In quantum field theory, the presence of antiparticles is accounted for through the concept of antiparticle states and creation/annihilation operators. Antiparticles are particles that have the same mass as their corresponding particles but possess opposite electric charge and other quantum numbers.
In quantum field theory, each elementary particle is associated with a quantum field. These quantum fields are operators that create and annihilate particles. For every particle, there is a corresponding antiparticle field that creates and annihilates antiparticles. The creation and annihilation operators are denoted by the symbols "a" and "a†" respectively.
The Fock space, which describes the state of a quantum field theory, includes both particle states and antiparticle states. The particle states are associated with positive energy solutions, while antiparticle states are associated with negative energy solutions.
An important property of antiparticles is their charge conjugation. Charge conjugation is an operation that transforms a particle into its corresponding antiparticle by changing the sign of its electric charge and other relevant quantum numbers.
The Dirac equation, which describes the behavior of fermions (particles with half-integer spin), also incorporates the concept of antiparticles. The equation predicts the existence of antiparticles as solutions with negative energy.
In summary, quantum field theory accounts for antiparticles by introducing antiparticle fields, creation/annihilation operators, and incorporating the concept of charge conjugation. This framework allows for the description and calculation of particle-antiparticle interactions and phenomena in a consistent manner.