International Journal of Modern Physics A

When a symmetry gets spontaneously broken in a phase transition, topological defects are typically formed. The theoretical picture of how this happens in a breakdown of a global symmetry, the Kibble–Zurek mechanism, is well established and has been tested in various condensed matter experiments. However, from the viewpoint of particle physics and cosmology, gauge field theories are more relevant than global theories. In recent years, there have been significant advances in the theory of defect formation in gauge field theories, which make precise predictions possible, and in experimental techniques that can be used to test these predictions in superconductor experiments. This opens up the possibility of carrying out relatively simple and controlled experiments, in which the nonequilibrium phase transition dynamics of gauge field theories can be studied. This will have a significant impact on our understanding of phase transitions in the early universe and in heavy ion collider experiments. In this paper, I review the current status of the theory and the experiments in which it can be tested.

We present a Bose operator Hamiltonian model for totally quantum mechanically describing energy and eigenfunctions of a rotating dipole in the presence of electric field. The corresponding Heisenberg equations of motion are derived which leads us to the generalized Ehrenfest theorem for rotating system. Remarkably, a zero-point angular momentum ℏ/2 appears in the generalized Ehrenfest theorem corresponding to the classical equation Iω=L.

We analyze a set of three PT-symmetric complex potentials, namely harmonic oscillator, generalized Pöschl–Teller and Scarf II, all of which reveal a double series of energy levels along with the corresponding superpotential. Inspired by the fact that two superpotentials reside naturally in order-two parasupersymmetry (PSUSY) and second-derivative supersymmetry (SSUSY) schemes, we complexify their frameworks to successfully account for the three potentials.

We develop the dynamics of the chiral superconducting membranes (with null current) in an alternative geometrical approach either making a Lagrangian description and a Hamiltonian point of view. Besides this, we show the equivalence of the resulting descriptions to the one known Dirac–Nambu–Goto (DNG) case. Integrability for chiral string model is obtained using a proposed light-cone gauge. In a similar way, domain walls are integrated by means of a simple ansatz. We compare the results with recent works that appeared in the literature.

In cases of both Abelian and non-Abelian gauge groups, we study the Higgs mechanism in the topologically massive gauge theories in an arbitrary space–time dimension. We show that when the conventional Higgs potential coexists with a topological term, gauge fields become massive by "eating" simultaneously both the Nambu–Goldstone boson and a higher-rank tensor field and instead a new massless scalar field is "vomitted" in the physical spectrum. Because of the appearance of this new massless field, the number of the physical degrees of freedom remains unchanged before and after the spontaneous symmetry breakdown. Moreover, the fact that the new field is a physical and positive norm state is rigorously proved by performing the manifestly covariant quantization of the model in three and four dimensions. In the mechanism at hand, the presence of a topological term makes it possible to shift the mass of gauge fields in a nontrivial manner compared to the conventional value.

Event-by-event fluctuations for high energy heavy-ion collisions are investigated. The Φ-measures are calculated for pions. It is found that multiparticle symmetrization correlation has great influence on the value of Φ if the phase space density is high. Previous derivation of Φ-measure has neglected multiparticle quantum correlation. So the explanation of Φ-measure as a measure of dynamical correlation is reasonable only when multiparticles quantum correlation effects are smaller. We argue that the Φ-measure might be applicable at the SPS energy where the pion phase space density is much less than one.

Anomalies arising from nonplanar triangle diagrams of noncommutative gauge theory are studied. Local chiral gauge anomalies for both noncommutative U(1) and U(N) gauge theories with adjoint matter fields are shown to vanish. For noncommutative QED with fundamental matters, due to UV/IR mixing a finite anomaly emerges from the nonplanar contributions. It involves a generalized ⋆-product of gauge fields.