Quantum mechanics (QM) and quantum field theory (QFT) are both powerful frameworks for describing the behavior of particles and their interactions at the microscopic level. While QFT builds upon QM, there are several key differences between the two. Apart from the relativistic treatment, some of the main features that distinguish QFT from QM are:
Particle Interactions: Quantum mechanics treats particles as discrete entities, each described by a wavefunction. Interactions between particles are typically treated as external forces or potential fields acting on the particles. In contrast, QFT incorporates the concept of fields, where particles are viewed as excitations of underlying quantum fields. In QFT, particles interact by exchanging virtual particles through the fields, providing a more fundamental and unified description of particle interactions.
Field Operators: In QM, the state of a particle is described by a state vector or wavefunction. In QFT, the fundamental entities are field operators that act on a field's quantum state. These operators create or annihilate particles and allow for the description of particle number changes and interactions.
Vacuum Fluctuations: In QM, the vacuum state is often considered as a state of no particles. However, in QFT, the vacuum state is rich with vacuum fluctuations. These fluctuations give rise to virtual particles that continuously pop in and out of existence, contributing to various physical phenomena, such as the Lamb shift and the Casimir effect.
Renormalization: QFT introduces the need for renormalization due to the occurrence of divergent quantities in certain calculations. This is a process that involves adjusting parameters in the theory to eliminate infinities and ensure meaningful results. Renormalization is a specific technique used in QFT to handle these infinities and obtain finite and physically meaningful predictions.
Treatment of Spin: In QM, particles' spin is described by mathematical objects called spinors, which are fundamental representations of the rotation group. In QFT, spin is naturally incorporated through the concept of fields and their corresponding excitations. Different fields correspond to particles with different spin values, and the equations of QFT are formulated in a way that naturally handles particles of any spin.
Unification of Forces: QFT allows for the description of all fundamental forces (electromagnetic, weak, strong, and gravitational, though gravity is not yet fully incorporated) within a unified framework. This is achieved through gauge theories, such as quantum electrodynamics (QED) and quantum chromodynamics (QCD), which treat interactions via the exchange of gauge bosons.
It's important to note that QFT is a more comprehensive and mathematically sophisticated framework than QM, providing a deeper understanding of particle interactions and enabling the incorporation of relativity. However, QM remains a highly successful and applicable theory in many non-relativistic scenarios and continues to be widely used in various branches of physics and engineering.