One meaning of "solved" is that we have a complete set of eigenstates of the fullLester said:A question I would like to get an answer is when is a QFT exactly solved?
That's not enough. But did you mean 2-point or 4-point? (Don't you need 4-point toE.g. if I know the solution of the equation for the two-point function I have got
all about the theory?
Could you give a more precise reference, pls?This equation is classical in nature being the two-point function defined in the
sense of distributions. I have read the original paper of Schwinger about QED2 and
he does exactly this.
Count Iblis said:I think that in QED there are only a few exact results, e.g. the exact expression for the pair creation probability per unit volume and time in a constant electric field. You can write this as a functional determinant and exactly evaluate it.
A QFT, or Quantum Field Theory, is a theoretical framework that combines elements of quantum mechanics and special relativity to describe the behavior of subatomic particles and their interactions.
Exact solutions for a QFT are mathematical expressions that accurately describe the behavior of a quantum field theory without any approximation or simplification. These solutions often involve complicated equations and can only be found for a limited set of QFT problems.
Exact solutions are important because they provide a precise understanding of the behavior of quantum field theories and allow for the prediction of physical phenomena with a high level of accuracy. They also serve as a benchmark for more approximate solutions and provide a way to test the validity of theoretical predictions.
Exact solutions for a QFT are typically found using advanced mathematical techniques such as perturbation theory, symmetry principles, and numerical methods. These methods require a deep understanding of the underlying principles of quantum mechanics and special relativity, as well as advanced mathematical skills.
Some examples of exact solutions for a QFT include the Dirac equation, which describes the behavior of spin-1/2 particles, and the Klein-Gordon equation, which describes the behavior of spin-0 particles. Other examples include the Schwinger-Dyson equations, which describe the behavior of quantum field theories in terms of correlation functions, and the Yang-Baxter equation, which describes the scattering of particles in two-dimensional quantum field theories.