Talks

For the past century, there has been much discussion and debate about the equations of motion satisfied by a classical point charge when the effects of its own electromagnetic field are taken into account. Derivations by Abraham (1903), Lorentz (1904), Dirac (1938) and others suggest that the "self-force" (or "radiation reaction force") on a point charge is given in the non-relativistic limit by a term proportional to the time derivative of the acceleration of the charge. However, the resulting equations of motion then become third order in time, and they admit highly unphysical "runaway" solutions. During the past century, there also has been much discussion and debate about the interpretation of these equations of motion and the conditions that can/should be imposed to eliminate the runaway behavior. We argue that the above difficulties stem from that fact that the usual notion of a point charge is mathematically ill defined. However, a mathematically rigorous notion of a point charge arises in a perturbative description of a body if one considers a limit wherein not only the size of a body but its charge and mass go to zero in an asymptotically self-similar manner. We show how the Abraham-Lorentz-Dirac self-force then arises in a perturbative description of the body's motion, but does not give rise to runaway behavior. As a biproduct of this work, we also rigorously derive dipole forces and resolve some paradoxes of elementary physics, such as how a magnetic dipole placed in a non-uniform magnetic field can gain kinetic energy despite the fact that the magnetic field can "do no work" on the body.

These three lectures cover several ideas of physics beyond the Standard Model. My focus is on ideas that give a natural stabilization solution to the electroweak scale, which is mysteriously light compared to the gravitational Planck scale. These ideas include supersymmetric field theories, extra dimensions, and Higgs boson physics. I shall describe what I think are the "best bets" among these approaches, and more importantly the ways they can be discerned by experiment. Special emphasis will be on theories that can be confirmed at the Large Hadron Collider (LHC) that is just now starting.

Recently, a new class of topological states has been theoretically predicted and experimentally realized. The topological insulators have an insulating gap in the bulk, but have topologically protected edge or surface states due to the time reversal symmetry. In two dimensions the edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. I shall review the theoretical prediction[1] of the QSH state in HgTe/CdTe semiconductor quantum wells, and its recent experimental observation[2]. The edge states of the QSH state supports fractionally charged excitations[3]. The QSH effect can be generalized to three dimensions as the topological magneto-electric effect (TME) of the topological insulators[4]. Bi2Te3, Bi2Se3 and Sb2Te3 are theoretically predicted to be topological insulators with a single Dirac cone on the surface[5]. I shall present a realistic experimental proposals to observe the magnetic monopoles on the surface of topological insulators[6]. Topological superconductors and superfluid have been theoretically proposed recently [7], in both two and three dimensions. They have a full pairing gap in the bulk, and their mean field Hamiltonian look identical to that of the topological insulators. However, the gapless surface states consists of a single Majorana cone, containing only half the degree of freedom compared to the single Dirac cone on the surface of a topological insulators. I shall discuss their physics properties and the search for these novel states in real materials. [1] A. Bernevig, T. Hughes and S. C. Zhang, Science, 314, 1757, (2006) [2] M. Koenig et al, Science 318, 766, (2007) [3] J. Maciejko, Chaoxing Liu, Yuval Oreg, Xiao-Liang Qi, Congjun Wu, and Shou-Cheng Zhang, , Phys. Rev. Lett. {\bf 102}, 256803 (2009). [4] Xiao-Liang Qi, Taylor Hughes and Shou-Cheng Zhang, Phys. Rev B. 78, 195424 (2008) [5] Haijun Zhang, Chao-Xing Liu, Xiao-Liang Qi, Xi Dai, Zhong Fang, and Shou-Cheng Zhang, Nature Physics 5, 438 (2009). [6] Xiao-Liang Qi, Run-Dong Li, Jiadong Zang and Shou-Cheng Zhang, Science 323, 1184 (2009). [7] Xiao-Liang Qi, Taylor L. Hughes, Srinivas Raghu and Shou-Cheng Zhang, Phys. Rev. Lett. 102, 187001 (2009)