Related papers: Onsager-Machlup functional for $\text{SLE}_{\kappa…
I present results for the two-loop self-energy functions for scalars in a general renormalizable field theory, using mass-independent renormalization schemes based on dimensional regularization and dimensional reduction. The results are…
Three-loop $\beta$-functions of the Minimal Supersymmetric Standard Model regularized by higher covariant derivatives are obtained for an arbitrary supersymmetric subtraction scheme. For this purpose we first calculate two-loop anomalous…
A generalized semiclassical quantization condition for cyclotron orbits was recently proposed by Gao and Niu \cite{Gao}, that goes beyond the Onsager relation \cite{Onsager}. In addition to the integrated density of states, it formally…
In a path-integral approach to quantum cosmology, the Lorenz gauge-averaging term is studied for Euclidean Maxwell theory on a portion of flat four-space bounded by two concentric three-spheres, but with arbitrary values of the gauge…
Loewner driving functions encode simple curves in 2-dimensional simply connected domains by real-valued functions. We prove that the Loewner driving function of a $C^{1,\beta}$ curve (differentiable parametrization with $\beta$-H\"older…
We study successive measurements of two observables using von Neumann's measurement model. The two-pointer correlation for arbitrary coupling strength allows retrieving the initial system state. We recover Luders rule, the Wigner formula…
Motivated by recent developments on random polymer models we propose a generalisation of reflected Brownian motion (RBM) in a polyhedral domain. This process is obtained by replacing the singular drift on the boundary by a continuous one…
Let $M_n$ be a simple triangulation of the sphere $S^2$, drawn uniformly at random from all such triangulations with n vertices. Endow $M_n$ with the uniform probability measure on its vertices. After rescaling graph distance on $V(M_n)$ by…
On a compact Riemannian manifold (V_{m},g), we consider the second order positive operator L_{\epsilon} = \epsilon\Delta_{g} +(b,\nabla) +c, where -\Delta_{g} is the Laplace-Beltrami operator and b is a Morse-Smale (MS) field, \epsilon a…
In this article, we prove the existence of measure-valued solutions to the Ericksen-Leslie system equipped with the Oseen-Frank energy. We introduce the concept of generalized gradient Young measures. Via a Galerkin approximation, we show…
We discuss the possible set of operators from various boundary conformal field theories to build meaningful correlators that lead via a Loewner type procedure to generalisations of SLE($\kappa,\rho$). We also highlight the necessity of…
We extend the Poincar\'{e}--Borel lemma to a weak approximation of a Brownian motion via simple functionals of uniform distributions on n-spheres in the Skorokhod space $D([0,1])$. This approach is used to simplify the proof of the…
The conformal loop ensemble (CLE) is the canonical conformally invariant probability measure on non-crossing loops in a simply connected domain in $\mathbb C$ and is indexed by a parameter $\kappa \in (8/3,8)$. We consider CLE$_\kappa$ on…
The $ \beta $-functions of marginal couplings are known to be closely related to the $ A $-function through Osborn's equation, derived using the local renormalization group. It is possible to derive strong constraints on the…
Wave function collapse models are considered as the modified theories of standard quantum mechanics at the macroscopic level. By introducing nonlinear stochastic terms in the Schr\"odinger equation, these models make predictions,…
The effective renormalizable theory describing electromagnetic and strong interactions of quarks of five light flavors ($n_f = 5$ QCD$\times$QED) is considered as a low-energy limit of the full Standard Model. Two-loop relation between the…
We present the beta functions of gauge and Yukawa couplings in general four-dimensional quantum field theory, at four and three loops, respectively. The essence of our approach is fixing unknown coefficients in the most general ansatz for…
We present a simple method for deriving the renormalization counterterms from the components of the energy-momentum tensor in curved space-time. This method allows full control over the finite parts of the counterterms and provides explicit…
The loop equation satisfied by Wilson's loops in QCD is reformulated as a functional Laplace equation. Discretizing the loop space by polygons, Green's function of the functional Laplacian is represented as a path integral of the Euclidean…
We compute the three-loop beta functions of long-range multi-scalar models with general quartic interactions. The long-range nature of the models is encoded in a kinetic term with a Laplacian to the power $0<\zeta<1$, rendering the…