# Perturbative quantization of two-dimensional space-time noncommutative QED

## TL;DR

This paper develops a perturbative quantization method for two-dimensional noncommutative QED, incorporating higher order derivatives and non-local interactions, and derives the modified canonical structure up to second order in coupling and noncommutativity.

## Contribution

It introduces a perturbative quantization approach for non-local noncommutative QED including fermions and bosons, accounting for higher derivatives and deriving the modified canonical algebra.

## Key findings

- Quantized noncommutative QED up to O(e^2,θ^3)
- Derived modified Lagrangian with higher derivatives
- Established equal-time commutation relations and current algebra

## Abstract

Using the method of perturbative quantization in the first order approximation, we quantize a non-local QED-like theory including fermions and bosons whose interactions are described by terms containing higher order space-time derivatives. As an example, the two-dimensional space-time noncommutative QED (NC-QED) is quantized perturbatively up to O(e^2,\theta^3), where e is the NC-QED coupling constant and \theta is the noncommutativity parameter. The resulting modified Lagrangian density is shown to include terms consisting of first order time-derivative and higher order space-derivatives of the modified field variables that satisfy the ordinary equal-time commutation relations up to O(e^2,\theta^3. Using these commutation relations, the canonical current algebra of the modified theory is also derived.