In quantum field theory (QFT), there are several conservation laws that govern the behavior of physical systems. These conservation laws arise from symmetries of the underlying theory. Here are some important conservation laws in QFT:
Conservation of Energy: The conservation of energy is a fundamental law in physics, and it holds true in QFT as well. The total energy of a system, including both particles and fields, is conserved over time.
Conservation of Momentum: Momentum is also conserved in QFT. The total momentum of a closed system remains constant if there are no external forces acting on it. This conservation law arises due to the translational symmetry of space.
Conservation of Angular Momentum: Angular momentum is conserved in QFT, just as in classical mechanics. The total angular momentum of a system remains constant if there are no external torques acting on it. This conservation law arises from the rotational symmetry of space.
Conservation of Electric Charge: Electric charge is conserved in QFT. The total electric charge of a closed system remains constant over time. This conservation law arises from the U(1) gauge symmetry of quantum electrodynamics (QED).
Conservation of Lepton Number: In certain QFT models, such as the Standard Model of particle physics, each lepton flavor (electron, muon, and tau) has an associated lepton number, which is conserved. The total lepton number, which is the sum of the individual lepton numbers, remains constant in interactions governed by these conservation laws.
Conservation of Baryon Number: Baryon number conservation is another important conservation law in QFT. Baryons, such as protons and neutrons, have a baryon number of +1, while their antiparticles have a baryon number of -1. The total baryon number of a closed system remains constant, assuming no processes violate this conservation law.
It's important to note that these conservation laws are approximate in certain situations, especially at high energies where new particles and interactions may become significant. Additionally, conservation laws related to certain quantum numbers, such as flavor, may be violated in certain rare processes, as observed in certain phenomena like neutrino oscillations.