Pak, Namık Kemal
We discuss the appearance of theta vacua and solitons with fractional spin in the S2-valued nonlinear sigma model in two space dimensions. We use a formulation of the sigma model in terms of Euler angles and work within the context of canonical quantization. We show that when the model is coupled to an SU(2) topologically massive theory, the theta sectors disappear and the topological mass is not quantized.


Topological unitarity identities in Chern-Simons theories
Fainberg, VY; Shikakhwa, MS (1996-05-15)
Starting from the generating functional of the theory of relativistic spinors in 2+1 dimensions interacting through the pure Chern-Simons gauge field, the S matrix is constructed and seen to be formally the same as that of spinor quantum electrodynamics in 2+1 dimensions with Feynman diagrams having external photon lines excluded, and with the propagator of the topological Chern-Simons photon substituted for the Maxwell photon propagator. It is shown that the absence of real topological photons in the compl...
Chaos from equivariant fields on fuzzy S4
Coşkun, Ü. H.; Kürkcüoğlu, Seçkin; Toga, G. C.; Ünal, G. (Springer Science and Business Media LLC, 2018-12)
We examine the 5d Yang-Mills matrix model in 0 + 1-dimensions with U(4N) gauge symmetry and a mass deformation term. We determine the explicit SU(4) ≈ SO(6) equivariant parametrizations of the gauge field and the fluctuations about the classical four concentric fuzzy four sphere configuration and obtain the low energy reduced actions(LEAs) by tracing over the SF 4s for the first five lowest matrix levels. The LEAs so obtained have potentials bounded from below indicating that the equivariant fluctuations ab...
Linear and nonlinear intersubband optical absorptions in an asymmetric rectangular quantum well
Karabulut, I.; Atav, U.; Safak, H.; Tomak, Mehmet (2007-02-01)
The linear and nonlinear intersubband optical absorptions in AlxlGa1-xlAs/GaAs/AlxrGa1-xrAs asymmetric rectangular quantum well are studied within the framework of the density matrix formalism. We have calculated the electron energy levels and the envelope wave functions using the effective mass approach. In addition, we have obtained an expression for saturation intensity. It is shown that the parameters such as asymmetry and width of potential well not only shift the peak positions in absorption spectrum ...
Pak, Namık Kemal (1992-09-01)
CP1 sigma model with Hopf interaction in 1 + 2 dimensions is quantized canonically using a lifted formulation. In this formulation the Hopf invariant is still a local functional of the fields. However, the constraint structure is as simple as that of a U(1) gauge theory without any nonlinearity constraints. As a by-product, the theta-dependent fractional spin is computed in this local setting.
Extended dynamical symmetries of Landau levels in higher dimensions
Kürkcüoğlu, Seçkin; YURDUŞEN, İSMET (Springer Science and Business Media LLC, 2020-02-14)
Continuum models for time-reversal (TR) invariant topological insulators (Tis) in d >= 3 dimensions are provided by harmonic oscillators coupled to certain SO(d) gauge fields. These models are equivalent to the presence of spin-orbit (SO) interaction in the oscillator Hamiltonians at a critical coupling strength (equivalent to the harmonic oscillator frequency) and leads to flat Landau Level (LL) spectra and therefore to infinite degeneracy of either the positive or the negative helicity states depending on...
Citation Formats
N. K. Pak and R. PERCACCI, “TOPOLOGY AND FRACTIONAL SPIN IN THE (2+1)-DIMENSIONAL SIGMA MODEL,” PHYSICAL REVIEW D, pp. 1375–1384, 1991, Accessed: 00, 2020. [Online]. Available: