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An Introduction to Loop Quantum Gravity (Lecture Notes)

by Sina Kazemian

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Authors (as registered SciPost users):

Sina Kazemian

Abstract

Loop Quantum Gravity (LQG) is an approach to reconcile general relativity with quantum mechanics without imposing a fixed background geometry. In LQG, spacetime itself is treated as a physical system with quantum properties rather than a fixed stage on which physics unfolds. At extremely small (near- Planck) scales, geometric quantities such as area and volume are expected to be granular—coming in tiny, discrete quanta—while at macroscopic scales these quanta collectively reproduce the smooth geometry described by Einstein’s theory. The guiding philosophy is conservative: retain the background independence of general relativity, apply the rules of quantum theory universally, and introduce as little additional structure as possible. The aim is not a “theory of everything,” but a consistent quantum description of spacetime that can be confronted with observation as the formalism matures—through arenas such as black-hole thermodynamics, early-universe cosmology, and other phenomenological windows. These notes begin with motivation and core ideas, then build up the minimal mathematical tools needed for later sections, keeping the focus on physical meaning and on what is known, what is conjectured, and what remains open.