Chakraborty for his guidance and encouragement. I also acknowledge with sincere gratitude, the guidance I received from Prof. F.G. Scholtz and am grateful to him for always being there to help me in my work. I record my sincere thanks to Dr. Biswajit Chakraborty for helping me throughout the course of this work and the timely completion of this thesis is a result of his support. It is also my duty and joy to thank the family of Dr. Chakraborty for their hospitality during my visits for professional discussions.I am grateful to Prof. S. Dattagupta, ex. Director of Satyendra Nath Bose National Centre for Basic Sciences (SNBNCBS), for giving me the opportunity to do research here. I am thankful to Prof. R. Banerjee, Academic Programme Coordinator, SNBNCBS, for the academic help rendered to me. I thank all the academic and administrative staff of SNBNCBS for helping me in many ways.In particular, I am thankful to the Library staff for the excellent assistance provided to me.It is my pleasure to thank my friends Mr. Arindam Ghosh Hazra and Mr. Anirban Saha who with their help and support in both academic and personal matters made my research an experience I cherish much.Finally and most importantly, I express my whole hearted gratitude to my family members. It is the love and unflinching support of my parents and grand parents that enabled me to pursue this line of study which finally culminated in this thesis. I dedicate this thesis to them. iv 7.7 Summary .

We show the twisted Galilean invariance of the noncommutative parameter, even in presence of space-time noncommutativity. We then obtain the deformed algebra of the Schrödinger field in configuration and momentum space by studying the action of the twisted Galilean group on the non-relativistic limit of the Klein-Gordon field. Using this deformed algebra we compute the two particle correlation function to study the possible extent to which the previously proposed violation of the Pauli principle may impact at low energies. It is concluded that any possible effect is probably well beyond detection at current energies.

Non(anti)commutativity in an open free superstring and also one moving in a background antisymmetric tensor field is investigated. In both cases, the non(anti)commutativity is shown to be a direct consequence of the non-trivial boundary conditions which, contrary to several approaches, are not treated as constraints. The above non(anti)commutative structures lead to new results in the algebra of super constraints which still remain involutive, indicating the internal consistency of our analysis.

Noncommutativity in an open bosonic string moving in the presence of a background Neveu-Schwarz two-form field B µν is investigated in a conformal field theory approach, leading to noncommutativity at the boundaries. In contrast to several discussions, in which boundary conditions are taken as Dirac constraints, we first obtain the mode algebra by using the newly proposed normal ordering, which satisfies both equations of motion and boundary conditions. Using these the commutator among the string coordinates is obtained. Interestingly, this new normal ordering yields the same algebra between the modes as the one satisfying only the equations of motion. In this approach, we find that noncommutativity originates more transparently and our results match with the existing results in the literature.

A new Lagrangian description that interpolates between the Nambu-Goto and Polyakov version of interacting strings is given. Certain essential modifications in the Poission bracket structure of this interpolating theory generates noncommutativity among the string coordinates for both free and interacting strings. The noncommutativity is shown to be a direct consequence of the nontrivial boundary conditions. A thorough analysis of the gauge symmetry is presented taking into account the new modified constraint algebra, which follows from the noncommutative structures and finally a smooth correspondence between gauge symmetry and reparametrisation is established.