Feynman checkers: Minkowskian lattice quantum field theory

Cornell University , 2022.

Скопенков М. Б., Устинов А. В.

We present a new completely elementary model which describes creation, annihilation and motion of non-interacting electrons and positrons along a line. It is a modification of the model known under the names Feynman checkers, or one-dimensional quantum walk, or Ising model at imaginary temperature. The discrete model is consistent with the continuum quantum field theory, namely, reproduces the known expected charge density as lattice step tends to zero. It is exactly solvable in terms of hypergeometric functions. We introduce interaction resembling Fermi theory and establish perturbation expansion.

Ключевые слова: Dirac equation, уравнение Дирака, Quantum walks, Feynman checkerboard, шахматная доска Фейнмана, квантовое блуждание, loop O(n) model, propagator, пропагатор