Dylan J Dance's claim that "There are no waves involved in quantum field theory" seems to be a misrepresentation or an oversimplification of the underlying concepts. In quantum field theory (QFT), waves play a fundamental role in describing the behavior of quantum fields.
In QFT, particles are considered as excitations or disturbances in their respective quantum fields. These fields pervade all of space and time and can exhibit wave-like behavior. The behavior of these fields is described by wave equations, such as the Klein-Gordon equation, the Dirac equation, or the electromagnetic wave equation.
Quantum field theory combines quantum mechanics with special relativity and treats particles as quanta of their respective fields. These fields are quantized, meaning that they can only have discrete amounts of energy. The particles associated with these fields can be thought of as wave packets, which are localized disturbances in the underlying quantum fields.
Wave-particle duality is a central concept in quantum mechanics, and it applies to quantum fields as well. The particles described by quantum fields can exhibit both particle-like and wave-like properties depending on the experimental context.
It is important to note that while waves are an integral part of quantum field theory, the interpretation and understanding of these waves in the context of quantum mechanics can be quite different from classical waves. The behavior of quantum fields is governed by complex mathematical equations and requires a sophisticated understanding of the underlying theory to fully appreciate and describe their nature.