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XX Escola de Verão Jorge André Swieca de Part́ıculas e Campos / ID: 28-1 1
Aspects of Quantum Field Theories in 2+1 Dimensions
Guilherme Delfino Silva, Julio Cesar Toledo Pinto, Pedro Rogerio Sergi Gomes Universidade Estadual de Londrina
In the usual 3+1 dimensional quantum field theories, fields always have either integer spins, which are called bosons, or half-integer spins, which are called fermions. The physics in 2+1 dimensions is very rich and presents some interesting aspects that are not shared with the usual 3+1 dimensional physics. In these lower dimensional theories, particles with any spin, called anyons, are allowed to exist. Anyons may have fractional statistics, that is, their wave functions can get an arbitrary phase upon exchange of identical particles, unlike the usual symmetric and anti-symmetric cases of bosons and fermions, respectively. The study of anyons is of great importance in the description of some quantum phenomena, such as the fractional quantum Hall effect and the topological insulators. In this work we present some general aspects of these theories and discuss the appearance of the anyons as well as their properties. To incorporate these new properties in a local quantum field theory, we consider the Chern-Simons theory. We analyze interesting properties of the Chern-Simons action, its meaning as a topological field theory and the ground state degeneracy when defined on a closed manifold. Furthermore, we discuss dynamical properties by including a Maxwell term for the gauge field and also consider the coupling to matter fields. In the end of the work, the equivalence to the so-called Self-Dual model is discussed.