Pak, Namık Kemal
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.


Pak, Namık Kemal (1991-05-16)
The CP(N) model with a theta-term 1 + 2 dimensions is quantized canonically. By employing a suitable parametrization we demonstrate that solitons carry theta-dependent fractional spins.
Hamiltonian methods for nonlinear sigma models
Pak, Namık Kemal; Percacci, Roberto (AIP Publishing, 1989-12)
Nonlinear sigma models are studied in n space dimensions with values in a coset space G/H as infinite dimensional Hamiltonian systems. An ‘‘intrinsic’’ formulation is discussed in terms of coordinates on G/H, an ‘‘embedded’’ formulation in terms of fields satisfying a constraint and a ‘‘lifted’’ formulation in terms of fields having values in G/H̄, where H̄ is a normal subgroup of H. The coupling of the sigma model to Yang–Mills fields with structure group G is then considered, and it is shown that this sys...
Magnetic field and curvature effects on pair production. I. Scalars and spinors
Karabali, D.; Kürkcüoğlu, Seçkin; Nair, V. P. (American Physical Society (APS), 2019-9-17)
The pair production rates for spin-0 and spin-1/2 particles are calculated on spaces of the form M x R-1,R-1, with M corresponding to R-2 (flat); T-2 (flat, compactified); S-2 (positive curvature); and H-2 (negative curvature), with and without a background magnetic field on M. The motivation is to elucidate the effects of the curvature and background magnetic field. Contrasting effects for positive and negative curvature on the two cases of spin are obtained. For positive curvature, we find enhancement for...
Dualisation of supergravity theories
Yılmaz, Nejat Tevfik; Sarıoğlu, Bahtiyar Özgür; Department of Physics (2004)
By using the Kaluza-Klein reduction, the derivation of the maximal supergravities from the D=11 supergravity theory, as well as the Abelian Yang-Mills supergravities from the D=10 type I supergravity theory are discussed. After a thorough review of the symmetric spaces the symmetric space sigma model is studied in detail. The first-order formulation of both the pure and the matter coupled symmetric space sigma model is presented in a general formalism. The dualisation of the non-gravitational Bosonic sector...
Spin force and torque in non-relativistic Dirac oscillator on a sphere
Shikakhwa, M. S. (2018-03-30)
The spin force operator on a non-relativistic Dirac oscillator (in the non-relativistic limit the Dirac oscillator is a spin one-half 3D harmonic oscillator with strong spin-orbit interaction) is derived using the Heisenberg equations of motion and is seen to be formally similar to the force by the electromagnetic field on a moving charged particle. When confined to a sphere of radius R, it is shown that the Hamiltonian of this non-relativistic oscillator can be expressed as a mere kinetic energy operator w...
Citation Formats
N. K. Pak, “HAMILTONIAN QUANTIZATION OF THE CP1 SIGMA MODEL IN 1+2 DIMENSIONS,” PROGRESS OF THEORETICAL PHYSICS, pp. 585–591, 1992, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/62254.