Related papers: Lecture notes on the Gaussian Free Field
Group field theory (GFT) models for quantum gravity coupled to a massless scalar field give rise to cosmological models that reproduce the (expanding or contracting) dynamics of homogeneous and isotropic spacetimes in general relativity at…
Linear free field theories are one of the few Quantum Field Theories that are exactly soluble. There are, however, (at least) two very different languages to describe them, Fock space methods and the Schroedinger functional description. In…
These lecture notes provide a comprehensive introduction to 2d conformal field theory, covering foundational topics such as free fields, minimal models, Zamolodchikov's $c$-theorem, Wess-Zumino-Witten models, modular invariant partition…
We study on the metric graphs two types of scalar Gaussian free fields (GFF), the usual one and the one twisted by a $\{-1,1\}$-valued gauge field. We show that the latter can be obtained, up to an additional deterministic transformation,…
These are lecture notes for an introductory course on noncommutative field and gauge theory. We begin by reviewing quantum mechanics as the prototypical noncommutative theory, as well as the geometrical language of standard gauge theory.…
We investigate the problem of metric fluctuations in the presence of the vacuum fluctuations of matter fields and critically assess the usual assertion that vacuum energy implies a Planckian cosmological constant. A new stochastic classical…
Effective field theories offer a powerful method to unify diverse models under a small set of control parameters, allowing systematic expansions around well-established theories. These techniques, developed in particle physics, were…
Starting from the equations of motion in a 1 + 1 static, diagonal, Lorentzian spacetime, such as the Schwarzschild radial line element, I find another metric, but with Euclidean signature, which produces the same geodesics x(t). This…
Within the framework of the effective field theory approach to the post-Newtonian approximation to General Relativity, we report the so far missing G^3 and G^4 sectors of the conservative two body dynamics at fourth perturbative order for…
We consider the relevance of a collective field theory description for the AdS/CFT correspondence. Collective field theory performs a systematic reorganization of the degrees of freedom of a (non-gravitational) field theory, replacing the…
Open effective field theories provide a systematic framework for describing systems coupled to an environment, where dissipation, noise, and modified conservation laws naturally arise. Working within the Schwinger-Keldysh formalism, we…
We describe two classes of Gaussian self-similar random fields: with strictly stationary rectangular increments and with mild stationary rectangular increments. We find explicit spectral and moving average representations for the fields…
A framework is developed which quantifies the local exchange of energy and momentum between matter and the linearized gravitational field. We derive the unique gravitational energy-momentum tensor consistent with this description, and find…
We define and study a set of operators that compute statistical properties of the Brownian Loop Soup, a conformally invariant gas of random Brownian loops (Brownian paths constrained to begin and end at the same point) in two dimensions. We…
We present a novel way of constructing the Gaussian Free Field on a weighted graph via a dynamical expansion of the Green function along an expanding family of subgraphs. Along the way we obtain the discrete analogue of the classical…
These lectures notes are based on courses given at National Taiwan University, National Chiao-Tung University, and National Tsing Hua University in the spring term of 2015. Although the course was offered primarily for graduate students,…
The requirement that both the matter and the geometry of a spacetime canonically evolve together, starting and ending on shared Cauchy surfaces and independently of the intermediate foliation, leaves one with little choice for…
We consider the Discrete Gaussian Free Field (DGFF) in domains $D_N\subseteq\mathbb Z^2$ arising, via scaling by $N$, from nice domains $D\subseteq\mathbb R^2$. We study the statistics of the values order $\sqrt{\log N}$ below the absolute…
An interpretation of general relativity is developed in which the energy used to lift a body in a static gravitational field increases its rest mass. Observers at different gravitational potentials would experience different mass reference…
This paper is the first in a series revisiting the Faraday effect, or more generally, the theory of electronic quantum transport/optical response in bulk media in the presence of a constant magnetic field. The independent electron…