Related papers: More Remarks on High Energy Evolution
A commuting $n$-tuple $(T_1, \ldots, T_n)$ of bounded linear operators on a Hilbert space $\clh$ associate a Hilbert module $\mathcal{H}$ over $\mathbb{C}[z_1, \ldots, z_n]$ in the following sense: \[\mathbb{C}[z_1, \ldots, z_n] \times…
We have in earlier papers presented an extension of Mueller's dipole cascade model, which includes subleading effects from energy conservation and running coupling as well as colour suppressed effects from pomeron loops via a ``dipole…
In this work, we derive a set of boost-weighted $w$ functionals of the metric, with $w\in\{2,1,0,-1,-2\}$, which transform semi-covariantly under the action of the near-horizon symmetry group. In particular, we demonstrate that the…
A complete classification of continuous, dually epi-translation invariant, and rotation equivariant valuations on convex functions is established. This characterizes the recently introduced functional Minkowski vectors, which naturally…
Density scaling has a rich history in density functional theory, providing exact conditions for use in the construction of ever more accurate approximations to the unknown exchange-correlation functional. We define a conjugate potential…
We study a class of self-adjoint operators defined on the direct sum of two Hilbert spaces: a finite dimensional one called sometimes a ``small subsystem'' and an infinite dimensional one -- a ``reservoir''. The operator, which we call a…
We study the Hilbert space structure of gauge-invariant operators emergent in large-$N$ multi-matrix quantum mechanics. Building on the framework of \cite{deMelloKoch:2025ngs}, we identify a class of light single-trace operators that behave…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
In a thermodynamical model of cosmological FLRW event horizons for the dark energy (DE), we consider a logarithmic corrective term in the entropy to which corresponds a new term in the DE density. This model of $\Lambda (t)$ in an…
For a Kahler manifold X, we study a space of test functions W* which is a complex version of H1. We prove for W* the classical results of the theory of Dirichlet spaces: the functions in W* are defined up to a pluripolar set and the…
In this note we study sub-Hardy Hilbert spaces on which the the action of the operator of multiplication by the coordinate function z is assumed to be weaker than that of an isometry. We identify such operators with a class of weighted…
Using the harmonic superspace techniques in D=2 N=4, we present an explicit derivation of a new hyper-Kahler metric associated to the Toda like self interaction $H ^{4+}(\omega, u)= (\frac{\xi^{++}}{\lambda})^{2}\exp(2\lambda \omega)$. Some…
We show how to relate Schramm-Loewner Evolutions (SLE) to highest-weight representations of infinite dimensional Lie Algebras using the conformal restriction properties studied by Lawler, Schramm and Werner in the paper…
We study integration in a class of Hilbert spaces of analytic functions defined on the $\mathbb{R}^s$. The functions are characterized by the property that their Hermite coefficients decay exponentially fast. We use Gauss-Hermite…
Ensemble density functional theory (eDFT) is an exact time-independent alternative to time-dependent DFT (TD-DFT) for the calculation of excitation energies. Despite its formal simplicity and advantages in contrast to TD-DFT (multiple…
In view of recent developments of the study of reproducing kernel Hilbert spaces, in particular with the context the Hardy spaces on tubes, aspects of rational approximation for functions of finite energy in several complex and several real…
The long time behavior of the reduced time evolution operator for unstable multilevel systems is studied based on the N-level Friedrichs model in the presence of a zero energy resonance.The latter means the divergence of the resolvent at…
This paper extends the theory of Zen spaces (weighted Hardy/Berg\-man spaces on the right-hand half-plane) to the Hilbert-space valued case, and describes the multipliers on them; it is shown that the methods of $H^\infty$ control can…
Field theories place one or more degrees of freedom at every point in space. Hilbert spaces describing quantum field theories, or their finite-dimensional discretizations on lattices, therefore have large amounts of structure: they are…
A two Higgs doublet model with special Yukawa interactions for the top quark and a softly broken discrete symmetry in the Higgs potential is proposed. In this model, the top quark is much heavier than the other quarks and leptons because it…