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Dec7-05, 12:44 PM
marlon's Avatar
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Quote Quote by EL
Quantum field theory is the application of quantum machanics to a dynamical system of fields.
This is not entirely accurate. Just check out the thread on "the difference between QM and QFT", where we have debated this issue recently.

Applying QM does not equal quantizising. QM cannot be applied onto a system with infinite or non-fixed degrees of freedom because one of the basic requirements of QM is a fixed finite number of particles. This explains the difference in interpretation of "an annihilation operator" in QM and QFT.

But in string theory we can start from a classical theory of a string,
What exactly is that ?

Then we quantize these fields in the usual manner, and hence achieves a 2-dimensional QFT. Why is this not a QFT?
Ok, "1) and 2)" mean the two notions i summed up in my previous post (eg HUP and superposition).

String Theory is a little more than that. What i meant with 1) and 2) is the fact that the gravitational interaction doees not know the concepts of superposition and the HUP. But these two notions are the basic ingredients of QFT, otherwise we could have omitted the letter Q in QFT. When you "quantizise" a field, this means that 1) and 2) become valid for these fields. But than again, how would you describe an interaction that does not recognize 1) and 2) in terms of fields that do. It is this manifest contradictio in terminis that determines the very foundation of string theory.

Besides, the most basic property of QFT are the fields of which the fluctuations correspond to elementary particles. In string theory, this basic property are indeed also fields of which the fluctuations produce strings. One of the clues of string theory is how to link quantum fields and strings. The reason that strings are used comes from the theory that governs gravity : General Relativity...Also keep in mind that in QFT, elementary particles are described in a fixed space time, while in string theory the fluctuations of the fields actually express the fluctuations of space time. I would say there is a fundamental difference here