arXiv subjects
Publications and source records attributed to Kai Lou.
The YM theory has been generalized to 2YM and 3YM theories. Similarly, we generalize the BFYM theory to "2BFYM" and "3BFYM" theories. Then, we show that these higher BFYM theories can give the formulations of the corresponding higher form YM theories. Finally, we study the gauge symmetries of these higher BFYM theories.
In this paper, we study the higher Yang-Mills theory in the framework of higher gauge theory. It was shown that the 2-form electromagnetism can be generalized to the 2-form Yang-Mills theory with the group $U(1)$ replaced by a crossed module of Lie groups. To extend this theory to even higher structure, we develop a 3-form Yang-Mills theory with a 2-crossed module of Lie groups. First, we give an explicit construction of non-degenerate symmetric $G$-invariant forms on the 2-crossed module of Lie algebras. Then, we derive the 3-Bianchi-Identities for 3-curvatures. Finally, we create a 3-form Yang-Mills action and obtain the corresponding field equations.
We first extend Generalized Differential Calculus (GDC) to higher structures and create generalized G-invariant bilinear forms. In addition, we also focus on developing generalized 2- and 3-connection theories in the framework of GDC. Then, we derive the higher Bianchi-Identities and study the gauge transformations for those generalized higher connections. Finally, we establish the generalized 2- and 3-form Yang-Mills theories based on GDC and obtain the corresponding fields equations.
The solidity of glassy materials is believed to be due to the cage formed around each particle by its neighbors, but in reality the details of cage-formation remain elusive [1-4]. This cage starts to be formed at the onset temperature/density at which the normal liquid begins to show the first signs of glassy dynamics. To study cage-formation we use here focused lasers to produce a local perturbation of the structure on the particle level in 2D colloidal suspensions and monitor by means of video microscopy the system's non-linear dynamic response. All observables we probed show a response which is non-monotonic as a function of the packing fraction, peaking at the onset density. Video microscopic images reveal that this maximum response is due to the buildup of domains with cooperative dynamics that become increasingly rigid and start to dominate the particle dynamics. This proof-of-concept from microrheological deformation demonstrates that in this glass-forming liquid cage formation is directly related to the merging of these domains, thus elucidating the first step in glass-formation [1, 5].
The glass is a disordered solid that processes distinct dynamical and elastic properties compared with crystal. How heterogeneous glassy materials can be and to what extent dynamics is encoded with structure and elasticity are long-standing puzzles in glass science. In this experiment, we probed the responses of binary colloidal glasses towards the excitations induced by highly focused laser pulses. We observed very similar excitation patterns when the laser was repeated in the linear region; directly proving that the dynamical heterogeneity is strongly encoded with structure. In the non-linear region, we identified a non-monotonic dynamical length scale as a function of area fraction, resulting from the non-monotonic coupling of momentum transfer in radial and orthogonal directions. Surprisingly, the excitation size and radius of gyration conformed to a universal scaling relation that covered both linear and non-linear regions. Our experiments offered a new strategy of actively probing the response of glassy materials on the microscopic level.