相关论文: Lecture notes on the Gaussian Free Field

We give a broad overview of a construction of a theory for matter on fixed causal set backgrounds. We introduce the Sorkin-Johnston formalism for a free (real) scalar field theory that is applicable to regions of continuum spacetimes as…

We summarize the main ideas behind TGFT condensate cosmology and sketch the technical steps that bring from the fundamental theory to the effective cosmological dynamics. This framework is presented as an explicit illustration of (and…

In recent years, investigations of gravitational interactions has led us to discover new facets of the fundamental force. With these discoveries the general theory of relativity is under greater scrutiny now than it was 100 years ago.…

These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric…

Miller and Sheffield introduced the notion of an imaginary surface as an equivalence class of pairs of simply connected proper subdomains of $\mathbb{C}$ and Gaussian free fields (GFFs) on them under the conformal equivalence. They…

We begin with isotropic Gaussian random fields, and show how the Bochner-Godement theorem gives a natural way to describe their covariance structure. We continue with a study of Mat\'ern processes on Euclidean space, spheres, manifolds and…

We study the motion of an inertial particle in a fractional Gaussian random field. The motion of the particle is described by Newton's second law, where the force is proportional to the difference between a background fluid velocity and the…

We examine the incorporation of gauge symmetries in the modern effective field theory (EFT) matching paradigm with a particular focus on spontaneously broken symmetries. The presence of gauge symmetries entails the introduction of…

We present a "dictionary" to expedite the identification of potential deviations in gravitational waveforms from those predicted by General Relativity (GR) during the inspiral phase of black hole binaries. Assuming deviations from GR can be…

We provide a generalization of the Gaussian Kinematic Formula (GKF) in Taylor(2006) for multivariate, heterogeneous Gaussian-related fields. The fields under consideration are non-Gaussian fields built out of smooth, independent Gaussian…

Quantization of Free Fields: The non-interacting field belonging to a new {\bf SO(1,3)\/} gauge field theory equivalent to General Relativity is canonically quantized in the Lorentz gauge and the physical Fock space for free gauge particles…

Assuming an effective quadratic Hamiltonian, we derive an approximate, linear stochastic equation of motion for the density-fluctuations in liquids, composed of overdamped Brownian particles. From this approach, time dependent two point…

We study a noncommutative deformation of general relativity where the gravitational field is described by a matrix-valued symmetric two-tensor field. The equations of motion are derived in the framework of this new theory by varying a…

An expression for the stress tensor near an external boundary of a discrete mechanical system is derived explicitly in terms of the constituents' degrees of freedom and interaction forces. Starting point is the exact and general coarse…

The quantum field theoretic description of general relativity is a modern approach to gravity where gravitational force is carried by spin-2 gravitons. In the classical limit of this theory, general relativity as described by the Einstein…

This thesis is split into two parts, which are united in the sense that they involve applying ideas from quantum information to fundamental physics. The first part is focused on examining discrete-time models in quantum computation…

We consider anisotropic self-similar random fields, in particular, the fractional Brownian sheet. This Gaussian field is an extension of fractional Brownian motion. We prove some properties of covariance function for self-similar fields…

General equations of the unified field theory, obtained using the curved and torsional space-time, are presented. They contain only independent geometrical parameters (metric and connections) of the metric-affine space, and describe the…

This report provides Green's functions (classical propagators) of gravitational fields appearing in general relativity. The existence of Green's function of the wave equation in curved space with an indefinite metric is ensured owing to the…

In this note, we show that the Local Molecular Field theory of Weeks et. al. can be re-derived as an extremum problem for an approximate Helmholtz free energy. Using the resulting free energy as a classical, fluid density functional yields…