If you have a solid understanding of quantum field theory (QFT) as presented in the first two books of Weinberg's series, you have a strong foundation for delving deeper into fundamental physics and the search for a theory of everything. Here are some areas of study that would be relevant for further exploration:
General Relativity: To develop a comprehensive theory of everything, it is important to understand the other pillar of modern physics: general relativity. General relativity describes gravity as the curvature of spacetime and provides a framework for understanding the dynamics of massive objects and the structure of the universe. Studying the principles and mathematics of general relativity will be crucial for a unified theory.
String Theory: String theory is a leading candidate for a theory of everything. It posits that fundamental particles are not point-like but are tiny, vibrating strings of energy. String theory combines quantum mechanics and general relativity, offering a potential framework to unify all the fundamental forces of nature. To pursue the theory of everything, you could dive into books and resources specifically focused on string theory.
Quantum Gravity: The unification of general relativity and quantum mechanics is a central challenge in theoretical physics. Quantum gravity aims to reconcile the principles of quantum mechanics with the gravitational force. This field includes approaches beyond string theory, such as loop quantum gravity and causal set theory. Exploring these alternative approaches to quantum gravity will broaden your understanding of the subject.
Cosmology: Understanding the origin, evolution, and large-scale structure of the universe is crucial in the quest for a theory of everything. Studying cosmology will provide insights into the early universe, inflation, dark matter, dark energy, and other cosmological phenomena. It will also connect fundamental theories to observational data and experiments.
Mathematical Physics: To tackle the complexities of a theory of everything, a solid foundation in mathematics is essential. Develop your mathematical skills in areas such as differential geometry, algebraic geometry, group theory, and mathematical methods in physics. These mathematical tools are integral to formulating and solving the equations of fundamental theories.
Particle Physics and Standard Model: Deepening your knowledge of the Standard Model of particle physics will help you understand the known fundamental particles and their interactions. Familiarize yourself with experimental techniques and discoveries in particle physics to stay up to date with the current state of research.
Remember that the study of a theory of everything is an ongoing and active area of research, and new developments are continuously emerging. It's important to keep up with the latest literature, attend conferences, and engage with the scientific community to stay informed about advancements in the field.