Relative entropy of vacuum vs coherent state for λφ⁴ in the Rindler wedge equals the classical interacting boost charge to O(λ) and obeys the Bekenstein bound.
Wave Equations on Lorentzian Manifolds and Quantization
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abstract
This book provides a detailed introduction to linear wave equations on Lorentzian manifolds (for vector-bundle valued fields). After a collection of preliminary material in the first chapter one finds in the second chapter the construction of local fundamental solutions together with their Hadamard expansion. The third chapter establishes the existence and uniqueness of global fundamental solutions on globally hyperbolic spacetimes and discusses Green's operators and well-posedness of the Cauchy problem. The last chapter is devoted to field quantization in the sense of algebraic quantum field theory. The necessary basics on C*-algebras and CCR-representations are developed in full detail. The text provides a self-contained introduction to these topics addressed to graduate students in mathematics and physics. At the same time it is intended as a reference for researchers in global analysis, general relativity, and quantum field theory.
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2026 2representative citing papers
Causal fermion systems are constructed for globally hyperbolic spacetimes such that their continuum limit satisfies the Euler-Lagrange equations of the causal action principle if and only if the coupled Einstein-Dirac equations hold.
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Relative entropy for $\lambda \phi^4$ in the Rindler wedge
Relative entropy of vacuum vs coherent state for λφ⁴ in the Rindler wedge equals the classical interacting boost charge to O(λ) and obeys the Bekenstein bound.
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The Continuum Limit Analysis of Causal Fermion Systems for Curved Spacetimes
Causal fermion systems are constructed for globally hyperbolic spacetimes such that their continuum limit satisfies the Euler-Lagrange equations of the causal action principle if and only if the coupled Einstein-Dirac equations hold.