Open AccessThe Hamiltonian theory of Landau-Lifschitz equation and the gauge transformations
Author(s) -
He Jin-Chun,
Shi Li-Na,
Hua Chen,
Nian-Ning Huang
Publication year - 2005
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.54.2007
Subject(s) - hamiltonian (control theory) , conserved quantity , integral equation , mathematical physics , isotropy , zeroth law of thermodynamics , physics , gauge theory , mathematics , mathematical analysis , classical mechanics , quantum mechanics , mathematical optimization
The coordinate and spectral integral representations of Hamiltonian in isotropic LandauLifschitz equation are given by a standard procedure.But,the problem of deriving the corresponding conserved quantity to connect two kinds of integral mentioned above is still open.In this paper,using the gauge invariance properties,the compatibility pair of LL equation is transformed to the form-ikσ3+O(1) by choosing an app ropriate tr ansformation.Hence,the conserved quantities are obtained.The zeroth conserved qu antity,I0,is zero.The first one,I1,which has coordinate an d spe ctral integral representations,coincide with the two desired integral representations of the Hamiltonian.