Nonperturbative Green's function approach to quantum field theory and arbitrariness of solutions

Green's function equations are considered for interacting spinor and (pseudo) scalar fields with interactions . These equations do not determine higher many-point functions if two-point functions are given as “input.” If vertex parts are given as input, two-point functions are determined but higher many-point functions are not determined.     

Comparison of retina damage thresholds simulating the femtosecond-laser in situ keratomileusis (fs-LASIK) process with two laser systems in the CW- and fs-regime

The femtosecond-laser in situ keratomileusis procedure affords the opportunity to correct ametropia by cutting transparent corneal tissue with ultra-short laser pulses. Thereby the tissue cut is generated by a laser-induced optical breakdown in the cornea with ultra-short laser pulses in the near-infrared range. Compared to standard procedures such as photorefractive keratectomy and laser in-situ keratomileusis with the excimer laser, where the risk potential for the eye is low due to the complete absorption of ultraviolet irradiation from corneal tissue, only a certain amount of the pulse energy is deposited in the cornea during the fs-LASIK process. The remaining energy propagates through the eye and interacts with the retina and the strong absorbing tissue layers behind. The objective of the presented study was to determine and compare the retina damage thresholds during the fs-LASIK process simulated with two various laser systems in the CW- and fs-regime.     

Green's function approach to quantum field theory in locally convex space and question of uniqueness

If the set of many point functions ((G ₂ -G ⁰,G ₄, ...,G _N )) satisfies the set of equations arising in the ø⁴ model of quantum field theory, then for a givenG _N the set ((G ₂ -G ⁰,G ₄, ...,G _N-2)), is unique in the domain $$V = \{ ((G_2 - G^0 ,G_4 , \ldots ,G_{N - 2} )) \vdots \left| {((G_2 } \right. - G^0 ,G_4 , \ldots ,G_{N - 2}^{irred} ))\left| {_\iota } \right.< f_l g^{ - {1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \forall \iota \in \Im \}$$ in a locally convex space equipped with a directed family of semi-norms, wheref _l are positive numbers that depend on details ofG _N , andg?1 is the effective coupling constant.     

Propagation of femtosecond surface plasmon polariton pulses on the surface of a nanostructured metallic film: space-time complex amplitude characterization

Ultrashort surface plasmon polariton (SPP) pulses, propagating on the surface of a nanostructured metallic film, are characterized in space and time using time-resolved spatial-heterodyne imaging. Optical pulses are coupled from free space into various surface modes using a 2D array of circular nanoholes, and spatial amplitude and phase characteristics of the scattered surface field are measured with femtosecond-scale time resolution. Demonstrated in-plane focusing of SPP pulse provides additional electromagnetic field localization with possible applications in SPP nanophotonics, nonlinear surface dynamics, biochemical sensing, and ultrafast surface studies.     

Descending problem in Green's function approach to quantum field theory

The question how to determine lower many-point functions in terms of higher ones, which we call the descending problem, is discussed for the (ø⁴)₁₊₃ model of quantum field theory. Equations to be considered are non-linear non-compact operator equations in complex Banach spaces.Several sufficient sets of conditions for convergence of successive approximation schemes are presented for small values of the renormalised coupling constant. Local uniqueness of solution is proved under certain conditions.     

Existence and local uniqueness of solutions of the Percus-Yevick equation

By means of nonlinear operator theory, the existence and local uniqueness of solutions of the Percus-Yevick equation are established under certain conditions.     

Green's functions in broken discrete symmetry

Scalar fields with interaction

Mass generation by self-interaction in non-minkowskian spacetimes

The one-loop contribution to the self-energy of a massless scalar particle with a λφ⁴ self-interaction is investigated in non-minkowskian spacetimes. It is found that the particle may acquire a mass in order λ in perturbation theory.     

High-resolution surface plasmon resonance sensor based on linewidth-optimized nanohole array transmittance

A high spectral resolution, 2D nanohole-array-based surface plasmon resonance sensor that operates at normal or near normal incidence--facilitating high spatial resolution imaging--is presented. The angular and spectral transmittance of the structure is modified from a Fano type to a pure Lorentzian line shape with a parallel and orthogonal polarizer-analyzer pair. This change leads to a linewidth narrowing that maximizes the sensor resolution, which we show to be of O(10(-5)) refractive index units (RIU). We estimate the potential of this system of O(10(-6)) RIU under optimal conditions.