Question

String field theory (in which string theory undergoes "second quantization") seems to reside in the backwaters of discussions of string theory. What does second quantization mean in the context of a theory that doesn't have Feynman diagrams with point-like vertices? What would a creation or annihilation operator do in the context of string field theory? Does string field theory provide a context in which (a) certain quantities are more easily calculated or (b) certain concepts become less opaque?

Answer 1

Dear , despite Moshe's expectations, I fully agree with him, but let me say it differently.

In QFT, we're talking about "first quantization" - this is not yet a quantum field theory but either a classical field theory or quantum mechanics for 1 particle. Those two have different interpretations - but a similar description. When it is "second-quantized", we arrive to QFT.

Feynman diagrams in QFT may be derived from "sums over histories" of quantum fields in spacetime; for example, the vertices come from the interaction terms in the Lagrangian, and the propagators arise from Wick contractions of quantum fields. This is the "second-quantized" interpretation of the Feynman diagrams.

There is also a first quantized interpretation. You may literally think that the propagators are amplitudes for an individual particle to get from x to y, and the vertices allow you to split or merge particles. You may think in terms of particles instead of fields. In QFT, this is an awkward approach because most particles have spins and it's confusing to write a 1-particle Schr