Andrei Terekidi | Fluidigm Corporation (original) (raw)
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Papers by Andrei Terekidi
Proquest Dissertations and Theses Thesis York University 2004 Publication Number Aainq99245 Isbn 9780612992450 Source Dissertation Abstracts International Volume 66 01 Section B Page 0321 253 P, 2004
We derive relativistic two-fermion wave equations variationaly from the expectation value of the ... more We derive relativistic two-fermion wave equations variationaly from the expectation value of the Hamiltonian of the QFT. We use a reformulation of QED in which the resulting modified Hamiltonian contains the photon propagator directly. A simple Fock-space trial function is used. It is required to be an eigenstate of the square of the total relativistic angular momentum operator (orbital plus spin), its projection, parity, and for particle-antiparticle pairs, charge conjugation. The interaction kernels of the equations are shown to be, in essence, the invariant M-matrix elements corresponding to one-photon exchange and virtual annihilation interactions. We classify all bound states of two fermion system. It is shown that in the case of different masses of the particles a mixing of singlet and triplet states takes place. For such quasi states, the total spin is not a good quantum number, so the energy eigenvalues of the system are characterized by the quantum numbers n and J only. For small coupling constants the fine structure up to fourth order for all states and mass ratios is analytically calculated. Comparison with results using other formalisms is presented.
Physical Review A, 2007
A relativistic wave equation for bound states of two fermions with arbitrary masses which are exp... more A relativistic wave equation for bound states of two fermions with arbitrary masses which are exposed to a magnetic field is derived from quantum electrodynamics. The interaction kernels are based upon the generalized invariant M -matrices for inter-fermion and fermion-field interactions. As an application we calculate the energy corrections in a weak homogeneous B field to obtain the Zeeman splitting of the hyperfine structure (HFS) and g-factors in the lowest order (i.e. to O (α 4 )). Landé g-factors are presented for several of the first excited states of hydrogen, muonium, and muonic-hydrogen.
We derive relativistic two-fermion wave equations variationaly from the expectation value of the ... more We derive relativistic two-fermion wave equations variationaly from the expectation value of the Hamiltonian of the QFT. We use a reformulation of QED in which the resulting modified Hamiltonian contains the photon propagator directly. A simple Fock-space trial function is used. It is required to be an eigenstate of the square of the total relativistic angular momentum operator (orbital plus spin), its projection, parity, and for particle-antiparticle pairs, charge conjugation. The interaction kernels of the equations are shown to be, in essence, the invariant M-matrix elements corresponding to one-photon exchange and virtual annihilation interactions. We classify all bound states of two fermion system. It is shown that in the case of different masses of the particles a mixing of singlet and triplet states takes place. For such quasi states, the total spin is not a good quantum number, so the energy eigenvalues of the system are characterized by the quantum numbers n and J only. For small coupling constants the fine structure up to fourth order for all states and mass ratios is analytically calculated. Comparison with results using other formalisms is presented.
A relativistic theory of the Zeeman splitting of hyperfine levels in two-fermion systems is prese... more A relativistic theory of the Zeeman splitting of hyperfine levels in two-fermion systems is presented. The approach is based on the variational equation for bound states derived from quantum electrodynamics [1]. Relativistic corrections to the g-factor are obtained up to O(alpha^2). Calculations are provided for all quantum states and for arbitrary fermionic mass ratio. In the one-body limit our calculations reproduce the formula for the g-factor (to O((Z*alpha)^2)) obtained from the Dirac equation. The results will be useful for comparison with high-precision measurements.
Journal of Physics: Conference Series, 2010
A relativistic theory of the Zeeman splitting of hyperfine levels in two-fermion systems is prese... more A relativistic theory of the Zeeman splitting of hyperfine levels in two-fermion systems is presented. The approach is based on the variational equation for bound states derived from quantum electrodynamics . Relativistic corrections to the g-factor are obtained up to O (α) 2 . Calculations are provided for all quantum states and for arbitrary fermionic mass ratio. In the one-body limit our calculations reproduce the formula for the g-factor (to O (Zα) 2 ) obtained from the Dirac equation. The results will be useful for comparison with high-precision measurements. (S 1 ) J and f (S 1 ) J are taken as f (S 1 ) J =
Journal of Mathematical Physics, 2004
We present a variational method for deriving relativistic two-fermion wave equations in a Hamilto... more We present a variational method for deriving relativistic two-fermion wave equations in a Hamiltonian formulation of QED. A reformulation of QED is performed, in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. The resulting modified Hamiltonian contains the photon propagator directly. The reformulation permits one to use a simple Fock-space variational trial state to derive relativistic fermion-antifermion wave equations from the corresponding quantum field theory. We verify that the energy eigenvalues obtained from the wave equation agree with known results for positronium.
