When a particle is created with momentum, several things occur. Let's consider the scenario within the framework of quantum field theory, where particles are represented as excitations of quantum fields.
Creation Operator: In quantum field theory, a particle is created by applying a creation operator on the vacuum state. The creation operator creates an excitation in the quantum field corresponding to the particle with a specific momentum. This excitation represents the presence of the particle.
Conservation Laws: The creation of a particle with momentum must adhere to certain conservation laws. In particular, conservation of energy and momentum must be maintained. This means that the total energy and momentum before and after the creation process must be the same. The newly created particle's momentum will be included in the total momentum of the system.
Wave Function: The particle's creation corresponds to a state in the quantum field that has a particular wave function associated with it. The wave function describes the probability amplitude of finding the particle at different positions. The precise form of the wave function depends on the specific particle and its momentum.
Particle Properties: When a particle is created, its properties, such as mass, charge, and spin, are determined by the underlying quantum field theory. Different particles have different properties, and these properties affect the particle's behavior and interactions.
Particle-Antiparticle Pair Creation: It's important to note that the creation of a particle with momentum can be accompanied by the creation of its corresponding antiparticle. Particle-antiparticle pair creation can occur due to energy conservation and obeying the principles of quantum field theory. The created particle and antiparticle will have opposite charges but equal magnitudes of momentum.
Overall, when a particle is created with momentum, it involves the excitation of a quantum field, conservation of energy and momentum, the establishment of a wave function, and the determination of the particle's properties according to the specific quantum field theory.