Quantum field theory (QFT) is generally considered more challenging to study than quantum mechanics. While both theories deal with the quantum behavior of particles, QFT extends quantum mechanics to incorporate fields, which are continuous quantities defined at every point in spacetime. QFT provides a framework for describing the interactions and behavior of particles as excitations of these fields.
There are several reasons why QFT can be more difficult to study:
Mathematical Complexity: QFT involves advanced mathematical techniques, such as functional analysis, group theory, and advanced calculus. The mathematical formalism of QFT, including concepts like operator-valued fields, path integrals, and renormalization, can be quite involved and requires a solid mathematical background.
Infiniteness and Renormalization: QFT encounters infinities in certain calculations, which require the process of renormalization to obtain physically meaningful results. Renormalization involves carefully subtracting and adjusting infinite quantities to recover finite, observable predictions. This aspect adds an additional layer of complexity and requires a deep understanding of the underlying concepts.
Interactions and Perturbation Theory: QFT deals with the interactions between particles, which introduces additional complexities compared to non-interacting systems in quantum mechanics. Perturbation theory is often employed in QFT to approximate the behavior of interacting fields, but it can become increasingly challenging as the order of perturbation increases.
Field Operators and Creation/Annihilation: QFT introduces the concept of field operators, which describe the creation and annihilation of particles. These operators can be more abstract and require a different way of thinking compared to the wave functions and observables of quantum mechanics.
That being said, quantum mechanics itself provides the foundation for understanding and studying QFT. It is common for physicists to first gain a solid understanding of quantum mechanics before diving into QFT. Many concepts and techniques from quantum mechanics, such as wave-particle duality, superposition, and the mathematical formalism of Hilbert spaces, are also applicable to QFT.
Overall, while QFT presents greater challenges due to its mathematical complexity and the inclusion of interacting fields, it is a fundamental and powerful framework for describing the behavior of particles and their interactions, particularly in the realm of particle physics.