An extra Abelian gauge symmetry is motivated in many new physics models in both supersymmetric and nonsupersymmetric cases. Such a new gauge symmetry may interact with both the observable sector and the hidden sector. We systematically investigate the most general residual discrete symmetries in both sectors from a common Abelian gauge symmetry. Those discrete symmetries can ensure the stabilit...

Connections on principal bundles play a fundamental role in expressing the equations of motion for mechanical systems with symmetry in an intrinsic fashion. A discrete theory of connections on principal bundles is constructed by introducing the discrete analogue of the Atiyah sequence, with a connection corresponding to the choice of a splitting of the short exact sequence. Equivalent represent...

The Wigner function provides a useful quasiprobability representation of quantum mechanics, with applications in various branches of physics. Many nice properties of the Wigner function are intimately connected with the high symmetry of the underlying operator basis composed of phase point operators: any pair of phase point operators can be transformed to any other pair by a unitary symmetry tr...

Based on a general formulation for discrete-time quantum mechanics, introduced in 1], symmetries in discrete-time quantum mechanics are investigated. It is shown that any classical continuous symmetry leads to a conserved quantity in classical mechanics, as well as quantum mechanics. The transformed wave function, however, has the correct evolution if and only if the symmetry is nonanomalous.

We consider a scenario in which the discrete weak symmetry between quarks and leptons is extended to the weak force by introducing exotic partners. We conjecture that there exists a hidden discrete symmetry P̃, defining a Z2 group, between standard and exotic quarks and leptons. The unified model SU(3) q × SU(3) q̃ × SU(2) ql̃ × SU(2) q̃l × U(1) Y × P̃ is discussed, where the unifying discrete symme...

The axion solution to the strong CP problem makes use of a global Peccei–Quinn U(1) symmetry which is susceptible to violations from quantum gravitational effects. We show how discrete gauge symmetries can protect the axion from such violations. PQ symmetry emerges as an approximate global symmetry from discrete gauge symmetries. Simple models based on ZN symmetries with N = 11, 12, etc are pre...

Anomaly of a discrete symmetry is defined as the Jacobian of the path-integral measure. Assuming that anomaly at low energy is cancelled by the Green-Schwarz (GS) mechanism at a fundamental scale, we investigate possible Kac-Moody levels for anomalous discrete family symmetries. As the first example we consider discrete abelian Baryon number and Lepton number symmetries in the minimal supersymm...

The anomaly of a discrete symmetry is defined as the Jacobian of the pathintegral measure. Assuming that the anomaly at low energies is cancelled by the Green-Schwarz (GS) mechanism at a fundamental scale, we investigate possible KacMoody levels for anomalous discrete family symmetries. As the first example, we consider discrete abelian baryon number and lepton number symmetries in the minimal ...

Discrete rotating waves are periodic solutions that have discrete spatiotemporal symmetries in addition to their purely spatial symmetries. We present a systematic approach to the study of local bifurcation from discrete rotating waves. The approach centers around the analysis of diffeomorphisms that are equivariant with respect to distinct group actions in the domain and the range. Our results...

In this work, we consider the Lie's method of infinitesimal transformation groups and discrete symmetries method for Burgers equation with time dependent flux at the origin. Following the Lie's method of infinitesimal transformation groups we determine the symmetry reductions and similarity solutions of the governing equation. By applying discrete symmetries analysis we have obtained three grou...