# THE PERTURBATIVE APPROACH TO PATH INTEGRALS: A SUCCINCT MATHEMATICAL TREATMENT

@article{Nguyen2016THEPA, title={THE PERTURBATIVE APPROACH TO PATH INTEGRALS: A SUCCINCT MATHEMATICAL TREATMENT}, author={Timothy Nguyen}, journal={Journal of Mathematical Physics}, year={2016}, volume={57}, pages={092301} }

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 involves a proper understanding of how Wick’s theorem allows one to evaluate integrals perturbatively, i.e., as a series expansion in a formal parameter irrespective of convergence properties. We establish invariance properties of such a Wick expansion under coordinate changes and the action of a Lie group of symmetries…

## 9 Citations

Quantum Yang-Mills Theory in Two Dimensions: Exact versus Perturbative

- Physics
- 2015

The standard Feynman diagrammatic approach to quantum field theories assumes that perturbation theory approximates the full quantum theory at small coupling even when a mathematically rigorous…

Wilson Loop Area Law for 2D Yang-Mills in Generalized Axial Gauge

- Mathematics
- 2016

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 analysis occurs within a…

Stochastic Feynman Rules for Yang-Mills Theory on the Plane

- Mathematics
- 2016

We analyze quantum Yang-Mills theory on $\mathbb{R}^2$ using a novel discretization method based on an algebraic analogue of stochastic calculus. Such an analogue involves working with "Gaussian"…

A Functional Integral Approaches to the Makeenko–Migdal Equations

- MathematicsCommunications in Mathematical Physics
- 2019

Makeenko and Migdal (1979) gave heuristic identities involving the expectation of the product of two Wilson loop functionals associated to splitting a single loop at a self-intersection point.…

Effective Locality QCD calculations and the Gribov copy problem

- Physics
- 2020

Standard functional manipulations have been proven to imply a remarkable property satisfied by the fermionic Green’s functions of QCD and dubbed effective locality. Resulting from a full gauge…

Dimensionally regularized Boltzmann–Gibbs statistical mechanics and two-body Newton’s gravitation

- PhysicsPhysica A: Statistical Mechanics and its Applications
- 2018

Newton’s gravitation-force’s classical average proof of a Verlinde’s conjecture

- PhysicsPhysica A: Statistical Mechanics and its Applications
- 2018

Dimensionally regularized Tsallis’ statistical mechanics and two-body Newton’s gravitation

- Physics
- 2018

A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2005{2009

- Mathematics
- 2015

(2 < p < 4) [200]. (Uq(∫u(1, 1)), oq1/2(2n)) [92]. 1 [273, 79, 304, 119]. 1 + 1 [252]. 2 [352, 318, 226, 40, 233, 157, 299, 60]. 2× 2 [185]. 3 [456, 363, 58, 18, 351]. ∗ [238]. 2 [277]. 3 [350]. p…

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