In quantum field theory (QFT), the integration over all oscillation modes is a mathematical tool used to describe the behavior of quantum fields. The infinite energy values that arise in these calculations are an artifact of an idealized and simplified mathematical model, and they do not correspond to physically measurable quantities.
In QFT, a quantum field is represented as an infinite collection of harmonic oscillators, each associated with a specific mode of vibration. These oscillators are quantized, meaning they can have discrete energy levels. The integration over all oscillation modes is performed to account for the superposition of these modes and their interactions.
However, when performing such calculations, infinities may arise due to the unbounded nature of the oscillation modes. These infinities are known as "divergences" and are a characteristic feature of many quantum field theories. They are a consequence of attempting to describe physics at arbitrarily small length scales or high energies, where our current understanding of physics breaks down.
To handle these divergences, physicists use a process called renormalization. Renormalization involves introducing appropriate mathematical procedures to remove or absorb these infinities, making the theory consistent and allowing for meaningful predictions. The resulting physical predictions from QFT, after renormalization, can be experimentally verified and are in agreement with observations.
It's important to note that the infinite energy values encountered during intermediate calculations in QFT do not have direct physical significance. They are mathematical artifacts that are resolved through renormalization, enabling the extraction of meaningful physical predictions from the theory.