Related papers: On the Form Factor for the Unitary Group
We sketch a group-theoretical framework, based on the Heisenberg-Weyl group, encompassing both quantum and classical statistical descriptions of mechanical systems. We re-define in group-theoretical terms the kinematical arena and the…
The quantum integrable systems associated with the quantum loop algebras $\mathrm U_q(\mathcal L(\mathfrak{sl}_{\, l + 1}))$ are considered. The factorized form of the transfer operators related to the infinite dimensional evaluation…
This is a self-contained review on the theory of quantum group and its applications to modern physics. A brief introduction is given to the Yang-Baxter equation in integrable quantum field theory and lattice statistical physics. The quantum…
We present a fluctuating $N$ formalism, based on second-quantization, to describe large $N$ vector models from field theory using Hamiltonian methods. We first present the method in the simpler setting of a quantum mechanical system with…
The strange-quark vector current form factors of the nucleon are analyzed within the framework of dispersion relations. Particular attention is paid to contributions made by $K\bar{K}$ intermediate states to the form factor spectral…
The calculation of massive three-loop QCD form factors using in particular the large moments method has been successfully applied to quarkonic contributions in [1]. We give a brief review of the different steps of the calculation and report…
We present an overview of the theory of finite groups, with regard to their application as flavour symmetries in particle physics. In a general part, we discuss useful theorems concerning group structure, conjugacy classes, representations…
Quantum systems with a finite number of states at all times have been a primary element of many physical models in nuclear and elementary particle physics, as well as in condensed matter physics. Today, however, due to a practical demand in…
Using the fact that any linear representation of a group can be embedded into permutations, we propose a constructive description of quantum behavior that provides, in particular, a natural explanation of the appearance of complex numbers…
In this communication, we consider the normal ordering of sums of elements of the form (a*^r a a*^s), where a* and a are boson creation and annihilation operators. We discuss the integration of the associated one-parameter groups and their…
The physics of the gravitational form factors of the proton, and their understanding within quantum chromodynamics, has advanced significantly in the past two decades through both theory and experiment. This Colloquium provides an overview…
Nucleon electromagnetic form factors are fundamental quantities related to the charge and magnetization distributions inside the nucleon. Understanding the nucleon electromagnetic structure in terms of the underlying quark and gluon degrees…
The spectral fluctuations of a quantum Hamiltonian system with time-reversal symmetry are studied in the semiclassical limit by using periodic-orbit theory. It is found that, if long periodic orbits are hyperbolic and uniformly distributed…
The probability that the commutator of two group elements is equal to a given element has been introduced in literature few years ago. Several authors have investigated this notion with methods of the representation theory and with…
In these lecture notes prepared for the 11th Taiwan Spring School, Taipei 1997}, and updated for the Saalburg summer school 1998, we review the solutions of O(N) or U(N) models in the large N limit and as 1/N expansions, in the case of…
We construct new examples of non-nil algebras with any number of generators, which are direct sums of two locally nilpotent subalgebras. As all previously known examples, our examples are contracted semigroup algebras and the underlying…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
The meaning of quantum group transformation properties is discussed in some detail by comparing the (co)actions of the quantum group with those of the corresponding Lie group, both of which have the same algebraic (matrix) form of the…
We give a complete list of indecomposable characters of the infinite symmetric semigroup. In comparison with the analogous list for the infinite symmetric group, one should introduce only one new parameter, which has a clear combinatorial…
We present a few combinatorial identities which were encountered in our work on the spectral theory of quantum graphs. They establish a new connection between the theory of random matrix ensembles and combinatorics.