15 research outputs found
Factorization of gravitational Compton scattering amplitude in the linearized version of general relativity
Gravitational Compton scattering process with a massive fermion is studied in
the context of the linearized gravity. Gravitational gauge invariance and
graviton transversality cause the transition amplitude to be factorized into
that of scalar QED Compton scattering and that of fermion QED Compton
scattering with an overall kinematical factor. The factorization is shown
explicitly and its physical implications are discussed.Comment: 11 pages, 1 figure(not included), Revtex 3.0, SNUTP 93-2
Beyond conventional factorization: Non-Hermitian Hamiltonians with radial oscillator spectrum
The eigenvalue problem of the spherically symmetric oscillator Hamiltonian is
revisited in the context of canonical raising and lowering operators. The
Hamiltonian is then factorized in terms of two not mutually adjoint factorizing
operators which, in turn, give rise to a non-Hermitian radial Hamiltonian. The
set of eigenvalues of this new Hamiltonian is exactly the same as the energy
spectrum of the radial oscillator and the new square-integrable eigenfunctions
are complex Darboux-deformations of the associated Laguerre polynomials.Comment: 13 pages, 7 figure
Factorization and polarization in linearized gravity
We investigate all the four-body graviton interaction processes:
, , and with
as an elementary particle of spin less than two in the context of linearized
gravity except the spin-3/2 case. We show explicitly that gravitational gauge
invariance and Lorentz invariance cause every four-body graviton scattering
amplitude to be factorized. We explore the implications of this factorization
property by investigating polarization effects through the covariant density
matrix formalism in each four-body graviton scattering process.Comment: 45 pages, figures are included (uses pictex), RevTe
Quantum isotonic nonlinear oscillator as a Hermitian counterpart of Swanson Hamiltonian and pseudo-supersymmetry
Within the ideas of pseudo-supersymmetry, we have studied a non-Hermitian
Hamiltonian H_{-}=\omega(\xi^{\dag} \xi+\1/2)+\alpha \xi^{2}+\beta \xi^{\dag
2}, where and is a first order differential
operator, to obtain the partner potentials and which are
new isotonic and isotonic nonlinear oscillators, respectively, as the Hermitian
equivalents of the non-Hermitian partner Hamiltonians . We have
provided an algebraic way to obtain the spectrum and wavefunctions of a
nonlinear isotonic oscillator. The solutions of which are Hermitian
counterparts of Swanson Hamiltonian are obtained under some parameter
restrictions that are found. Also, we have checked that if the intertwining
operator satisfies , where and is the first order differential operator,
which factorizes Hermitian equivalents of .Comment: 11 page