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Michael Karowski

Publications and source records attributed to Michael Karowski.

9 recordsLinked to original sources
arXiv2025

Structure Functions for small DIS $x$

Structure Functions for small DIS (deep inelastic scattering) $x$ for integrable models are investigated, in particular, for the $O(N)$~$\sigma $-model and $SU(N)$ chiral Gross-Neveu model, which are asymptotically free. We get the universal behavior $x^{-1}\ln^{-2}x$ at small Bjorken variable $x$ and confirm a Balog Weisz conjecture. For a the second group of models, the Sine-Gordon, sinh-Gordon and $Z(N)$, we find power behavior $x^{-\lambda}$. The special behavior of the structure function for the Sine-Gordon model is probably crucial for future investigation in 4D QCD.

hep-th↗
arXiv2021

Asymptotic factorization of n-particle SU(N) form factors

We investigate the high energy behavior of the SU(N) chiral Gross-Neveu model in 1 + 1 dimensions. The model is integrable and matrix elements of several local operators (form factors) are known exactly. The form factors show rapidity space clustering, which means factorization, if a group of rapidities is shifted to infinity. We analyze this phenomenon for the SU(N) model. For several operators the factorization formulas are presented explicitly.

hep-th↗
arXiv2017

Form factors of the O(6) Gross Neveu-model

The isomorphism $SU(4) \simeq O(6)$ is used to construct the form factors of the O(6) Gross-Neveu model as bound state form factors of the SU(4) chiral Gross-Neveu model. This technique is generalized and is then applied to use the O(6) as the starting point of the nesting procedure to obtain the O(N) form factors for general even N.

hep-th↗
arXiv2016

Bethe Ansatz and exact form factors of the O(N) Gross Neveu-model

We apply previous results on the O(N) Bethe Ansatz [1 to 3] to construct a general form factor formula for the O(N) Gross-Neveu model. We examine this formula for several operators, such as the energy momentum, the spin-field and the current. We also compare these results with the 1/N expansion of this model and obtain full agreement. We discuss bound state form factors, in particular for the three particle form factor of the field. In addition for the two particle case we prove a recursion relation for the K-functions of the higher level Bethe Ansatz.

hep-th↗
arXiv2013

Exact form factors of the O(N) $σ$-model

A general form factor formula for the $O(N)σ$-model is constructed and applied to several operators. The large N limits of these form factors are computed and compared with the 1/N expansion of the $O(N)σ$-model in terms of Feynman graphs and full agreement is found. In particular, O(3) and O(4) form factors are discussed. For the $O(3)σ$-model several low particle form factors are calculated explicitly.

hep-th↗
arXiv2009

Exact form factors of the SU(N) Gross-Neveu model and 1/N expansion

The general SU(N) form factor formula is constructed. Exact form factors for the field, the energy momentum and the current operators are derived and compared with the 1/N-expansion of the chiral Gross-Neveu model and full agreement is found. As an application of the form factor approach the equal time commutation rules of arbitrary local fields are derived and in general anyonic behavior is found.

hep-th↗
arXiv2006

The Form Factor Program: a Review and New Results - the Nested SU(N) Off-Shell Bethe Ansatz

The purpose of the ''bootstrap program'' for integrable quantum field theories in 1+1 dimensions is to construct explicitly a model in terms of its Wightman functions. In this article, this program is mainly illustrated in terms of the sinh-Gordon model and the SU(N) Gross-Neveu model. The nested off-shell Bethe ansatz for an SU(N) factorizing S-matrix is constructed. We review some previous results on sinh-Gordon form factors and the quantum operator field equation. The problem of how to sum over intermediate states is considered in the short distance limit of the two point Wightman function for the sinh-Gordon model.

hep-th↗
arXiv2006

The nested SU(N) off-shell Bethe ansatz and exact form factors

The form factor equations are solved for an SU(N) invariant S-matrix under the assumption that the anti-particle is identified with the bound state of N-1 particles. The solution is obtained explicitly in terms of the nested off-shell Bethe ansatz where the contribution from each level is written in terms of multiple contour integrals.

hep-th↗