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Superstring amplitudes of an arbitrary genus are calculated through super-Schottky parameters by a summation over the fermion strings. For a calculation of divergent multi-loop fermion string amplitudes a supermodular invariant…
We introduce a new Hopf algebra that operates on pairs of finite interval partitions and permutations of equal length. This algebra captures vincular patterns, which involve specifying both the permutation patterns and the consecutive…
We have recently proposed arXiv:2105.11565 a powerful method for computing group factors of the perturbative series expansion of the Wilson loop in the Chern-Simons theory with $SU(N)$ gauge group. In this paper, we apply the developed…
We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in…
Recently, we have derived the changes in the absorption spectrum of an exciton when this exciton is photocreated close to a metal. The resolution of this problem -- which has similarities with Fermi edge singularities -- has been made…
Two programs for the computation of perturbative expansions of quantum field theory amplitudes are provided. feyngen can be used to generate Feynman graphs for Yang-Mills, QED and $\varphi^k$ theories. Using dedicated graph theoretic tools…
We study the principal aspects of the interaction between acoustic phonons and two-dimensional electrons in quantizing magnetic fields corresponding to even denominator fractions. Using the composite fermion approach we derive the vertex of…
A new method of calculation of amplitudes of different processes in quantum electrodynamics is proposed. The method does not use the Feynman technique of trace of product of matrices calculation. The method strongly simplifies calculation…
We rewrite the (extended) Ooguri-Vafa partition function for colored HOMFLY-PT polynomials for torus knots in terms of the free-fermion (semi-infinite wedge) formalism, making it very similar to the generating function for double Hurwitz…
The multiple scale expansion method is used to derive amplitude equations for a system with thermohaline convection in the neighborhood of Hopf and Taylor bifurcation points and at the double zero point of the dispersion relation. A complex…
We propose an exact map from commuting lattice spin systems with gauge interactions to fermionic models in an arbitrary number of dimensions.
The matrix element squared for Compton scattering of a heavy photon on a longitudinally polarized electron is calculated. The gauge-invariant tensor structure of the heavy photon polarization is considered, assuming that all kinematical…
A number theoretic algorithm is given for writing gauge theory amplitudes in a compact manner. It is possible to write down all details of the complete $L$ loop amplitude with two integers, or a complex integer. However, a more symmetric…
Explicit treatment of many-body Fermi statistics in path integral Monte Carlo (PIMC) results in exponentially scaling computational cost due to the near cancellation of contributions to observables from even and odd permutations. Through…
We present an alternative approach for calculating helicity amplitudes for processes involving both massless and massive fermions. With this method one can easily obtain covariant expressions for the helicity amplitudes. The final…
We present an algorithm for the numerical calculation of one-loop QCD amplitudes. The algorithm consists of subtraction terms, approximating the soft, collinear and ultraviolet divergences of one-loop amplitudes and a method to deform the…
Attractive interaction between fermions can lead to pairing and superfluidity in an optical lattice. In contrast to the `continuum', on a lattice the trap induced density variation can generate a non monotonic profile of the pairing…
A mapping technique is used to derive in the context of constituent quark models effective Hamiltonians that involve explicit hadron degrees of freedom. The technique is based on the ideas of mapping between physical and ideal Fock spaces…
We develop a novel amplitude bootstrap technique manifestly free of unphysical poles for classically spinning particles interacting with gravitons utilizing only the double-copy and physical factorization limits. Combined with…
Let $H$ be a semisimple Hopf algebras over an algebraically closed field $k$ of characteristic $0.$ We define Hopf algebraic analogues of commutators and their generalizations and show how they are related to $H',$ the Hopf algebraic…