相关论文: Scaling function and universal amplitude combinati…
We show that the average size of self-avoiding polygons (SAP) with a fixed knot is much larger than that of no topological constraint if the excluded volume is small and the number of segments is large. We call it topological swelling. We…
We study scaling limits of periodically weighted skew plane partitions with semilocal interactions and general boundary conditions. The semilocal interactions correspond to the Macdonald symmetric functions which are $(q,t)$-deformations of…
We construct bases of polynomials for the spaces of square-integrable harmonic functions which are orthogonal to the monogenic and antimonogenic $\mathbb{R}^3$-valued functions defined in a prolate or oblate spheroid.
Generalised bi-adjoint scalar amplitudes, obtained from integrations over moduli space of punctured $\mathbb{CP}^{k-1}$, are novel extensions of the CHY formalism. These amplitudes have realisations in terms of Grassmannian cluster…
While discrete harmonic functions have been objects of interest for quite some time, this is not the case for discrete polyharmonic functions, as appear for instance in the asymptotics of path counting problems. In this article, a novel…
We study spatially localized, time-periodic solutions (breathers) of scalar field theories with various self-interacting potentials on Anti-de Sitter (AdS) spacetimes in $D$ dimensions. A detailed numerical study of spherically symmetric…
The recently-developed "scalar-scaffolding" formulation of gluon amplitudes casts the Yang-Mills (YM) amplitude as a well-defined Laurent series expansion in scalar variables, valid for any spacetime dimension and helicity configuration. In…
We solve the one loop effective scalar field equations for spatial plane waves in massless, minimally coupled scalar quantum electrodynamics on a locally de Sitter background. The computation is done in two different gauges: a non-de Sitter…
We consider logarithmic extensions of the correlation and response functions of scalar operators for the systems with aging as well as Schr\"odinger symmetry. Aging is known to be the simplest nonequilibrium phenomena, and its physical…
Extensions of standard one-dimensional supersymmetric quantum mechanics are discussed. Supercharges involving higher order derivatives are introduced leading to an algebra which incorporates a higher order polynomial in the Hamiltonian. We…
We show how one-loop corrections to scattering amplitudes of scalars and gauge bosons can be obtained from tree amplitudes in one higher dimension. Starting with a complete tree-level scattering amplitude of n+2 particles in five…
The paper contains a geometrization of the autonomous multi-time Lagrangian function of electrodynamics. We point out that this multi-time Lagrangian function comes from electrodynamics and the theory of bosonic strings.
Rational coefficients of special functions in scattering amplitudes are known to simplify on singular surfaces, often diverging less strongly than the na\"ive expectation. To systematically study these surfaces and rational functions on…
We give an explicit recursive formula for the all L-loop integrand for scattering amplitudes in N=4 SYM in the planar limit, manifesting the full Yangian symmetry of the theory. This generalizes the BCFW recursion relation for tree…
In this thesis we show that the partial sums of the Maclaurin series for a certain class of entire functions possess scaling limits in various directions in the complex plane. In doing so we obtain information about the zeros of the partial…
We introduce new function spaces $\mathcal{L}_{W,s}^{q,p}(\mathbb{R}^{n})$ that yield a natural reformulation of the $\ell^{q}L^{p}$ decoupling inequalities for the sphere and the light cone. These spaces are invariant under the Euclidean…
This is a rather personal review of the problem of self-avoiding walks and polygons. After defining the problem, and outlining what is known rigorously and what is merely conjectured, I highlight the major outstanding problems. I then give…
The CHY formalism for massless scattering provides a cohesive framework for the computation of scattering amplitudes in a variety of theories. It is especially compelling because it elucidates existing relations among theories which are…
In this article we study polynomial logarithmic $q$-forms on a projective space and characterize those that define singular foliations of codimension $q$. Our main result is the algebraic proof of their infinitesimal stability when $q=2$…
We construct and apply the classic balayage (sweeping out) of measures and subharmonic functions on closed system of rays in the complex plane with vertex at the origin, including measures and subharmonic functions and infinite order. The…