Papers by Mohammad Shikakhwa
We investigate the spin dynamics and the conservation of helicity in the first order $S-$matrix o... more We investigate the spin dynamics and the conservation of helicity in the first order $S-$matrix of a Dirac particle in any static magnetic field. We express the dynamical quantities using a coordinate system defined by the three mutually orthogonal vectors; the total momentum $\mathbf{k}=\mathbf{p_f}+\mathbf{p_i}$, the momentum transfer $\mathbf{q}=\mathbf{p_f-p_i}$, and $\mathbf{l}=\mathbf{k\times q}$. We show that this leads to an alternative symmetric description of the conservation of helicity in a static magnetic field at first order. In particular, we show that helicity conservation in the transition can be viewed as the invariance of the component of the spin along $\mathbf{k}$, and the flipping of its component along $\mathbf{q}$, just as what happens to the momentum vector of a ball bouncing off a wall. We also derive a "plug and play" formula for the transition matrix element where the only reference to the specific field configuration, and the incident and outgo...
The structure of the spin interaction operator (SI) (the interaction that remains after space var... more The structure of the spin interaction operator (SI) (the interaction that remains after space variables are integrated out) in the first order S-matrix element of the elastic scattering of a Dirac particle in a general helicity-conserving vector potential is investigated.It is shown that the conservation of helicity dictates a specific form of the SI regardless of the explicit form of the vector potential. This SI closes the SU(2) algebra with other two operators in the spin space of the particle. The directions of the momentum transfer vector and the vector bisecting the scattering angle seem to define some sort of "intrinsic" axes at this order that act as some symmetry axes for the whole spin dynamics . The conservation of helicity at this order can be formulated as the invariance of the component of the helicity of the particle along the bisector of the scattering angle in the transition.
Physical Review D, 1996
Starting from the generting functional of the theory of relativistic spinors in 2 + 1 dimensions ... more Starting from the generting 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 complete set of vector states of the total Hilbert space leads in a given order of perturbation theory to topological unitarity identities that demand the vanishing of the gauge-invariant sum of the imaginary parts of the Feynman diagrams with a given number of internal on-shell free toplogical photon lines. It is also shown, that these identities can be derived outside the framework of perturbation theory.The identities are verified explicitly for the scattering of a fermion-antifermion pair in one-loop order.
Physical Review D, 2003
A partial wave analysis using the basis of the total angular momentum operator J3 is carried out ... more A partial wave analysis using the basis of the total angular momentum operator J3 is carried out for the first order Born amplitude of a Dirac particle in an Aharonov-Bohm (AB) potential. It is demonstrated that the s-partial wave contributes to the scattering amplitude in contrast to the case with scalar non-relativistic particles. We suggest that this explains the fact that the first order Born amplitude of a Dirac particle coincides with the exact amplitude expanded to the same order, where it does not for a scalar particle. An interesting algebra involving the Dirac velocity operator and the angular observables is discovered and its consequences are exploited.
The Aharonov–Casher Scattering: The Effect of the ∇ · e Term
Modern Physics Letters A, 2010
In the Aharonov–Casher (AC) scattering, a neutral particle interacts with an infinitesimally thin... more In the Aharonov–Casher (AC) scattering, a neutral particle interacts with an infinitesimally thin, long charge filament resulting in a phase shift. In the original AC treatment, a ∇ · E term proportional to the charge density at the…
Journal of Physics A: Mathematical and Theoretical, 2012
The question of gauge-covariance in the non-Abelian gauge-field formulation of two spacedimension... more The question of gauge-covariance in the non-Abelian gauge-field formulation of two spacedimensional systems with spin-orbit coupling relevant to spintronics is investigated. Although, these are generally gauge-fixed models, it is found that for the class of gauge fields that are spacetime independent and satisfy a U(1) algebra, thus having a vanishing field strength, there is a residual gauge freedom in the Hamiltonian. The gauge transformations assume the form of a spacedependent rotation of the transformed wave functions with rotation angles and axes determined by the specific form of the gauge-field, i.e., the spin-orbit coupling. The fields can be gauged away, reducing the Hamiltonian to one which is isospectral to the free-particle Hamiltonian, and giving rise to the phenomenon of persistent spin helix reported first by B. A. Bernevig et al. [Phys. Rev. Lett. 97, 236601 (2006)]. The investigation of the global gauge transformations leads to the derivation of a continuity equation where the component of the spin-density along given directions, again fixed by the specific form of the gauge field, is conserved.
