Quantum field theory (QFT) is a framework that describes particles and their interactions based on fields, which are continuous quantities defined at every point in space and time. In QFT, particles are not viewed as localized objects with definite positions, but rather as excitations or quanta of their respective fields.
According to the principles of quantum mechanics, particles can exhibit wave-particle duality, meaning they can behave both as waves and particles. This duality is reflected in QFT through the concept of wave functions associated with fields, which describe the probability amplitudes for finding a particle at different locations.
In QFT, the fields are quantized, which means they are treated as operators that create and annihilate particles. The behavior of these particles is described by specific mathematical objects known as field operators. These field operators encode the creation and annihilation of particles, their momentum, and other properties.
Crucially, in QFT, particles are not considered to have well-defined positions until they are observed or measured. Instead, the theory focuses on the probabilities associated with different possible outcomes of measurements. The wave function associated with a particle field gives the probability distribution for finding a particle at different locations when a measurement is made.
The non-localized nature of particles in QFT is consistent with the principles of Heisenberg's uncertainty principle, which states that there is a fundamental limit to the precision with which certain pairs of physical properties, such as position and momentum, can be simultaneously known. This uncertainty leads to the inherent indeterminacy of particle positions in quantum mechanics.
In summary, QFT describes particles as excitations of quantum fields and emphasizes the probabilistic nature of their positions until measured. It provides a framework for understanding the behavior of particles that don't have well-defined locations by focusing on their wave-like properties and the statistical outcomes of measurements.