Related papers: Schwarzian functional integrals calculus

A mathematically correct approach to study theories with infinite-dimensional groups of symmetries is presented. It is based on quasi-invariant measures on the groups. In this paper, the properties of the measure on the group of…

We derive the general rules of functional integration in the theories of the Schwarzian type, and evaluate explicitly the functional integrals assigning correlation functions in the SYK model.

An explicit form of the functional measure on the factor space $Diff^{1}_{+}(S^{1})/SL(2,\textbf{R})$ is obtained that makes Schwarzian functional integrals calculus simpler and more transparent.

A decomposition of the Wiener measure based on its quasi-invariance under the group of diffeo- morphisms is proposed. As a result, functional integrals in the Schwarzian theory can be written as the Fourier transform of the integrals in a…

We derive the explicit form of the polar decomposition of the Wiener measure, and obtain the equation connecting functional integrals in conformal quantum mechanics to those in the Schwarzian theory. Using this connection we evaluate some…

Let $\mathcal{A}$ denote the class of analytic functions $f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ normalized by $f(0)=0$, $f'(0)=1$. In the present article, we obtain the sharp estimates of the Schwarzian norm for…

Using simple models in D=0+0 and D=0+1 dimensions we construct partition functions and compute two-point correlations. The exact result is compared with saddle-point approximation and solutions of Schwinger-Dyson equations. When integrals…

The core of this article is a general theorem with a large number of specializations. Given a manifold $N$ and a finite number of one-parameter groups of point transformations on $N$ with generators $Y, X_{(1)}, \cdots, X_{(d)} $, we…

A consistent functional calculus approach to the spectral theorem for strongly commuting normal operators on Hilbert spaces is presented. In contrast to the common approaches using projection-valued measures or multiplication operators,…

A normalized analytic function f is shown to be univalent in the open unit disk D if its second coefficient is sufficiently small and relates to its Schwarzian derivative through a certain inequality. New criteria for analytic functions to…

In this paper, we study integral functionals defined on spaces of functions with values on general (non-separable) Banach spaces. We introduce a new class of integrands and multifunctions for which we obtain measurable selection results.…

The explicit evaluation of the partition function in the Schwarzian theory is presented.

Let $\mathcal{A}$ denote the class of analytic functions $f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ normalized by $f(0)=0$, $f'(0)=1$. For $-\pi/2<\alpha<\pi/2$, let $\mathcal{S}_{\alpha}$ be the subclass of $\mathcal{A}$…

There exists an extensive and fairly comprehensive discrete analytic function theory which is based on circle packing. This paper introduces a faithful discrete analogue of the classical Schwarzian derivative to this theory and develops its…

Let $\mathcal{A}$ be the class of analytic functions $f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ with the normalized conditions $f(0)=0$, $f'(0)=1$. For $-\pi/2<\alpha<\pi/2$ and $0\le \beta<1$, let…

In the present article, we discuss about the estimate of the pre-Schwarzian and Schwarzian norms for locally univalent harmonic functions $f=h+\overline{g}$ in the unit disk $\mathbb{D}:=\{z\in\mathbb{C}:\, |z|<1\}$. In this regard, we…

We study correlation functions of the probabilistic Schwarzian Field Theory. We compute cross-ratio correlation functions exactly in the case when the corresponding Wilson lines do not intersect, confirming predictions made in the physics…

We develop the integral calculus for quasi-standard smooth functions defined on the ring of Fermat reals. The approach is by proving the existence and uniqueness of primitives. Besides the classical integral formulas, we show the…

The Schwarzian derivative plays a fundamental role in complex analysis, differential equations, and modular forms. In this paper, we investigate its higher-order generalizations, known as higher Schwarzians, and their connections to…

Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…