Related papers: Building Momentum Kernel from Shapovalov Form
In the uniformly discrete case of virtual persistence diagram groups $K(X,A)$, we construct a translation-invariant heat semigroup. The kernels are supported on a countable subgroup $H$, and the restriction to $H$ has Fourier exponent…
The aim of these lectures is to give a self-contained introduction to nonrelativistic potential models, to their formulation as well as to their possible applications. At the price of some lack of (in a mathematical sense) rigorous…
Different forms of the BFKL kernel both in coordinate and momentum representations may appear as a result of different gauge choices and/or inner scalar products of the color singlet states. We study a spectral representation of the BFKL…
A low momentum nucleon-nucleon (NN) potential $V_{low-k}$ is derived from meson exhange potentials by integrating out the model dependent high momentum modes of $V_{NN}$. The smooth and approximately unique $V_{low-k}$ is used as input for…
We study modules over stacks of deformation quantization algebroids on complex Poisson manifolds. We prove finiteness and duality theorems in the relative case and construct the Hochschild class of coherent modules. We prove that this class…
We review the recent developments of quantum invariants of 3-manifolds and links: $\hat{Z}$ and $F_L$. They are $q$-series invariants originated from mathematical physics. They exhibit rich features, for example, quantum modularity,…
Recent cross section (e,e'pN) short-range correlation experiments have clearly shown the strong dominance of tensor correlations for (e,e'p) missing momenta greater than the Fermi momentum; while recent D(e,e'p)n and 4He(e,e'p)t asymmetry…
We perform a comprehensive analysis of the homogeneous finite modular group $\Gamma'_4\equiv S'_4$ which is the double covering of $S_4$ group. The weight 1 modular forms of level 4 are constructed in terms of Dedekind eta function, and…
We calculate the leading quantum corrections to the meson form factors of nonrelativistic kinks, at momentum transfer much higher than the meson mass. We consider general scalar theories which need not be integrable. Our approach is much…
A comparative study of the liquid-drop model (LDM) type expansions of energy $E$ and compression modulus $K_A$ is made within the energy density formalism using Skyrme interactions. As compared to the energy expansion, it is found that, in…
Random operator tuples possess a rich second-moment structure that is not visible at the level of pointwise operator inequalities. This paper shows that their averaged word moments form a positive kernel whose behavior is controlled by a…
We construct the one-loop effective action in Yang-Mills and Pure Quantum Gravity theories with heat kernel(or proper time method), which maintains manifest covariance during and after quantization (gauge and diffeomorphism invariance are…
We study the $\varphi$-Verma modules of the Heisenberg subalgebra $\mathcal{H}_m$ of the universal central extension of $\mathfrak{sl}_2 \otimes A_m$, where $A_m$ is the coordinate ring of the superelliptic curve $u^m = P(t)$, and ask how…
This document is the first iteration of an attempt to collate information about small-rank groups of Lie type over small fields, and their representation theory over the defining field. This information is important in the author's work on…
Fix any Borcherds-Kac-Moody $\mathbb{C}$-Lie algebra (BKM LA) $\mathfrak{g}=\mathfrak{g}(A)$ of BKM-Cartan matrix $A$, and Cartan subalgebra $\mathfrak{h}\subset \mathfrak{g}$. In this paper, we obtain explicit weight formulas of any…
We study the production of Mueller-Navelet jets at hadron colliders in the Balitsky-Fadin-Kuraev-Lipatov (BFKL) framework. We show that a measurement of the relative azimuthal angle \Delta\Phi between the jets can provide a good testing…
We show that in the presence of massive particles such as nucleons, the standard low energy expansion in powers of meson momenta and light quark masses in general only converges in part of the low energy region. The expansion of the scalar…
The nuclear magnetic moment is an important physical observable and serves as a useful tool for the stringent test of nuclear models. For the past decades, the covariant density functional theory and its extension have been proved to be…
Let $\mathfrak{g}$ be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker $\mathfrak{g}$-modules $Y(\chi, \eta)$ introduced by Kostant. We prove that the set of all contravariant…
Background: The major challenge for nuclear theory is to describe and predict global properties and collective modes of atomic nuclei. Of particular interest is the response of the nucleus to a time-dependent external field that impacts the…