The dynamical breaking of the supergauge symmetry in the massless supergauge Wess–Zumino model is discussed without adding the Fayet–Iliopoulos term to the Lagrangian. It is shown, in terms of the Nambu–Jona-Lasinio mechanism, that the supergauge symmetry breaking can be realized dynamically in the massless supergauge Wess–Zumino model. The supergauge symmetry behavior at finite temperatures is also investigated and it is shown that the supergauge symmetry broken dynamically at zero temperature can be restored at finite temperatures.

Extending the supersymmetric method proposed by Tkachuk to the complex domain, we obtain general expressions for superpotentials allowing generation of quasi-exactly solvable PT-symmetric potentials with two known real eigenvalues (the ground state and first-excited state energies). We construct examples, namely those of complexified nonpolynomial oscillators and of a complexified hyperbolic potential, to demonstrate how our scheme works in practice. For the former we provide a connection with the sl(2) method, illustrating the comparative advantages of the supersymmetric one.

In the gravity without metric formalism of Capovilla, Jacobson and Dell, the topological θ-term appears through a canonical transformation. The origin of this canonical transformation is probed here. It is shown here that when θ-term appears cosmological, λ-term also appears simultaneously.

The equations of motion of quantum Yang–Mills theory (in the planar "large-N" limit), when formulated in loop-space are shown to have an anomalous term, which makes them analogous to the equations of motion of WZW models. The anomaly is the Jacobian of the change of variables from the usual ones, i.e. the connection one-form A, to the holonomy U. An infinite-dimensional Lie algebra related to this change of variables (the Lie algebra of loop substitutions) is developed, and the anomaly is interpreted as an element of the first cohomology of this Lie algebra. The Migdal–Makeenko equations are shown to be the condition for the invariance of the Yang–Mills generating functional Z under the action of the generators of this Lie algebra. Connections of this formalism to the collective field approach of Jevicki and Sakita are also discussed.

We consider radiative electromagnetic corrections, at order α, to the process at finite density and temperature. This process represents one of the main contributions to the cooling of stellar environments in the late stages of star evolution. We find that these corrections affect the energy loss rate by a factor (-4-1)% with respect to the tree level estimate, in the temperature and density ranges where the neutrino pair production via e⁺e^- annihilation is the most efficient cooling mechanism.