arXiv subjects
Publications and source records attributed to Jan Kotanski.
The main features of the cusp anomalous dimension in N=4 supersymmetri c Yang-Mills theory are reviewed. Moreover, the strong coupling expansion of the cusp derived is presented.
The four reggeized gluon states for non-vanishing Lorentz conformal spin $n_h$ are considered. To calculate their spectrum the Q-Baxter method is used. As a result we describe normalizable trajectory-like states, which form continuous spectrum, as well as discrete point-like solutions, which turn out to be non-normalizable. The point-like solutions exist due to symmetry of the Casimir operator where conformal weights $(h,\bar h) \to (h,1-\bar h)$.
Supersymmetric Yang-Mills quantum mechanics (SYMQM) in four dimensions for SU(2) gauge group is considered. In this work a two-fermionic sector with the angular momentum j=0 in discussed. Energy levels from discrete and continuous spectra are calculated. To distinguish localized states from non-localized ones the virial theorem is applied.
The spectrum of Supersymmetric Yang-Mills Quantum Mechanics (SYMQM) in D=4 dimensions for SU(2) gauge group is computed for a maximal number of bosonic quanta $B\le60$ in the two-fermion sector with the angular momentum $j=0$. We analyse the eigenfunctions of discrete and continuous spectra, test the scaling relation for the continuous spectrum and confirm the dispersion relation to high accuracy.
N-Reggeized gluon states in Quantum Chromodynamics are described by BKP equation. In order to solve this equation for N>3 particles the Q-Baxter operator method is used. Spectrum of the integrals of motion of the system exhibits a complicated structure. In this work we consider the case with N=4 Reggeons where complicated relations between q_3-spectrum and q_4-spectrum are analysed. Moreover, corrections to WKB approximation for N=4 and q_3=0 are computed.
The scattering amplitude of hadrons in high energy Regge limit can be rewritten in terms of reggeized gluons, i.e. Reggeons. We consider three-Reggeon states that possess either C=+1 or C=-1 parity. In this work using Janik-Wosiek method the spectrum of conformal charges is calculated for states with conformal Lorentz spin n_h=0,1,2,3,... . Moreover corrections to WKB approximation are computed.
The reggeized gluon states, which are also called Reggeons, appear in the scattering amplitude of hadrons in Regge limit. The wave-function of Reggeons satisfy the BKP equation, which in multi-colour limit of Quantum Chromodynamics is equivalent to the Schrodinger equation of the XXX Heisenberg SL(2,C) spin chain model. In this work we solve the BKP equation, show the spectrum of the energy and other integrals of motion for a number of Reggeons N=2,...,8. Moreover, we consider deep inelastic scattering where due to the reggeized gluons states we are able to calculate anomalous dimensions and corresponding to their twists.
Solving the BKP equation and comparing with the structure function of hadron for deep inelastic scattering processes we are able to find a relation between reggeized N-gluon states and anomalous dimensions of QCD. To this end we perform analytical continuation of the Reggeon energy and compare exponents of two different twist-series expansions for the hadron structure function. This makes possible to calculate the anomalous dimensions and determine the twist related to them.
We study the properties of the colour-singlet compound states of reggeized gluons in multi-colour QCD. Applying the methods of integrable models, we calculate their spectrum and discuss the application of the obtained results to high-energy asymptotics of the scattering amplitudes in perturbative QCD.
The quantization conditions which come from the requirement of the singlevaluedness of the odderon wave function are formulated and solved numerically in the 4 dimensional space of the odderon charge q3 and the conformal weight h. It turns out that these conditions are fulfilled along one dimensional curves parametrized by a discrete set of values of Re(h) in 3 dimensional subspace (Im(h),Im(q3),Re(q3)). The odderon energy calculated along these curves corresponds in all cases to the intercept lower than 1.