Related papers: On the Form Factor for the Unitary Group
In these notes we will survey recent results on various finitary approximation properties of infinite groups. We will discuss various restrictions on groups that are approximated for example by finite solvable groups or finite-dimensional…
I describe recent advances in our understanding of the hadronic form factors governing semileptonic meson transitions. The resulting framework provides a systematic approach to the experimental data, as a means of extracting precision…
The main statement of the nucleon constituent quark model with a fixed number of particles as basic ansatz are considered in a framework of the single-time (quasipotential) approach to the bound state problem. The scaling law breacking for…
We extend the relation between quasi-modular forms and modular forms to a wider class of functions. We then relate both forms to vector-valued modular forms with symmetric power representations, and prove a general structure theorem for…
We reanalyze the world data on the electromagnetic form factors of the nucleon. The calculations are performed in the framework of an algebraic model of the nucleon combined with vector meson dominance.
We analyse various $U(1)_{EM}$ form factors of mesons at strong coupling in an $\mathcal{N}=2$ flavored version of $\mathcal{N}=4$ $SYM$ which becomes conformal in the UV. The quark mass breaks the conformal symmetry in the IR and generates…
This paper is dedicated to a detailed analysis and computation of quantum states of causal fermion systems. The mathematical core is to compute integrals over the unitary group asymptotically for a large dimension of the group, for various…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
This is a survey of recent progress in several areas of combinatorial algebra. We consider combinatorial problems about free groups, polynomial algebras, free associative and Lie algebras. Our main idea is to study automorphisms and, more…
Using generating functions, we enumerate regular semisimple conjugacy classes in the finite classical groups. For the general linear, unitary, and symplectic groups this gives a different approach to known results; for the special…
This is the second one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with almost simple unitary groups.
The electromagnetic form factors of hadrons at large momentum transfer have been the subject of intense theoretical and experimental scrutiny over the past two decades, yet there is still not a universally-accepted framework for their…
We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…
The boundary contribution of an amplitude in the BCFW recursion relation can be considered as a form factor involving boundary operator and unshifted particles. At the tree-level, we show that by suitable construction of Lagrangian, one can…
The nucleon form factors of the energy-momentum tensor are studied in the large-Nc limit in the framework of the chiral quark-soliton model.
In this note a combinatorial formula related to the symmetric group is generalized to an arbitrary finite Weyl group.
We study the electromagnetic on-shell form factor of quarks in massless perturbative QCD. We derive the complete pole part in dimensional regularization at three loops, and extend the resummation of the form factor to the…
The composite system, formed by two $S=1$ particles, is considered. The field operators of constituents are transformed on the $(1,0)\oplus (0,1)$ representation of the Lorentz group. The problem of interaction of $S=1$ particle with the…
We show how to use quantum mechanics on the group manifold U(N) as a tool for problems in U(N) representation theory. The quantum mechanics reduces to free fermions on the circle, which in the large N limit become relativistic. The theory…
The quarkonic contributions to the three-loop heavy-quark form factors for vector, axial-vector, scalar and pseudoscalar currents are described by closed form difference equations for the expansion coefficients in the limit of small…