Aspects of finite size effects on Bose Einstein condensation

In this thesis, the number of particles calculations of Pathria for a 3 dimensional box is shortly reviewed. After that, the works of Toms and Kirsten which use the Mellin Barnes integral representation and heat kernel approximation to calculate the partition function summation is reviewed. Toms and Kirsten's approach is worked out in d dimension to calculate some thermodynamic quantities such as the number of particles, internal energy, heat capacity at constant volume and constant pressure, isothermal compressibility, adiabatic compressibility etc. The discontinuity of the heat capacity and the derivative of the heat capacity around the critical temperature is investigated. The results are checked at the bulk level to see that at d = 3 they are consistent with the ones given in Pathria. Lastly, the results are generalized to p to the s for s = 2k case and also an expression for the discontinuity of the heat capacity at constant volume is written.