When particles are smashed together in high-energy experiments, such as in particle accelerators, it does not mean that we are literally smashing the quantum field of those particles into themselves. Rather, we are colliding the particles themselves, which are excitations or quanta of their respective quantum fields.
According to quantum field theory, all elementary particles are associated with their own quantum fields. These fields permeate all of space and time. Particles can be thought of as localized excitations or disturbances in these fields.
In a particle accelerator, two particles are accelerated to high speeds and then made to collide. During the collision, the energy carried by the particles is converted into various forms, including the creation of new particles. The collision is described in terms of the interactions between the quantum fields associated with the colliding particles.
The concept of "smashing" particles together is often used as a metaphor to describe the high-energy collisions. The actual collision process involves complicated interactions mediated by fundamental forces described by quantum field theory. The outcome of these collisions provides valuable information about the properties and behavior of particles and their associated quantum fields.