Quantum Fields and Quantum Geometry

Dear Colleagues,

The Special Issue aims to collect contributions on all aspects of quantum field theory in curved space, from de Sitter and Anti-de-Sitter space–times to the most recent advances in quantum geometry, or the theory of operator field algebras. 

There are already many books, e.g., Birrell and Davis (1982), Wald (1994) and (2018), Fulling (1989), Kay (1988), Ford (2002), Parker and Toms (2009), Bär and Fredenhagen (2009), etc.), reviews, e.g., the seminal BS DeWitt (1975), and uncountable articles on the subject, e.g., the recent arXiv:2206.10780v1, arXiv:2202.03357, etc. Nevertheless, these topics are rapidly evolving, and this Special Issue gives all researchers in this promising domain the opportunity to contribute in the form of a review or a specialised article. 

All available models that point to quantum gravity start from the principles of quantum field theory and general relativity. However, one cannot obtain complete consistency between them. In this regard, quantum field theory in curved space–time needs to be studied in depth. We need a precise understanding of the Hilbert space construction, field operator algebra, the renormalisability problem, and the quantum state evolution. Quantum field theory in de Sitter and Anti-de Sitter spaces are the best examples for this purpose. Quantum de Sitter geometry represents the best model for the consideration of quantum geometry. The quantum state of geometry and its evolution are the challenging concepts of quantum geometry. The evolution of the quantum state may be given in terms of the total entropy of the universe. The de Sitter geometry quantum state evolution must be introduced with an observer-independent perspective. For this purpose, the relative entropy or von Neumann entropy must be used, which is defined in terms of in eigenstates in the appropriate Hilbert space. 

We invite submissions of both original papers and review articles to this Special Issue, which places particular emphasis on ideas and framework problems based on quantum field theory in curved spacetime and quantum geometry. We believe that such frameworks have the potential to explain the quantum state of the universe in an observer-independent way. We are interested in collecting contributions focusing on a broad range of approaches and ideas, which emphasize quantum gravity and geometry and related issues, such as the question of evolution of quantum states in quantum gravity.

Prof. Dr. Jean-Pierre Gazeau
Prof. Dr. Mohammad-Vahid Takook
Guest Editors

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• quantum geometry
• quantum field theory in curved spacetime
• quantum gravity