Related papers: Functional Equations and Separation of Variables f…
Graphical functions have emerged as a powerful framework for evaluating multi-loop Feynman integrals in perturbative quantum field theory. Defined as massless three-point position-space integrals, they reveal rich analytic structures and…
We establish square function estimates for integral operators on uniformly rectifiable sets by proving a local $T(b)$ theorem and applying it to show that such estimates are stable under the so-called big pieces functor. More generally, we…
We prove large deviation principles for $\int_0^t \gamma(X_s)ds$, where $X$ is a $d$-dimensional self-similar Gaussian process and $\gamma(x)$ takes the form of the Dirac delta function $\delta(x)$, $|x|^{-\beta}$ with $\beta\in (0,d)$, or…
Correlation functions of the XXZ spin chain in the critical regime is studied at zero-temperature. They are exactly represented in the Fredholm determinant form and are related with an operator-valued Riemann-Hilbert problem. Analyzing this…
We apply the monodromy method for the calculation of the functional determinant of a special second order differential operator $F=-d^2/d\tau^2+{\ddot g}/g$, $\ddot g= d^2g/d\tau^2$, subject to periodic boundary conditions with a periodic…
Nonlocal QFT of one-component scalar field $\varphi$ in $D$-dimensional Euclidean spacetime is considered. The generating functional (GF) of complete Green functions $\mathcal{Z}$ as a functional of external source $j$, coupling constant…
We propose a general path-integral definition of two-dimensional quantum field theories deformed by an integrable, irrelevant vector operator constructed from the components of the stress tensor and those of a $U(1)$ current. The deformed…
The formalism developed in the first paper of the series [arXiv:0901.1060] is applied to two thermodynamic systems: (i) of three global observables (the energy, the total electron number and the spin number), (ii) of one global observable…
We review the construction of the fermionic basis for sinh-Gordon model and investigate numerically the ultra-violet limit of the one-point functions. We then compare the predictions obtained from this formalism against previously…
This paper studies the performance of time-dependent density-functional theory (TDDFT) for calculating the dielectric function of semiconductors and insulators at finite momentum transfer, comparing against the standard Bethe-Salpeter…
The entanglement entropy in three-dimensional conformal field theories (CFTs) receives a logarithmic contribution characterized by a regulator-independent function $a(\theta)$ when the entangling surface contains a sharp corner with opening…
We study the statistical mechanics of the self-gravitating gas at thermal equilibrium with two kinds of particles. We start from the partition function in the canonical ensemble which we express as a functional integral over the densities…
After a brief review of the definition and properties of the quantum effective Hamiltonian action we describe its renormalization flow by a functional RG equation. This equation can be used for a non-perturbative quantization and study also…
We derive a linearized kinetic equation for fermionic excitations with an ultrasoft momentum, g^2T, from the Kadanoff-Baym equation in a Yukawa model and quantum electrodynamics (QED) at extremely high T, where g is the coupling constant.…
We show that the partition function for a scalar field in a static spacetime background can be expressed as a functional integral in the corresponding optical space, and point out that the difference between this and the functional integral…
We provide a unified method for obtaining upper bounds for certain functional integrals appearing in quantum mechanics and non-relativistic quantum field theory, functionals of the form $E\left[\exp(A_T)\right]$, the (effective) action…
(R-channel) TBA is elaborated to find the effective central charge dependence on the boundary parameters for the massless boundary sine-Gordon model with the coupling constant $(8\pi) /\beta^2 = 1+ \lambda $ with $\lambda$ a positive…
This work inaugurates a series of complementary studies on Richardson-Gaudin integrable models. We begin by reviewing the foundations of classical and quantum integrability, recalling the algebraic Bethe ansatz solution of the Richardson…
E-functions are entire functions with algebraic Taylor coefficients satisfying certain arithmetic conditions, and which are also solutions of linear differential equations with polynomial coefficients. They were introduced by Siegel in 1929…
Density functional theory (DFT) and thermal DFT (thDFT) calculations were used to evaluate the energy band structure, bandgap, and the total energy of various graphene quantum dots (GQDs). The DFT calculations were performed using local…