Dirac猜想的限制
Restriction on Dirac's Conjecture
摘要：
规范理论的规范形式中的第一类约束可能产生将一个状态映射到其物理等价状态的变换。这就是狄拉克猜想。有两个例子可以作为猜想的反例。一个是Cawley发现的玩具模型，另一个是作者提出的双局部模型。对双局域模型的量子分析表明，该模型具有时空的临界维数，令人惊讶地等于4。然而，推导是基于这样的假设，即系统的真正对称性是由第一类约束产生的，如果满足狄拉克猜想，则该假设成立。本文在一般规范理论中对狄拉克猜想进行了详细的、严格的数学分析，并引入了半规范不变性等新概念。我们找到了这个猜想成立的条件。这是一组方程的生成函数的转换，表示的泊松括号和M括号中介绍的文件。上述条件缩小了狄拉克猜想成立的规范理论的范围。我们发现，除了某些例外，双局部模型满足上述条件。最后用一些例子来说明我们的方法。
英文摘要：
First class constraints in a canonical formalism of a gauge theory might generate transformations which map a state to its physically equivalent state. This is called Dirac's conjecture. There are two examples which may be candidates of counter-example of the conjecture. One is the toy model found by Cawley, and another is the bilocal model proposed by the author. A quantum analysis of the bilocal model shows that the model has the critical dimension of spacetime, which is surprisingly equal to four. The derivation, however, is based on the assumption that true symmetry of the system is generated by the first class constraints, which holds if Dirac's conjecture is satisfied. In the present paper we give detailed and mathematically rigorous analysis of Dirac's conjecture in general gauge theories, which involves new concept like semi-gauge invariance. We find the condition for the conjecture to hold. This is a set of equations for the generating function of the transformation, expressed in terms of Poisson brackets and M-brackets introduced in the paper. The above condition reduces the range of gauge theories where Dirac's conjecture holds. Along with the general prescription described in the paper we find that the bilocal model satisfies the above condition with some exceptions. Some examples are used to illustrate our method.
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