The order in which one studies quantum mechanics, quantum field theory (QFT), and general relativity (GR) can vary depending on personal preferences and educational paths. However, in general, it is common for students to first learn quantum mechanics before delving into QFT and GR.
Quantum mechanics is the foundational theory that describes the behavior of particles at the microscopic level. It provides a framework for understanding the wave-particle duality, uncertainty principles, and the behavior of quantum systems. Many fundamental concepts and mathematical tools used in QFT and GR are built upon the principles of quantum mechanics. Therefore, having a solid understanding of quantum mechanics is usually considered essential before studying more advanced topics.
Once you have a good grasp of quantum mechanics, you can move on to studying quantum field theory. QFT extends the principles of quantum mechanics to fields and is crucial for understanding particle physics and the fundamental forces of nature. It provides a framework for describing particles as excitations of quantum fields and enables calculations of particle interactions. However, QFT builds upon quantum mechanics and requires a solid understanding of its principles and mathematical formalism.
General relativity, on the other hand, is a theory of gravitation and the description of spacetime on a macroscopic scale. It is based on the principle of general covariance and introduces the concept of curved spacetime. While general relativity does not directly rely on quantum mechanics, it is helpful to have a foundation in quantum mechanics before exploring the potential interactions between quantum mechanics and gravity, which is an ongoing field of research.
In summary, while there may be some exceptions, it is generally recommended to study quantum mechanics before diving into quantum field theory and general relativity. Having a solid understanding of quantum mechanics will provide you with the necessary foundation and mathematical tools to comprehend and explore more advanced theories in physics.