Is there some role for Bose-Einstein Statistics or Fermi-Dirac Statistics or Maxwell-Boltzmann Statistics in social sciences. Can there be some application of Statistical Field Theory in Social science research?
I think that economists mostly know nothing about physics and its methods and thus do not apply that. To my opinion, methods from statistical physics can be useful. For example, motion in phase space of income and wealth. However, one cannot blindly use equations from physics but has to derive them using economic assumptions. This is a work for people with 2 educations - in physics and economics - but still acceptance level might be low, since there are very few referee in journals with similar education.
About an attempt to bring physics closer to economics you may look at my paper on RG:
Econo-physics: A Perspective of Matching Two Sciences (2007)
I came across an interesting paper DOI:10.1214/08-BA318, by Andrew
Gelman in the Journal Bayesian Analysis 3, Number 3, pp. 445-450, titled " Objections to Bayesian statistics" 2008, International Society for Bayesian Analysis.