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In this thesis we study field theories written on a particular model ofnoncommutative spacetime, the Groenewold-Moyal (GM) plane. We start withbriefly reviewing the novel features of field theories on GM plane e.g. the$\ast$-product, restoration of Poincar\'e-Hopf symmetry and twisted commutationrelations. We then discuss our work on renormalization of field theories on GMplane. We show that any generic noncommutative theory involving pure matterfields with polynomial interactions, is a renormalizable theory if theanalogous commutative theory is renormalizable. We further show that all suchnoncommutative theories will have same fixed points and $\beta$-functions forthe couplings, as that of the analogous commutative theory. The unique featureof these field theories is the twisted statistics obeyed by the particles.Motivated by it, we look at the possibility of twisted statistics by deforminginternal symmetries instead of spacetime symmetries. We construct two differenttwisted theories which can be viewed as internal symmetry analogue of the GMplane and dipole field theories which arise in the low energy limit of certainstring configurations. We further study their various properties like the issueof causality and the scattering formalism. Having studied the mathematicalproperties of noncommutative and twisted internal symmetries we move on todiscuss their potential phenomenological signatures. We first discuss thenoncommutative thermal correlation functions and show that because of thetwisted statistics, all correlation functions except two-point function getmodified. Finally we discuss the modifications in Hanbury-Brown Twiss (HBT)correlation functions due to twisted statistics on GM plane and the potentialof observing signatures of noncommutativity by doing a HBT correlationexperiment with Ultra High Energy Cosmic Rays (UHECRs).

Spin-Statistics Correlations in Various Noncommutative Field Theories