Unit:
Κατεύθυνση Πυρηνική Φυσική και Φυσική Στοιχειωδών ΣωματιδίωνLibrary of the School of Science
Supervisors info:
Εμμανουήλ Φλωράτος, Ομότιμος Καθηγητής, Τμήμα Φυσικής, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Original Title:
Anyon model for the alternating group A4
Translated title:
Anyon model for the alternating group A4
Summary:
In this master thesis the Quantum Double anyon model for the Alternating group A4 is constructed. In the first part, we present an overview of the statistical properties of anyons, both abelian and non-abelian, through the Bohm-Aharonov effect as well as their use in quantum computation. In particular, we discuss the Braiding and Fusion rules for anyons as they are expressed through the R-matrix, the F-matrix and the fusion bases.
In the second part, we focus on the alternating group A4 and by determining the superselection sectors through the conjugacy classes and their centralizers, we present the representations of each quantum double D(A4). We next compute the modular S-matrix and using the Verlinde formula we construct the fusion rules of the model. Also, we determine the modular T-matrix as well as the charge conjugation operator of the theory. Due to the high complexity of the model, we restrict the discussion to a small superselection sector whose fusion rules are closed and we calculate explicitly the R and F matrices. Finally, we show that the algebra D(A4) does not contain the necessary quantum gates for universal quantum computation.
Main subject category:
Science
Keywords:
Anyons, Anyon model, Quantum Double, Fusion Rules, Generalized Pentagon equation, Generalized Hexagon equation
