Inconsistency of Minkowski higher-derivative theories

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• 作者：Ugo G. Aglietti ; Damiano Anselmi
• 刊名：The European Physical Journal C
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：77
• 期：2
• 全文大小：554KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Elementary Particles, Quantum Field Theory; Nuclear Physics, Heavy Ions, Hadrons; Quantum Field Theories, String Theory; Measurement Science and Instrumentation; Astronomy, Astrophysics and Cosmology;
• 出版者：Springer Berlin Heidelberg
• ISSN：1434-6052
• 卷排序：77

文摘

We show that Minkowski higher-derivative quantum field theories are generically inconsistent, because they generate nonlocal, non-hermitian ultraviolet divergences, which cannot be removed by means of standard renormalization procedures. By “Minkowski theories” we mean theories that are defined directly in Minkowski spacetime. The problems occur when the propagators have complex poles, so that the correlation functions cannot be obtained as the analytic continuations of their Euclidean versions. The usual power counting rules fail and are replaced by much weaker ones. Self-energies generate complex divergences proportional to inverse powers of D’Alembertians. Three-point functions give more involved nonlocal divergences, which couple to infrared effects. We illustrate the violations of the locality and hermiticity of counterterms in scalar models and higher-derivative gravity.