23/03/11 00:22:24.08 8g4xRswg.net
>>292
つづき
5. Conclusions
It is not at all clear whether supersymmetry plays a role in nature. But if it
does, this is a field in which mathematical input may make a significant
contribution to physics.
One outstanding mathematical problem is certainly the problem of giving a
sound mathematical formulation to the infinite dimensional structures discussed
in §4. This is (part of) "constructive field theory".
Another outstanding question is the generalization of the considerations of
§4 to other theories. Supersymmetric scalar field theory in the interesting case
of three space dimensions may be formulated by analogy with the discussion in
§4 but with one essential difference. The starting point is Kahler geometry
rather than real differential geometry. However, for supersymmetric gauge
theories it is not at all clear what the right mathematical structure is, and this is
even less clear in the case of supersymmetric theories of gravity. If supersymmetry
does play a role in physics, many other questions calling for a significant
application of mathematical ideas are bound to emerge in the course of time.
(引用終り)
数学屋さんのための注
１）fieldは、物理の”場”です。数学の”体”ではない！ｗ
２）supersymmetryは、フェルミオンとボソンの入れ替えで不変だということ 参考 超対称性： URLﾘﾝｸ(ja.wikipedia.org)
３）"constructive field theory"は、確か 実際の物理の場ではなく、数学的なトイモデル（簡単化したモデル）を考えたという意味だった
４）scalar field theory は、これに対比されるベクトル場の理論というのがあって、それとの区別を言っていると思う
この４つくらいを注意して読めば、Conclusions だけは 読めるでしょう（私もそんな程度です）
以上