In quantum field theory (QFT), quantum fields are fundamental entities that permeate all of space and describe the behavior of elementary particles. These fields are associated with particles, and their excitations manifest as particles with specific properties such as mass and charge.
In QFT, fields are treated as operators that can create or annihilate particles. These operators evolve in time and can undergo various interactions and transformations. Quantum fields are pervasive and exist throughout space, even in regions where no particles are present.
Regarding energy, quantum fields do have associated energy. According to the principles of quantum mechanics, energy and momentum are conserved quantities, and particles can be created or annihilated in interactions. The energy of a quantum field corresponds to the total energy of its excitations or particles.
In QFT, the energy of a field can be quantized into discrete units known as quanta or particles. Each quantum of energy corresponds to a particle with specific properties. The energy of a field is distributed among these particles, and the total energy is the sum of the energies of all the particles present.
However, it's important to note that the energy of a quantum field is not a fixed, static value. Due to the Heisenberg uncertainty principle, the energy of a field can fluctuate, even in its ground state (lowest energy state). These fluctuations, known as vacuum fluctuations, give rise to phenomena such as the Casimir effect.
In summary, quantum fields in QFT do have associated energy. The energy of a field is distributed among its particles or excitations and can fluctuate due to the inherent uncertainties of quantum mechanics.