Journal of Mathematical Physics, 2005
We consider a reformulation of quantum electrodynamics in which covariant Green functions are use... more We consider a reformulation of quantum electrodynamics in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. The resulting modified Hamiltonian contains the photon propagator directly. A simple Fock-state variational trial function is used to derive relativistic two-fermion equations variationally from the expectation value of the Hamiltonian of the field theory. The interaction kernel of the equation is shown to be, in essence, the invariant M matrix in lowest order. Solutions of the two-body equations are presented for muoniumlike systems for small coupling strengths. The results compare well with the observed muonium spectrum, as well as that for hydrogen and muonic hydrogen. Anomalous magnetic moment effects are discussed.
Canadian Journal of Physics, 2007
We present a formulation of the Hamiltonian variational method for QED which enables the derivati... more We present a formulation of the Hamiltonian variational method for QED which enables the derivation of relativistic few-fermion wave equation that can account, at least in principle, for interactions to any order of the coupling constant. We derive a relativistic two-fermion wave equation using this approach. The interaction kernel of the equation is shown to be the generalized invariant M matrix including all orders of Feynman diagrams. The result is obtained rigorously from the underlying QFT for arbitrary mass ratio of the two fermions. Our approach is based on three key points: a reformulation of QED, the variational method, and adiabatic hypothesis. As an application we calculate the one-loop contribution of radiative corrections to the two-fermion binding energy for singlet states with arbitrary principal quantum number n, and ℓ = J = 0 . Our calculations are carried out in the explicitly covariant Feynman gauge. (tr)Jms Jm J f J (p)Y ms 1 s 2 J
Proquest Dissertations and Theses Thesis York University 2004 Publication Number Aainq99245 Isbn 9780612992450 Source Dissertation Abstracts International Volume 66 01 Section B Page 0321 253 P, 2004
We derive relativistic two-fermion wave equations variationaly from the expectation value of the ... more We derive relativistic two-fermion wave equations variationaly from the expectation value of the Hamiltonian of the QFT. We use a reformulation of QED in which the resulting modified Hamiltonian contains the photon propagator directly. A simple Fock-space trial function is used. It is required to be an eigenstate of the square of the total relativistic angular momentum operator (orbital plus spin), its projection, parity, and for particle-antiparticle pairs, charge conjugation. The interaction kernels of the equations are shown to be, in essence, the invariant M-matrix elements corresponding to one-photon exchange and virtual annihilation interactions. We classify all bound states of two fermion system. It is shown that in the case of different masses of the particles a mixing of singlet and triplet states takes place. For such quasi states, the total spin is not a good quantum number, so the energy eigenvalues of the system are characterized by the quantum numbers n and J only. For small coupling constants the fine structure up to fourth order for all states and mass ratios is analytically calculated. Comparison with results using other formalisms is presented.
Physical Review A, 2007
A relativistic wave equation for bound states of two fermions with arbitrary masses which are exp... more A relativistic wave equation for bound states of two fermions with arbitrary masses which are exposed to a magnetic field is derived from quantum electrodynamics. The interaction kernels are based upon the generalized invariant M -matrices for inter-fermion and fermion-field interactions. As an application we calculate the energy corrections in a weak homogeneous B field to obtain the Zeeman splitting of the hyperfine structure (HFS) and g-factors in the lowest order (i.e. to O (α 4 )). Landé g-factors are presented for several of the first excited states of hydrogen, muonium, and muonic-hydrogen.
