partition function

To explore how rigid rotation affects the thermodynamic properties of free relativistic bosons, we employ the standard imaginary time formalism of thermal field theory to calculate the free propagator of complex scalar fields under rotation. We introduce the corresponding partition function and explicitly compute it by expanding the modes in cylindrical coordinates. The resulting propagator is in full agreement with similar findings in the existing literature.

In this paper, we consider the q-analog of Kostant's Partition Function of Lie algebras  $\mathfrak{sl_\textrm{4}(\mathbb{C})} $ and $\mathfrak{sp_\textrm{6}(\mathbb{C})}$ and present a closed formula for the values of these functions.

A well-known enumerative problem is to count the number of ways a positive integer $n$ can be factorised as $n=n_1\times n_2\times\cdots\times n_{k}$, where $n_1\geqslant n_2 \geqslant \cdots \geqslant n_{k} >1$. In this paper, we give some recursive formulas for the number of ordered/unordered factorizations of a positiveinteger $n$ such that each factor is at least $\ell$. In particular, by using elementary techniques, we give an explicit formula in cases where $k=2,3,4$.