By Gerald Dunne
Self-duality significantly reduces the mathematical problems of a thought however it is usually a inspiration of substantial actual importance. the recent category of self-dual Chern-Simons theories mentioned intimately during this ebook come up within the context of anyonic quantum box idea and feature functions to versions reminiscent of the quantum corridor impact, anyonic superconductivity, and Aharonov-Bohm scattering. There also are attention-grabbing connections with the idea of integrable types. the writer provides the abelian and non-abelian types for relativistic and non-relativistic realizations of the self-dual Chern-Simons theories and finishes with a few purposes in quantum physics. The e-book is written for complex scholars and researchers in mathematical, particle, and condensed subject physics.
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Additional info for Self-dual Chern-Simons theories
52) vanishes. These transformations therefore correspond to symmetries of tIle system. 43). TIle otIler two are 5. 53) 6. 54). :J p(t, x) i ax ) :J = det ( -a. 21), transform covariantly , '-I) . )Olld to symmetry operatiolls. The correspolldillg cOllserved gellerators call be obtailled fronl Noetller's theorenl. 46) call also l)e fOUlld froll1 tIle energy-Ill011lelltulll tellsor. 63) does 110t equal tIle 11l01llen- as ,vould be tIle case ill a relativistic tIleory. However, tIlis tlleory is rotatiollally illvariallt, alld so tIle stress tellsorTij is symmetric.
However, tIlis tlleory is rotatiollally illvariallt, alld so tIle stress tellsorTij is symmetric. 64) wllich reflects the COllformal illvariance of tllis nOllrelativistic systelll (contrast witll a relativistic cOllforlllally illvariallt 11l0del, for wllicll £ = L,i T ii ). Tllis relatioll l)et\Veell tIle ellergy alld tIle trace of tIle stress tellsor will l)e illll)Ortallt ill tIle cillalltizatioll of tllese systeills - see Cllal)ter 6. 46) are: 1. 65 ) 2. 66) 30 3. 67) 4. 68) and are stalldard for any Galilean invariant theory.
97) and the conforlual cllarge (2. 99) and corresponds to n solitolls superiluposed at tIle origin. 100) Note that there are 4n real parameters involved in tllis solution: 2n real parameters x;; (a = 1, ... n) solitons, and 2n real parameters Ca describing tIle locations of the (a = 1, ... n) corresponding to the scale and phase of eacll solit011. 100) llas ill fact beell ShOWll, by all index tlleory counting argumellt, to be tIle most general multi-solitoll solution . 82) to be a doubly periodic function .
Self-dual Chern-Simons theories by Gerald Dunne