Wave-particle duality is a fundamental concept in quantum mechanics that describes the behavior of particles and waves at the microscopic scale. According to wave-particle duality, particles such as electrons and photons can exhibit both particle-like and wave-like properties, depending on how they are observed or measured.
Quantum field theory (QFT) provides a framework that extends quantum mechanics to incorporate special relativity and describe the behavior of quantum fields and their associated particles. In QFT, particles are not treated as distinct entities but as excitations or quanta of their respective fields. Each fundamental particle is associated with a quantum field that permeates all of space.
The concept of wave-particle duality is incorporated into quantum field theory through the wave-like behavior of quantum fields. These fields are described by wave equations, such as the Klein-Gordon equation for scalar fields or the Dirac equation for fermionic fields. The solutions to these equations represent field configurations that can be interpreted as both particles and waves.
In the framework of QFT, particles are understood as excitations or disturbances in their respective fields. These excitations can propagate through spacetime as waves, and when measured or observed, they exhibit particle-like behavior by being localized at a specific position or momentum. The wave-like behavior of the field allows for phenomena such as interference and superposition, which are characteristic of waves.
The wave-particle duality in quantum field theory is thus manifested in the behavior of quantum fields and their associated excitations. The fields themselves exhibit wave-like properties, while the excitations of these fields can exhibit both particle-like and wave-like behavior, depending on the context of observation or measurement.
It's worth noting that quantum field theory provides a more comprehensive and unified framework compared to non-relativistic quantum mechanics. It allows for the consistent description of particles with arbitrary energies and momenta, and it naturally incorporates concepts like creation and annihilation of particles, particle interactions, and the conservation of quantum numbers.