We derive relativistic two-fermion wave equations variationaly from the expectation value of the ... more We derive relativistic two-fermion wave equations variationaly from the expectation value of the Hamiltonian of the QFT. We use a reformulation of QED in which the resulting modified Hamiltonian contains the photon propagator directly. A simple Fock-space trial function is used. It is required to be an eigenstate of the square of the total relativistic angular momentum operator (orbital plus spin), its projection, parity, and for particle-antiparticle pairs, charge conjugation. The interaction kernels of the equations are shown to be, in essence, the invariant M-matrix elements corresponding to one-photon exchange and virtual annihilation interactions. We classify all bound states of two fermion system. It is shown that in the case of different masses of the particles a mixing of singlet and triplet states takes place. For such quasi states, the total spin is not a good quantum number, so the energy eigenvalues of the system are characterized by the quantum numbers n and J only. For small coupling constants the fine structure up to fourth order for all states and mass ratios is analytically calculated. Comparison with results using other formalisms is presented.
A relativistic theory of the Zeeman splitting of hyperfine levels in two-fermion systems is prese... more A relativistic theory of the Zeeman splitting of hyperfine levels in two-fermion systems is presented. The approach is based on the variational equation for bound states derived from quantum electrodynamics [1]. Relativistic corrections to the g-factor are obtained up to O(alpha^2). Calculations are provided for all quantum states and for arbitrary fermionic mass ratio. In the one-body limit our calculations reproduce the formula for the g-factor (to O((Z*alpha)^2)) obtained from the Dirac equation. The results will be useful for comparison with high-precision measurements.
Journal of Physics: Conference Series, 2010
A relativistic theory of the Zeeman splitting of hyperfine levels in two-fermion systems is prese... more A relativistic theory of the Zeeman splitting of hyperfine levels in two-fermion systems is presented. The approach is based on the variational equation for bound states derived from quantum electrodynamics . Relativistic corrections to the g-factor are obtained up to O (α) 2 . Calculations are provided for all quantum states and for arbitrary fermionic mass ratio. In the one-body limit our calculations reproduce the formula for the g-factor (to O (Zα) 2 ) obtained from the Dirac equation. The results will be useful for comparison with high-precision measurements. (S 1 ) J and f (S 1 ) J are taken as f (S 1 ) J =
Journal of Mathematical Physics, 2004
We present a variational method for deriving relativistic two-fermion wave equations in a Hamilto... more We present a variational method for deriving relativistic two-fermion wave equations in a Hamiltonian formulation of QED. A reformulation of QED is performed, in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. The resulting modified Hamiltonian contains the photon propagator directly. The reformulation permits one to use a simple Fock-space variational trial state to derive relativistic fermion-antifermion wave equations from the corresponding quantum field theory. We verify that the energy eigenvalues obtained from the wave equation agree with known results for positronium.
Journal of Mathematical Physics, 2005
We consider a reformulation of quantum electrodynamics in which covariant Green functions are use... more We consider a reformulation of quantum electrodynamics in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. The resulting modified Hamiltonian contains the photon propagator directly. A simple Fock-state variational trial function is used to derive relativistic two-fermion equations variationally from the expectation value of the Hamiltonian of the field theory. The interaction kernel of the equation is shown to be, in essence, the invariant M matrix in lowest order. Solutions of the two-body equations are presented for muoniumlike systems for small coupling strengths. The results compare well with the observed muonium spectrum, as well as that for hydrogen and muonic hydrogen. Anomalous magnetic moment effects are discussed.
Canadian Journal of Physics, 2007
We present a formulation of the Hamiltonian variational method for QED which enables the derivati... more We present a formulation of the Hamiltonian variational method for QED which enables the derivation of relativistic few-fermion wave equation that can account, at least in principle, for interactions to any order of the coupling constant. We derive a relativistic two-fermion wave equation using this approach. The interaction kernel of the equation is shown to be the generalized invariant M matrix including all orders of Feynman diagrams. The result is obtained rigorously from the underlying QFT for arbitrary mass ratio of the two fermions. Our approach is based on three key points: a reformulation of QED, the variational method, and adiabatic hypothesis. As an application we calculate the one-loop contribution of radiative corrections to the two-fermion binding energy for singlet states with arbitrary principal quantum number n, and ℓ = J = 0 . Our calculations are carried out in the explicitly covariant Feynman gauge. (tr)Jms Jm J f J (p)Y ms 1 s 2 J