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Generalization of the Stueckelberg formalism to the massive Yang-Mills field (an example of non-Abelian gauge field) is performed in a way analogous to the Abelian gauge vector field. The compensating scalar fields in our case do not satisfy simple Klein-Gordon equations in contrast to the Abelian case where we introduce a scalar field with a certain mass value. It is also shown that the redundant fields can be eliminated by a suitable unitary transformation and therefore give no physical importance. §I. Introducti.on It has been a long cherished desire to interprete massive vector mesons as the quanta of gauge field just as photon is.l) For the Abelian gauge field, it has been shown by employing the generalized Stueckelberg formalism that we can introduce massive vector gauge fielcls.~1 The putpose of this paper is to show that we can also introduce non-zero mass to non-Abelian gauge vector fields.Classically the requirement of gauge mvanance was based upon the indifference of Maxwell's equation for the electromagnetic potential AIL under the following inhomogeneous transformation, for an arbitrary function A of space time.The corresponcLng situation m quantum electrodynamics is given by the invariance of the theory agai~1st the following phase transformation of charge bearing field X, with the same function A. In this familiar situation, one recognizes thac the requirement of gauge invariance has a well founded reason to be imposed. However, it seems customary nowadays to regard gauge invariance as a principle and to assert that the electromagnetic field is introduced in order to satisfy the principle. It is precisely the latter aspect that has led some authors 3 ). 4 ). ) to the

ZnO nanomaterials with controlled size, shape and surface chemistry are required for applications in diverse areas, such as optoelectronics, photocatalysis, biomedicine and so on. Here, we report on ZnO nanostructures with rod-like and spherical shapes prepared via laser ablation in liquid using a laser with millisecond-long pulses. By changing laser parameters (such as pulse width and peak power), the size or aspect ratio of such nanostructures could be tuned. The surface chemistry and defects of the products were also strongly affected by applied laser conditions. The preparation of different structures is explained by the intense heating of liquid media caused by millisecond-long pulses and secondary irradiation of already-formed nanostructures.

Broad-band dielectric measurements for fructose-water mixtures with fructose concentrations between 70.0 and 94.6 wt% were carried out in the frequency range of 2 mHz to 20 GHz in the temperature range of -70 to 45 degrees C. Two relaxation processes, the alpha process at lower frequency and the secondary beta process at higher frequency, were observed. The dielectric relaxation time of the alpha process was 100 s at the glass transition temperature, T(g), determined by differential scanning calorimetry (DSC). The relaxation time and strength of the beta process changed from weaker temperature dependences of below T(g) to a stronger one above T(g). These changes in behaviors of the beta process in fructose-water mixtures upon crossing the T(g) of the mixtures is the same as that found for the secondary process of water in various other aqueous mixtures with hydrogen-bonding molecular liquids, polymers, and nanoporous systems. These results lead to the conclusion that the primary alpha process of fructose-water mixtures results from the cooperative motion of water and fructose molecules, and the secondary beta process is the Johari-Goldstein process of water in the mixture. At temperatures near and above T(g) where both the alpha and the beta processes were observed and their relaxation times, tau(alpha) and tau(beta), were determined in some mixtures, the ratio tau(alpha)/tau(beta) is in accord with that predicted by the coupling model. Fixing tau(alpha) at 100 s, the ratio tau(alpha)/tau(beta) decreases with decreasing concentration of fructose in the mixtures. This trend is also consistent with that expected by the coupling model from the decrease of the intermolecular coupling parameter upon decreasing fructose concentration.

The effect of liquid medium and its pressure on the photoluminescence of ZnO nanoparticles prepared via laser ablation of Zn targets in various water-ethanol mixtures is studied. As the ethanol content increases, the photoluminescence of the product changes, while metallic zinc is observed to emerge in nanomaterials prepared in ethanol-rich environments. The applied pressure had a less profound effect, mainly affecting materials produced in water or water-ethanol, and much less those generated in pressurized ethanol. Tuning the reactivity of the liquid and pressurizing it during laser ablation is demonstrated to be promising for tailoring the emission properties of the product.

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Two methods of the renormalization are proposed for unstable particles. One is connected with the resonance in scattering and the other with the time development of the unstable particle state. The relation between the two formulations is discussed. Arbitrariness in the choice of the renormalization procedure comes from the uncertainty principle of the quantum mechanics.ii) When the coupling constant g is small, our theory has to give the same result as obtained by the perturbation method.iii) After the renorxp.alization proced,ure 1s performed, the theory contains no divergences.vi) Needless to say, the theory must be simple and convenient and physically intuitive.Under such wide restr1ct10ns, theories that we can construct consistently are not unique. We believe that the following two theories are most reasonable and simplest. It is our aim to construct general theories, but for an illustrative purpose, we shall first confine ourselves to the well-known Lee modePJ with a change in the mass relation, i.e., m v > mN+ p. This permits the natural decay of the V particle.One of the most reasonable methods treating the unstable particle V is based on the resonance scattering of fJ and N through the formation of V. As in the resonance theory for the atomic nuclei, we can define the "observed" mass of V by the energy at which the phase shift o becomes rr /2, (the pole of the reaction matrix 2 l K). The lifetime of V can be defined as the reciprocal of the width of the resonance. Above procedure can be performed compactly in terms of the modified propagator S;, (E) of the V particle. And the renormalization of the coupling constant can be performed analogously to the st:~.ble case. ( § 2.)The second method is based on the analytic continuation of the S-matrix 3 l for the N+fJ scatterin.g. S,~(E) has a pole at E=m8 -irs/2 in the lower half plane of the complex variable E. This pole can be shown to coincide with that of the S-matrix, and the " observed " m<'.ss and the width of V can be defined by ms and r 8 • The renormalization con.st<'.n.t of the coupling constant can be defined as the residue of S ~~ (E) at this point. Contrary to the first method, this turns out to be a complex number. This fact may be the major defect of the present procedure. Using the above defined m8 and r.~, it can be shown that the amplitude for the one particle V state obeys the radioactive decay law. ( § 3.) The difference between above two procedures is due to the difference in the choice of the parameters, such as the mass and the coupling constant. Both theories give exactly the same value for the "renormalization invariants", e. g., scattering amplitudes and the phase shifts. They give actually different values to the mass and the life-time of the V particle. This circumstance originates in the difference of the definitions fer those quantities, the measurements of which correspond to different experimental methods. In principle, the mass and the life-time given by one of the two theories can be expressed as the known functions of them...

We have developed a thermally conductive flexible elastomer as a composite material with slide-ring (SR) materials and boron nitride (BN) particles surface-modified via plasma in solution. This composite shows excellent properties as a flexible insulator for thermal management. Surface modification of BN particles using plasma in solution increases the tensile strength, extension ratio at break, toughness, and rubber characteristics of the composites, compared to SR and non-modified BN, while the Young's modulus values are identical. Furthermore, the thermal conductivity also improved as a result of plasma surface modification.