ترغب بنشر مسار تعليمي؟ اضغط هنا

Semi-classical scalar products in the generalised SU(2) model

180   0   0.0 ( 0 )
 نشر من قبل Ivan K. Kostov
 تاريخ النشر 2014
  مجال البحث فيزياء
والبحث باللغة English
 تأليف Ivan Kostov




اسأل ChatGPT حول البحث

In these notes we review the field-theoretical approach to the computation of the scalar product of multi-magnon states in the Sutherland limit where the magnon rapidities condense into one or several macroscopic arrays. We formulate a systematic procedure for computing the 1/M expansion of the on-shell/off-shell scalar product of M-magnon states in the generalised integrable model with SU(2)-invariant rational R-matrix. The coefficients of the expansion are obtained as multiple contour integrals in the rapidity plane.



قيم البحث

اقرأ أيضاً

We show that the dual partition function of the pure $mathcal N=2$ $SU(2)$ gauge theory in the self-dual $Omega$-background (a) is given by Fredholm determinant of a generalized Bessel kernel and (b) coincides with the tau function associated to the general solution of the Painleve III equation of type $D_8$ (radial sine-Gordon equation). In particular, the principal minor expansion of the Fredholm determinant yields Nekrasov combinatorial sums over pairs of Young diagrams.
In this paper we reconsider the problem of the Euler parametrization for the unitary groups. After constructing the generic group element in terms of generalized angles, we compute the invariant measure on SU(N) and then we determine the full range o f the parameters, using both topological and geometrical methods. In particular, we show that the given parametrization realizes the group $SU(N+1)$ as a fibration of U(N) over the complex projective space $mathbb{CP}^n$. This justifies the interpretation of the parameters as generalized Euler angles.
Within the context of Supersymmetric Quantum Mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the usual restrict ion of shape invariance for intertwined potentials, it is suggested to require a similar relation for Hamiltonians in the hierarchy separated by an arbitrary number of levels, N. By requiring further that these two Hamiltonians be in fact identical up to an overall shift in energy, a periodic structure is installed in the hierarchy of quantum systems which should allow for its solution. Specific classes of orthogonal polynomials characteristic of such periodic hierarchies are thereby generated, while the methods of Supersymmetric Quantum Mechanics then lead to generalised Rodrigues formulae and recursion relations for such polynomials. The approach also offers the practical prospect of quantum modelling through the engineering of quantum potentials from experimental energy spectra. In this paper these ideas are presented and solved explicitly for the cases N=1 and N=2. The latter case is related to the generalised Laguerre polynomials, for which indeed new results are thereby obtained. At the same time new classes of integrable quantum potentials which generalise that of the harmonic oscillator and which are characterised by two arbitrary energy gaps are identified, for which a complete solution is achieved algebraically.
It is emphasized that for interactions with derivative couplings, the Ward Identity (WI) securing the preservation of a global U(1) symmetry should be modified. Scalar QED is taken as an explicit example. More precisely, it is rigorously shown in sca lar QED that the naive WI and the improved Ward Identity (Master Ward Identity, MWI) are related to each other by a finite renormalization of the time-ordered product (T-product) for the derivative fields; and we point out that the MWI has advantages over the naive WI - in particular with regard to the proof of the MWI. We show that the MWI can be fulfilled in all orders of perturbation theory by an appropriate renormalization of the T-product, without conflict with other standard renormalization conditions. Relations with other recent formulations of the MWI are established.
86 - G. Sardanashvily 2016
We consider classical gauge theory on a principal bundle P->X in a case of spontaneous symmetry breaking characterized by the reduction of a structure group G of P->X to its closed subgroup H. This reduction is ensured by the existence of global sect ions of the quotient bundle P/H->X treated as classical Higgs fields. Matter fields with an exact symmetry group H in such gauge theory are considered in the pairs with Higgs fields, and they are represented by sections of a composite bundle Y->P/H->X, where Y->P/H is a fiber bundle associated to a principal bundle P->P/H with a structure group H. A key point is that a composite bundle Y->X is proved to be associated to a principal G-bundle P->X. Therefore, though matter fields possess an exact symmetry group H, their gauge G-invariant theory in the presence of Higgs fields can be developed. Its gauge invariant Lagrangian factorizes through the vertical covariant differential determined by a connection on a principal H-bundle P->P/H. In a case of the Cartan decomposition of a Lie algebra of G, this connection can be expressed in terms of a connection on a principal bundle P->X, i.e., gauge potentials for a group of broken symmetries G.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا