Dual families of noncommutative quantum systems

Abstract

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 .

Schwinger model in noncommutating space–time

“…This is a physical effect carrying NC signature. In this context it may be mentioned that generation of interactions by casting non-interacting theories in NC coordinates have been observed in other contexts also [38,39,40].…”

Aharonov-Bohm Phase for an Electric Dipole on a Noncommutative Space

“…In this case, v = −(1/mc)B × d) + const may be inserted in Equation (28), which becomes an equation in the variable r ′ only (here we assume v = v 1 = v 2 ). In most cases the solution of this equation represents a bound oscillatory motion and will contain terms of the type sin(ωt +ϕ) or cos(ωt + ϕ), where ω is the frequency and ϕ is a constant phase.…”

“…And in Mirza and Zarei [16] the limit for the space noncommutativity parameter is 1/ √ θ ≥ 10 −7 GeV. The authors of Harms and Micu [23], Dayi and Jellal [24] and Chakraborty et al [25][26][27][28][29][30] have studied the noncommutative quantum Hall effect, and in Harms and Micu [23] a limit of 1/ √ θ ≥ 10GeV is given. The noncommutative spin Hall effect (SHE) is discussed through a semiclassical constrained Hamiltonian and interesting results are obtained in Dayi and Elbistan [31].…”

Effects of Two-Dimensional Noncommutative Theories on Bound States Schrödinger Diatomic Molecules under New Modified Kratzer-Type Interactions

“…The noncommutativity of space-time, which known firstly by Heisenberg and was formalized by Snyder at 1947, suggest by the physical recent results in string theory [9]. Motivated by these, over the past few years, theoretical physicists have shown a great deal of interest in solving Schrödinger equation, Klein-Gordon and Dirac equation for various potentials in NC space-phase to obtaining profound interpretations at microscopic scale [10][11][12][13][14][15][16][17][18][19][20][21][22][23] and in particularly, our previously works . The notions of noncommutativity of space and phase based essentially on Seiberg-Witten map, the Bopp's shift method and the star product, which modified the ordinary product ( )( ) …”