This book presents the most common types of instabilities arising in classical field theories, namely tachyonic, Laplacian, ghost-like or strong coupling instabilities, also commenting on their quantum implications. The authors provide a detailed account on the Ostrogradski theorem and its implications for higher-order time-derivative field theories. After presenting the general concepts and formalism, they dive into its applications to particular field theories, using mainly modified gravity theories as examples. The book is intended for advanced undergraduate/graduate students, but can also be useful for researchers, for having a unified exposition of general results on instabilities in field theory and examples of their applications.

Autorentext

Adrià Delhom obtained his undergraduate and master degrees in Physics and Advanced Physics at the University of Valencia, with a semester abroad in Rutgers University (New Jersey) and three internships at IFISC (Mallorca), IFIC (Valencia), and Johannes Guttenberg University (Mainz). Later, he got the PhD at the University of Valencia, focusing on theoretical and observational aspects of metric-affine gravity. Subsequently, he held a postdoc position as a Research Fellow at the Laboratory of Theoretical Physics (Tartu University). Currently, Adrià is a postdoctoral Research Fellow at Louisiana State University, where he works on relativistic quantum information and quantum properties of analog gravity systems, while still involved in understanding the stability properties of field theories in general and modified gravity theories. He gained experience as lecturer, having taught graduate-level courses on instabilities in field theory and gravity.

Alejandro Jiménez Cano studied at the University of Granada, where he got his bachelor and master degrees in Physics and Mathematics, with a 3-month stay in Tartu (Estonia). He obtained the PhD at the University of Granada, focusing on gauge theoretical aspects and viability of theories within the metric-affine framework. After, he has been working at the Laboratory of Theoretical Physics (Tartu University) as postdoc. Alejandro works in several collaborations and he contributes to the academic environment and its development, by taking part in PhD and master courses.

Francisco José Maldonado Torralba earned a bachelor in Physics from the University of Granada and a master degree in Theoretical Physics from the University Complutense of Madrid. He obtained a dual PhD title between the University of Groningen and the University of Cape Town, focusing on the stability and phenomenology of Poincaré gauge theories of gravity and their possible non-local extension. After, he was a postdoctoral researcher at the University of Cape Town and a visitor researcher at the Institute of Theoretical Astrophysics of the University of Oslo. Currently, he is a postdoc at the University of Tartu. Francisco is involved in several projects concerning the stability and the (im)possibility of removing spacetime singularities of gravitational theories beyond General Relativity.