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<p>We develop a heat kernel method to compute the one-loop effective action for a general class of nonlinear electrodynamic (NLED) theories in four dimensional Minkowski spacetime. Working in the background field formalism, we extract the logarithmically divergent part of the effective action, the so-called <i>induced action</i>, corresponding to the DeWitt <i>a</i><sub>2</sub> coefficient of the heat kernel. In NLED, quantisation yields non-minimal differential operators, for which standard heat kernel techniques are not immediately applicable. Considering the weak-field regime, we calculate the <i>a</i><sub>0</sub>, <i>a</i><sub>1</sub> and <i>a</i><sub>2</sub> contributions to leading order in the background electromagnetic field strength. Finally, we consider conformal NLED theories and compute the <i>a</i><sub>0</sub> contribution to all orders. For this class, we comment on the role of causality being necessary and sufficient for the convergence of the exact <i>a</i><sub>1</sub> and <i>a</i><sub>2</sub> contributions.</p>

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Heat kernel approach to the one-loop effective action for nonlinear electrodynamics

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月4日

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  • Evgeny I. Buchbinder,
  • Darren T. Grasso,
  • Joshua R. Pinelli

摘要

We develop a heat kernel method to compute the one-loop effective action for a general class of nonlinear electrodynamic (NLED) theories in four dimensional Minkowski spacetime. Working in the background field formalism, we extract the logarithmically divergent part of the effective action, the so-called induced action, corresponding to the DeWitt a2 coefficient of the heat kernel. In NLED, quantisation yields non-minimal differential operators, for which standard heat kernel techniques are not immediately applicable. Considering the weak-field regime, we calculate the a0, a1 and a2 contributions to leading order in the background electromagnetic field strength. Finally, we consider conformal NLED theories and compute the a0 contribution to all orders. For this class, we comment on the role of causality being necessary and sufficient for the convergence of the exact a1 and a2 contributions.