Studying quantum field theory (QFT) is indeed a crucial step towards understanding the foundations of quantum gravity and developing a theory of everything. However, it's important to note that creating a comprehensive theory of quantum gravity or a theory of everything is an ongoing challenge in theoretical physics, and it requires a deep understanding of various fields beyond QFT. That being said, here are some areas you should focus on to embark on this ambitious journey:
Quantum Field Theory (QFT): QFT provides the framework for describing elementary particles and their interactions. It would be beneficial to study advanced topics in QFT, such as renormalization, path integrals, gauge theories (e.g., quantum electrodynamics and quantum chromodynamics), and spontaneous symmetry breaking.
General Relativity (GR): Quantum gravity aims to reconcile Einstein's theory of general relativity with quantum mechanics. A thorough understanding of GR is essential, including concepts like curvature, the Einstein field equations, black holes, and gravitational waves.
Quantum Mechanics: Having a strong foundation in quantum mechanics is vital. This includes topics like wave-particle duality, quantum superposition, the uncertainty principle, quantum measurement, and quantum entanglement.
String Theory: String theory is one of the most prominent approaches to quantum gravity. Studying string theory will introduce you to concepts such as extra dimensions, branes, supersymmetry, and the holographic principle.
Mathematical Methods: A deep understanding of advanced mathematical techniques is crucial. Topics like differential geometry, group theory, functional analysis, and topology play a significant role in both general relativity and quantum field theory.
Quantum Information Theory: Quantum information theory explores the quantum nature of information and computation. Since a theory of everything may involve understanding the information content of the universe, studying this field can provide valuable insights.
Cosmology: Understanding the large-scale structure and evolution of the universe is important in the context of a theory of everything. Studying cosmology will expose you to concepts like the Big Bang theory, cosmic inflation, dark matter, and dark energy.
It's worth noting that the path to developing a theory of everything is highly challenging and requires contributions from multiple branches of physics and mathematics. Engaging with current research, staying up to date with the latest developments, and seeking guidance from experts in the field will be invaluable in your pursuit.