Non-relativistic fermions interacting through the Chern-Simons field and the Aharonov-Bohm scattering amplitude
Journal of Physics A: Mathematical and General, 1998
Starting from the non-relativistic field theory of spin-0305-4470/31/15/017/img1 fermions interac... more Starting from the non-relativistic field theory of spin-0305-4470/31/15/017/img1 fermions interacting through the Abelian Chern-Simons term, we show that the quantized field theory leads, in the two-particle sector, to a two-particle Aharonov-Bohm-like Schrödinger equation with an antisymmetric (fermionic) wavefunction and without a delta function term. Calculating perturbatively the field-theoretic two-particle scattering amplitude up to one-loop order, we show that, in contrast
International Journal of Theoretical Physics, 2005
In the presence of an external Aharonov-Bohm potential, we investigate the two QED processes of t... more In the presence of an external Aharonov-Bohm potential, we investigate the two QED processes of the emission of a bremsstrahlung photon by an electron, and the production of an electronpositron pair by a single photon. Calculations are carried out using the Born approximation within the framework of covariant perturbation theory to lowest non-vanishing order in α. The matrix element for each process is derived, and the corresponding differential cross-section is calculated. In the non-relativistic limit, the resulting angular and spectral distributions and some polarization properties are considered, and compared to results of previous works.
International Journal of Theoretical Physics, 2007
The structure of the interaction Hamiltonian in the first order S-matrix element of a Dirac parti... more The structure of the interaction Hamiltonian in the first order S-matrix element of a Dirac particle in an Aharonov-Bohm (AB) field is analyzed and shown to have interesting algebraic properties. It is demonstrated that as a consequence of these properties, this interaction Hamiltonian splits both the incident and outgoing waves in the the first order S-matrix into their Σ 3 2 -components ( eigenstates of the third component of the spin). The matrix element can then be viewed as the sum of two transitions taking place in these two channels of the spin. At the level of partial waves, each partial wave of the conserved total angular momentum is split into two partial waves of the orbital angular momentum in a manner consistent with the conservation of the total angular momentum quantum number.
European Journal of Physics, 2009
The angular part of the Schrödinger equation for a central potential is brought to the onedimensi... more The angular part of the Schrödinger equation for a central potential is brought to the onedimensional "Schrödinger form" where one has a kinetic energy plus potential energy terms. The resulting polar potential is seen to be a family of potentials characterized by the square of the magnetic quantum number m. It is demonstrated that this potential can be viewed as a confining potential that attempts to confine the particle to the xy-plane, with a strength that increases with increasing m. Linking the solutions of the equation to the conventional solutions of the angular equation, i.e. the associated Legendre functions , we show that the variation in the spatial distribution of the latter for different values of the orbital angular quantum number l can be viewed as being a result of "squeezing" with different strengths by the introduced "polar potential".
Turkish Journal of …, 2004
The Born scattering amplitude of a non-relativistic spin one-half particle in an Aharonov-Bohm po... more The Born scattering amplitude of a non-relativistic spin one-half particle in an Aharonov-Bohm potential is calculated up to second order. It is demonstrated that perturbation theory works well for this model, in contrast with the case of scalar particles, thanks to the spin-magnetic moment interaction term. The first order amplitude is shown to coincide with the exact amplitude when expanded to the same order; the second order amplitude is finite and null. The polarized scattering cross section is found to be different from the unpolarized one only if the incident particle has a spin component perpendicular to the flux tube.
American Journal of Physics, 2011
Journal of Physics A: Mathematical and General, 1997
The covariant path integral quantization of the theory of the scalar and spinor particles interac... more The covariant path integral quantization of the theory of the scalar and spinor particles interacting through the Abelian and non-Abelian pure Chern-Simons gauge fields is carried out and is shown to be mathematically ill defined due to the absence of the transverse components of these gauge fields. This is remedied by the introduction of the Maxwell or the Maxwell-type (in th non-abelian case) term which makes the theory superrenormalizable and guarantees its gauge-invariant regularization and renormalization . The generating functionals are constructed and shown to be formally the same as those of QED (or QCD) in 2+1 dimensions with the substitution of the Chern-Simons propagator for the photon (gluon) propagator. By constructin the propagator in the general case; the existence of two limits; pure Chern-Simons and QED (QCD) after renormalization is demonstrated. By carrying out carefully the path integral quantization of the non-Abelian Chern-Simons theories using the De Witt-Fadeev-Popov and the Batalin-Fradkin -Vilkovisky
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Papers by Mohammad Shikakhwa