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14 - Quantum Fields and Relativistic Horizons

from Part III - Canonical Field Theories with Gravity

Published online by Cambridge University Press:  01 March 2026

Piljin Yi
Affiliation:
Korea Institute for Advanced Study
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Summary

Canonical quantization of matter fields admits a surprisingly simple extension into curved spacetime as long as there exists a suitable time foliation. The main conceptual difficulty arises when multiple time foliations compete, with nontrivial Bogoliubov transformations mixing up the notions of particle and antiparticle. With the Minkowski spacetime written in the Rindler coordinates as a prototype, we explore how various distinct vacua appear and how to choose one based on physics considerations. For eternal black hole geometry, smooth event horizons demand the Hartle–Hawking vacuum, while, for black holes made from gravitational collapse, the radiation vacuum of Hawking naturally emerges. After a brief stop on black hole thermodynamics, we close the volume with a simple observation of how all these are connected to the primordial density perturbation of the cosmic inflation scenario.

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