49 Further Topics
There is a long list of other topics that belong in a more complete discussion of the general subject of this volume. Some of these are standard topics which are well-covered in many physics or mathematics textbooks. In this chapter we’ll just give a short list of some of the most important things that have been left out.
Several of these have to do with quantum field theory:
• Lower dimensional quantum field theories. The simplest examples of quantum field theories are those with just one dimension of space (and one dimension of time, so often described as “1 + 1” dimensional). While it would have been pedagogically a good idea to first examine in detail this case, keeping the length of this volume under control led to the decision to not take the time to do this, but to directly go to the physical case of “3 +1” dimensional theories. The case of two spatial dimensions is another lower dimensional case with simpler behavior than the physical case.
• Topological quantum field theories. One can also formulate quantum field theories on arbitrary manifolds. An important class of such quantum field theories has Hamiltonian = 0 and observables that only depend on the topology of the manifold. The observables of such “topological quantum field theories” provide new sorts of topological invariants of manifolds and such theories are actively studied by mathematicians and physicists. We have already mentioned a simple supersymmetrical quantum mechanical model of this kind in section 33.3.
Chapter contents
- 49.1 Connecting quantum theories to experimental results
- 49.2 Other important mathematical physics topics
来源与版本
正文：英文 · OCR 机器稿 · 待校对
核对状态：OCR 机器稿 · 待校对
原书 PDF · 印刷页 530、531、532
来源版本：2025-10-20
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