Related papers: On Fock-Bargmann space, Dirac delta function, Feyn…
We study spinning particle/defect geometries in the context of AdS$_3$/CFT$_2$. These solutions lie below the BTZ threshold, and can be obtained from identifications of AdS$_3$. We construct the Feynman propagator by solving the bulk…
We generalize Gopakumar's microscopic derivation of Witten diagrams in large N free quantum field theory [1] to interacting theories in perturbative expansion. For simplicity we consider a matrix scalar field with $\Phi^h$ interaction in d…
The $N=4$ SU(2)$_k$ superconformal algebra has the global automorphism of SO(4) $\approx$ SU(2)$\times$SU(2) with the {\it left} factor as the Kac-Moody gauge symmetry. As a consequence, an infinite set of independent algebras labeled by…
We derive new results about properties of the Witten zeta function associated with the group SU(3), and use them to prove an asymptotic formula for the number of n-dimensional representations of SU(3) counted up to equivalence. Our analysis…
In this paper we consider 4d $\mathrm{SU}(N)$ gauge theories with $N+1$ fundamentals, five antifundamentals and a conjugate two index antisymmetric tensor. The model has been shown to be in a mixed phase in the IR, splitting in an…
A supersymmetric extension of the Hahn algebra is introduced. This quadratic superalgebra, which we call the Hahn superalgebra, is constructed using the realization provided by the Dunkl oscillator model in the plane, whose Hamiltonian…
Special-relativistic dynamically-generated elementary-particle mass is represented by a self-adjoint energy operator acting on a rigged Hilbert space (RHS) of functions over the 6-dimensional Euclidean-group manifold. The energy operator is…
After some introductory comments on the peculiar features of slowly running theories, I will report results obtained using the Schrodinger functional technique for two gauge theories that are believed to lie near the bottom of the conformal…
We derive a new asymptotic formula for the Wigner $9j$-symbol, in the limit of one small and eight large angular momenta, using a novel gauge-invariant factorization for the asymptotic solution of a set of coupled wave equations. Our…
In this paper we continue the development of a spectral triple-like construction on a configuration space of gauge connections. We have previously shown that key elements of bosonic and fermionic quantum field theory emerge from such a…
In the context of the composite boson interpretation, we construct the exact general solution of the Dirac--K\"ahler equation for the case of the spherical Riemann space of constant positive curvature, for which due to the geometry itself…
Total-angular-momentum (TAM) waves provide a set of basis functions for scalar, vector, and tensor fields that can be used in place of plane waves and that reflect the rotational symmetry of the spherical sky. Here we discuss three-point…
Dirac's leaping insight that the normalized anti-commutator of the {\gamma}^{\mu} matrices must equal the timespace signature {\eta}^{\mu}{\nu} was decisive for the success of his equation. The {\gamma}^{\mu}-s are the same in all Lorentz…
The irreducible representations of the Lie algebra ${\frak su}$(3) describe rotational bands in the context of the nuclear shell and interacting boson models. The density matrices associated with ${\frak su}$(3) provide an alternative…
SU(3) gauge theory with overlap fermions in the 2-index symmetric (sextet) and fundamental representations is considered. A priori it is not known what the pattern of chiral symmetry breaking is in a higher dimensional representation…
We study a 3-loop 5-propagator Feynman Integral, which we call the vacuum seagull, with arbitrary masses and spacetime dimension using the Symmetries of Feynman Integrals method. It is our first example with potential numerators. We…
A novel realization of the classical SU(2) algebra is introduced for the Dirac relativistic hydrogen atom defining a set of operators that, besides, allow the factorization of the problem. An extra phase is needed as a new variable in order…
The relevance of the contracted SU(4) group as a symmetry group of the pion nucleon scattering amplitudes in the large $N_c$ limit of QCD raises the problem on the construction of effective Lagrangians for SU(4) supermultiplets. In the…
In this work we study symplectic unitary representations for the Galilei group. As a consequence the Schr\"odinger equation is derived in phase space. The formalism is based on the non-commutative structure of the star-product, and using…
We report on the status of our programme to simulate Sp($2N$) gauge theories on the lattice. Motivated by the potential realization of an SU($4$)/Sp($4$)$\sim$SO($6$)/SO($5$) composite Higgs model and the applications to self interacting…