41. In general partition functions depend on a metric but the above examples are shown to be metric-independent. 42. The partition function can be related to thermodynamic properties because it has a very important statistical meaning. 43. As explained here, the average energy in a mode can be expressed in terms of the partition function : 44. However, in the end each contribution of a Feynman diagram to the partition function has the generic form 45. If the partition function has no special surface potential terms, this is the surface of a hard solid. 46. Technically, an anomalous symmetry in a quantum theory is a symmetry of the partition function as a whole. 47. See partition function for the case where the numbers in question are the energy levels of a physical system. 48. Here we note that is a typical infinitesimal phase space volume used in the calculation of a partition function . 49. The partition function in quantum field theory is a special case of the statistical partition function in statistical mechanics. 50. The partition function in quantum field theory is a special case of the statistical partition function in statistical mechanics. 