10 citations · 26 across the 8 of their papers we have counts for
11 papers
A Response to Economics as Gauge Theory
Timothy Nguyen
We provide an analysis of the recent work by Malaney-Weinstein on "Economics as Gauge Theory" presented on November 10, 2021 at the Money and Banking Workshop hosted by University…
Stochastic Feynman Rules for Yang-Mills Theory on the Plane
Timothy Nguyen
We analyze quantum Yang-Mills theory on using a novel discretization method based on an algebraic analogue of stochastic calculus. Such an analogue involves working…
Wilson Loop Area Law for 2D Yang-Mills in Generalized Axial Gauge
Timothy Nguyen
We prove that Wilson loop expectation values for arbitrary simple closed contours obey an area law up to second order in perturbative two-dimensional Yang-Mills theory. Our analysi…
Quantum Yang-Mills Theory in Two Dimensions: Exact versus Perturbative
Timothy Nguyen
The standard Feynman diagrammatic approach to quantum field theories assumes that perturbation theory approximates the full quantum theory at small coupling even when a mathematica…
The Perturbative Approach to Path Integrals: A Succinct Mathematical Treatment
Timothy Nguyen
We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This in…
Quantization of the Nonlinear Sigma Model Revisited
Timothy Nguyen
We revisit the subject of perturbatively quantizing the nonlinear sigma model in two dimensions from a rigorous, mathematical point of view. Our main contribution is to make precis…
Lagrangian correspondences and Donaldson's TQFT construction of the Seiberg-Witten invariants of 3-manifolds
Timothy Nguyen
Using Morse-Bott techniques adapted to the gauge-theoretic setting, we show that the limiting boundary values of the space of finite energy monopoles on a connected 3-manifold with…
Anisotropic Function Spaces and Elliptic Boundary Value Problems
Timothy Nguyen
In this paper, we study anisotropic Bessel potential and Besov spaces, where the anisotropy measures the extra amount of regularity in certain directions. Some basic properties of…
The Seiberg-Witten Equations on Manifolds with Boundary II: Lagrangian Boundary Conditions for a Floer Theory
Timothy Nguyen
In this paper, we study the Seiberg-Witten equations on the product R x Y, where Y is a compact 3-manifold with boundary. Following the approach of Salamon and Wehrheim in the inst…
The Seiberg-Witten Equations on Manifolds with Boundary I: The Space of Monopoles and Their Boundary Values
Timothy Nguyen
In this paper, we study the Seiberg-Witten equations on a compact 3-manifold with boundary. Solutions to these equations are called monopoles. Under some simple topological assumpt…
On discrete features of the wave equation in singular pp-wave backgrounds
Oleg Evnin, Timothy Nguyen
We analyze the wave equation in families of pp-wave geometries developing strong localized scale-invariant singularities in certain limits. For both cases of well-localized pp-wave…