弱耦合下Moyal平面上实标量四次QFT配分函数的非微扰计算
Nonperturbative evaluation of the partition function for the real scalar quartic QFT on the Moyal plane at weak coupling
摘要：
Moyal平面上的实标量四次量子场论的显着性质与其与Kontsevich模型的相似性相结合，使模型的配分函数成为一个有趣的研究对象。然而，直接的评价是阻碍了交织的领域的各种模式。一个因式分解过程，以规避这个问题，提出并讨论在这里的背景下，真正的标量四次qft的Moyal平面。这种分解包括对对称随机矩阵的对角子多面体的渐近体积积分。这一数额是为此目的确定的。用这种方法计算了弱耦合区的配分函数。使用相同的方法，也可以确定其他状态的配分函数和自由能量密度。
英文摘要：
The remarkable properties of the real scalar quartic quantum field theory on the Moyal plane in combination with its similarity to the Kontsevich model make the model's partition function an interesting object to study. However, direct evalua- tions is obstructed by the intertwining of the field's various modes. A factorization procedure to circumvent this problem is proposed and discussed here in the context of the real scalar quartic qft on the Moyal plane. This factorization consists of integrating against the asymptotic volume of the diagonal subpolytope of symmet- ric stochastic matrices. This volume has been determined to this end. Using this method the partition function for regime of weak coupling is computed. Using the same method it is as well possible to determine the partition function and free energy density for other regimes.
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