We study a notion of non-commutative integration, in the spirit of modular spectral triples, for the quantum group $SU_{q}(2)$. In particular we define the non-commutative integral as the residue at the spectral dimension of a zeta function, which is constructed using a Dirac operator and a weight. We consider the Dirac operator introduced by Kaad and Senior and a family of weights depending on two parameters, which are related to the diagonal automorphisms of $SU_{q}(2)$. We show that, after fixing one of the parameters, the non-commutative integral coincides with the Haar state of $SU_{q}(2)$. Moreover we can impose an additional condition on the zeta function, which also fixes the second parameter. For this unique choice the spectral dimension coincides with the classical dimension.
Riemann Hypothesis: Architecture of a conjecture "along" the lines of Pólya. From trivial zeros and Harmonic Oscillator to information about non-trivial zeros of the Riemann zeta-function
On the concept of determinant for the differential operators of Quantum Physics
无限维空间中线性算子行列式的概念是通过使用算子的zeta函数的导数（遵循Ray和Singer）并最终通过其zeta函数迹来解决的。对像$\pm I$（$I$是恒等运算符）及其变体一样简单的运算符的一点尝试表明，存在非交换异常（即，事实上，det $(AB) \neq$ det $A$ det $B$）是不可避免的，甚至对于交换，并且值得注意的是，对于几乎常数的算子也是如此。在狄拉克型算子的情况下，类似的基本论点导致结论-与通常的知识相矛盾-尽管是$\det (\slash D +im) = \det (\slash D -im)$（从$\slash D$ -谱的对称性条件可以得出），但这些行列式可能{ \it not}等于$\sqrt{\det (\slash D^2 +m^2)}$，仅仅因为$\det [(\slash D +im) (\slash D -im)] \neq \det (\slash D +im) \det (\slash D -im)$。这一事实的证明，通过一个非常简单的例子，使用运营商的谐振子频谱和满足对称性条件。如果在狄拉克算符中加上质量项（或取代质量项），化学势的贡献就可以与物理相关。
