Dear all, in a lot of undergraduate textbooks you find the claim that antiparticles can be motivated by Einstein's energy-momentum relation ## E^2 = p^2 + m^2 ##, which has both 'negative' and 'positive energy' solutions. In the context of a single wave function this is problematic. In the context of quantum fields however, I thought that these 'negative' energy solutions correspond to those modes of the field which annihilate a particle with that specific energy (which is positive). So how is this related to the concept of antiparticles? The simplest example I can think of is the real scalar field, as treated in e.g. Peskin&Schroeder. You make the usual expansion in plane waves and find that the 'negative energy solutions' have as a coefficient the operator which annihilates the particle, where all particles have positive energy. No antiparticles here. So what's the precise relation between the existence of antiparticles and the quadratic nature of Einstein's ## E^2 = p^2 + m^2 ##? I'd say this quadratic nature is linked to the creation and annihilation of particles, and antiparticles arise as soon as you consider complex conjugates of the fields.