Renormalization Group Approach to Spectral Problems with Application to Theory of Radiation

In this talk I will describe some analytical problems in Quantum Field Theory (QFT) and some of the recent results and approaches. I will not assume any prior knowledge of the subject and I will try to show how it arises from Classical Field Theory, i.e. partial differential equations. In other words I will view QFT as Quantum Mechanics of infinitely many degrees of freedom or of extended objects (strings, surfaces, etc).