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Perturbative quantum field theory usually uses second quantisation and Feynman diagrams. The worldline formalism provides an alternative approach based on first quantised particle path integrals, similar in spirit to string perturbation theory. Here we review the history, main features and present applications of the formalism. Our emphasis is on recent developments such as the path integral representation of open fermion lines, the description of colour using auxiliary worldline fields, incorporation of higher spin, and extension of the formalism to non-commutative space.
Stochastic mechanics---the study of classical stochastic systems governed by things like master equations and Fokker-Planck equations---exhibits striking mathematical parallels to quantum mechanics. In this article, we make those parallels more trans
We develop a dynamical symmetry approach to path integrals for general interacting quantum spin systems. The time-ordered exponential obtained after the Hubbard-Stratonovich transformation can be disentangled into the product of a finite number of th
The simulation of dense fermionic matters is a long-standing problem in lattice gauge theory. One hopeful solution would be the use of quantum computers. In this paper, digital quantum simulation is designed for lattice gauge theory at nonzero densit
The evolution of the distribution-theoretic methods in perturbative quantum field theory is reviewed starting from Bogolyubovs pioneering 1952 work with emphasis on the theory and calculations of perturbation theory integrals.
This is the introductory chapter to the volume. We review the main idea of the localization technique and its brief history both in geometry and in QFT. We discuss localization in diverse dimensions and give an overview of the major applications of t