7162

6668

كارشناسي ارشد

ذرات بنيادي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده فيزيك

1390

[هفت]، 59ص.: مصور، جدول، نمودار

ص.ع. به فارسي و انگليسي

احمد شيرزاد

بهروز ميرزا

6/8/91

جلال سرابادي، منصور حقيقت

1396/09/20

كتابنامه

فيزيك

فيزيك

ID6668

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

۶ Quantization of a Massive Open Bosonic String in Background B Field And The associated Casimir effect Yoosof Koohsarian koohsarian ramian@yahoo com January 25 2012 Department of Physics Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Supervisor Ahmad Shirzad shirzad@ipm ir Abstract In this thesis we first study the quantization of a massive open bosonic string in the presence of a background B field and then survey associated Casimir effect Initially using classical lagrangian of the system get the boundary conditions then putting these conditions as the Dirac constraints and according to consistency condition that means the constraintsmust be true all the time we achieve two infinite chains of constraints at the end points of the string Subsequently we impose these sets of constraints on Fourier expansions of initial fields of the phase space of the string and reach reduced phase space which is based on discrete physical modes There we use symplectic approach to find Poisson brackets of the physical modes and using the symmetry of the problem we show that all of the discrete physical modes are canonical pairs especially zero modes will be canonic that one can simply prove that it exactly is the consequence of using above symmetry Finally we can use above Poisson brackets of the physical modes to find the Poisson brackets of string fields in reduced phase space which are the same as Dirac brackets of the string fields These Dirac brackets apparently show that coordinates fields as well as conjugate momentum fields are no longer commutating objects in fact they anticommute in the end points of string due to the mass of string and the background B field Our canonical Hamiltonian will simply be found using above mod expansions of string fields This Hamiltonian shows that bosonic string can be regarded as a superposition of a set of harmonic oscillators We then obtain dynamical equations of string modes that give us the oscillation frequency of string modes In the next step we use these oscillation frequencies to find zero point energy of bosonic string obviously it would be infinite in fact as a consequence of definition of energy in quantum field theory as we know To find the convergent part of zero point energy that is also called the Casimir energy we use a powerful mathematical technique namely the Abel plana formula We see the Casimir energy of our massive bosonic string is a function of background B field as well as mass and length of the string in fact B field plays a role only in the constant part of Casimir energy that can be neglected Casimir force is simply achieved deriving Casimir energy to the length of string we will see the force does not depend on B field as is expected Then we plot the casimir force to the length for several value of mass and show the force has a logical behavior at large value of mass or length of the string Finally employing a useful expansion namely the heat kernel expansion we find divergent parts of the zero point energy and will have a glance at the connection between these divergences and the theme of renormalization and provide some suggestions for more studies Keywords Dirac constraints Reduced phase space Symplectic approach Casimir force Heat kernel expansion

احمد شيرزاد

بهروز ميرزا

جلال سرابادي، منصور حقيقت