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The Lee-Wick-Chern-Simons pseudo-quantum electrodynamics

M. J. Neves

TL;DR

The paper develops a Lee-Wick extension of pseudo-electrodynamics in 1+2 dimensions augmented by a non-local Chern-Simons term, yielding a gauge-invariant, causal theory with two massive modes controlled by the LW mass $M$ and CS parameter $\theta$. It derives the gauge propagator with poles at $\bar{k}^2=0$, $\bar{k}^2=M^2$, and $\bar{k}^2=\theta^2$, and uses it to compute the static potential and retarded Green function, confirming causality. The fermion sector is extended to include a heavy LW fermion $M_f$ alongside the light electron mass $m$, with Ward identities linking self-energies and vertex corrections and enabling finite one-loop corrections (electron self-energy, vacuum polarization, and the 3-vertex) whose magnitudes are regulated by $M$. The study demonstrates tree-level unitarity via the optical theorem and reveals Lamb-shift-like and g-2 corrections that depend on $M$, $\theta$, and $M_f$, while recovering known CS-PQED results in appropriate limits, thereby providing a consistent 1+2D framework for planar topological and LW electrodynamics.

Abstract

The Lee-Wick pseudo-quantum electrodynamics in the presence of a Chern-Simons term is studied in this paper. The paper starts with a non-local lagrangian density that sets the pseudo-Lee-Wick electrodynamics defined on a $1+2$ space-time added to a Chern-Simons topological term. We investigate classical aspects as the potential energy for the interaction of static charges through the gauge propagator. The causality of theory is discussed through the retarded Green function in the coordinate space. The gauge field of the Lee-Wick-Chern-Simons pseudo-electrodynamics is minimally coupled to the fermions sector that includes new degree of freedoms, as a Lee-Wick heavy fermion partner of the electron. The perturbative approach for the theory is presented via effective action in which we obtain the Ward identities. We study the radiative corrections at one loop, as the electron self-energy, the vacuum polarization, and the $3$-vertex. We show that the Lee-Wick mass has a fundamental role in these results, where it works like a natural regulator of the ultraviolet divergences. The $g-2$ factor for the electron is obtained as function of the LW mass, and of the CS parameter. Through the optical theorem, the theory is unitary at the tree level.

The Lee-Wick-Chern-Simons pseudo-quantum electrodynamics

TL;DR

The paper develops a Lee-Wick extension of pseudo-electrodynamics in 1+2 dimensions augmented by a non-local Chern-Simons term, yielding a gauge-invariant, causal theory with two massive modes controlled by the LW mass and CS parameter . It derives the gauge propagator with poles at , , and , and uses it to compute the static potential and retarded Green function, confirming causality. The fermion sector is extended to include a heavy LW fermion alongside the light electron mass , with Ward identities linking self-energies and vertex corrections and enabling finite one-loop corrections (electron self-energy, vacuum polarization, and the 3-vertex) whose magnitudes are regulated by . The study demonstrates tree-level unitarity via the optical theorem and reveals Lamb-shift-like and g-2 corrections that depend on , , and , while recovering known CS-PQED results in appropriate limits, thereby providing a consistent 1+2D framework for planar topological and LW electrodynamics.

Abstract

The Lee-Wick pseudo-quantum electrodynamics in the presence of a Chern-Simons term is studied in this paper. The paper starts with a non-local lagrangian density that sets the pseudo-Lee-Wick electrodynamics defined on a space-time added to a Chern-Simons topological term. We investigate classical aspects as the potential energy for the interaction of static charges through the gauge propagator. The causality of theory is discussed through the retarded Green function in the coordinate space. The gauge field of the Lee-Wick-Chern-Simons pseudo-electrodynamics is minimally coupled to the fermions sector that includes new degree of freedoms, as a Lee-Wick heavy fermion partner of the electron. The perturbative approach for the theory is presented via effective action in which we obtain the Ward identities. We study the radiative corrections at one loop, as the electron self-energy, the vacuum polarization, and the -vertex. We show that the Lee-Wick mass has a fundamental role in these results, where it works like a natural regulator of the ultraviolet divergences. The factor for the electron is obtained as function of the LW mass, and of the CS parameter. Through the optical theorem, the theory is unitary at the tree level.

Paper Structure

This paper contains 7 sections, 88 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The Lee-Wick pseudo-electrodynamics with Chern-Simons term
  3. The Lee-Wick-Chern-Simons pseudo-quantum electrodynamics
  4. Effective action and the Ward identity
  5. Radiative corrections at one loop in CSLW PQED
  6. The discussion of the unitarity in LWCSPED
  7. Conclusions

Figures (3)

  • Figure 1: The static energy as function of the radial distance. We choose the values $e=0.3$, $M=100$, and the colored lines means the $\theta$-values : $\theta=0.0$ (dashed line), $\theta=10$ (red line), $\theta=20$ (blue line) and $\theta=50$ (green line).
  • Figure 2: The static potential energy corrected by the vacuum polarization at one loop as function of the radial distance. We choose the values of $m=0.5$, $M_{f}=50$, $M=100$, and $\beta=0.003$, in which the colored lines means the $\theta$-values : $\theta=0$ (dashed line), $\theta=1.0$ (red line), $\theta=2.0$ (blue line) and $\theta=3.0$ (green line).
  • Figure 3: The correction to the electron anomalous momentum as function of dimensionless parameter $M/m$ (the Lee-Wick mass over the electron mass). The curve is plotted for $\beta=0.003$ (graphene), with the CS parameter of $\theta=0.1$, and the fine structure constant $\alpha=1/137$.