Quantum field theory (QFT) is accurately described as an "operator-valued distribution" rather than a simple "operator function" at spacetime points. This distinction is crucial as the values of fields at each point do not represent independent degrees of freedom in the traditional sense. Instead, degrees of freedom are defined either at fixed time points in 3-space or on a mass shell in momentum space, particularly in relativistic contexts. Understanding this framework is essential for grasping the complexities of QFT.
PREREQUISITESPhysicists, quantum field theorists, and advanced students in theoretical physics seeking to deepen their understanding of operator-valued functions and degrees of freedom in quantum field theory.
plasmon said:Is it correct to express quantum field theory as "operator valued function" or "operator function" to spacetimepoints. Also, how value of field at each point act as a separate degrees of freedom.