On the concept of virtual states

The technique of the decomposed Feynman propagator is used to establish the equivalence between the Feynman and field theoretic formalisms. It is shown that for an nth order process, each of the 2n−1 decomposed Feynman diagrams is equivalent to a certain group in the n! field theoretic diagrams. This is demonstrated for the fourth order Compton scattering of an electron by identifying the energy denominators in the two formalisms

On the decomposition of the Feynman propagator

The Feynman propagator, in momentum representation, is a four-dimensional transform over space and time variables. If the space and time integrations are performed separately, the propagator can be decomposed into two parts, one corresponding to positive and the other to negative energy intermediate state. By the use of this decomposed propagator, the relative contributions of the positive and negative energy intermediate states to the matrix element can be estimated. For example in Compton scattering it leads to the apparently paradoxical result that in the "non-relativistic approximation" it is only the negative energy intermediate state that contributes to the matrix element

Preparation and characterization of whey protein isolate films reinforced with porous silica coated titania nanoparticles

Whey protein isolate (WPI) films embedded with TiO2@@SiO2 (porous silica (SiO2) coated titania (TiO2)) nanoparticles for improved mechanical properties were prepared by solution casting. A WPI solution of 1.5 wt% TiO2@@SiO2 nanoparticles was subjected to sonication at amplitudes of 0, 16, 80 and 160 μm prior to casting in order to improve the film forming properties of protein and to obtain a uniform distribution of nanoparticles in the WPI films. The physical and mechanical properties of the films were determined by dynamic mechanical analysis (DMA), thermogravimetric analysis (TGA), and tensile testing. Water vapor permeability (WVP) measurements revealed that the water vapor transmission rates are slightly influenced by sonication conditions and nanoparticle loading. The DMA results showed that, at high sonication levels, addition of nanoparticles prevented protein agglomeration. The thermal stability of the materials revealed the presence of 3–4 degradation stages in oxidizing the protein films. The addition of nanoparticles strengthens the WPI film, as evidenced by tensile stress analysis. Sonication improved nanoparticle distribution in film matrix; such films can potentially become effective packaging materials to enhance food quality and safety

Tailoring the toughness and CTE of high temperature bisphenol E cyanate ester (BECy) resin

The objective of the present work is to enhancing the toughness and minimizing the CTE of a special class of bisphenol E cyanate ester (BECy) resin by blending it with a thermoplastic toughening agent. Poly(ether sulfone) was chosen as a high temperature resistant thermoplastic resin to enhance the thermo-mechanical properties of BECy. The influence of poly(ether sulfone)/BECy blend composition on the morphology and phase behavior was studied using scanning electron microscopy and dynamic mechanical analysis. The mechanical properties of the blends were evaluated by flexural tests, which demonstrated significant enhancement in the material’s toughness with an increase in PES concentration from 0 to 15 wt%. The coefficient of thermal expansion of pure BECy was reduced from 61 to 48 ppm/°C in the blends with PES, emphasizing the multi-functional benefits of PES as a toughening agent in BECy

The physical basis of quantum field theory

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