טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentSmolkin Michael
SubjectScale Symmetry Breaking in Quantum Field Theory
DepartmentDepartment of Physics
Supervisors Professor Emeritus Moshe Moshe
Dr. Joshua Feinberg


Abstract

In this study we apply large-N techniques and path integration to study the three-dimensional O(N) symmetric bosonic vector model and its sypersymmetric extension. We set all dimensional parameters to zero and tune the dimensionless coupling to a certain critical value, thus rendering the models under consideration scale invariant. We show that scale invariance is broken spontaneously, in the sense that the gap equations for the masses of O(N) vector particles possess solutions with arbitrary mass. This claim is proved by explicitly calculating the trace of the improved energy momentum tensor.

In addition, in both models one finds massless bound states, the so-called dilaton, in the scalar case, and massless dilaton and dilatino in the supersymmetric model. These massless bound states can be interpreted as the massless Goldstone particles associated with spontaneous breaking of scale invariance.

Finally, we discuss both models at finite temperature. In particular, the effect of finite temperature on scale invariance is elucidated. Euclidean path integral formalism with appropriately applied boundary conditions is used to calculate various thermodynamic quantities.

It is shown that under certain conditions the trace of the energy momentum tensor vanishes at any temperature. At zero temperature it reveals spontaneous breaking of scale invariance mentioned above. In addition, the behavior of the various masses as a function of temperature is analyzed