Radiation vector

Both A(3> and B(3> are longitudinally directed and are nonzero in the vacuum. Both A(3> and B(3> are phaseless, but propagate with the radiation [47-62] and with their (1) and (2) counterparts. The radiated vector potential A<3 does not give rise to a photon on the low-energy scale, because it has no phase with which to construct annihilation and creation operators. On the high-energy scale, there is a superheavy photon [44] present from electroweak theory with an SU(2)x SU(2) symmetry. The existence of such a superheavy photon has been inferred empirically [44], However, the radiated vector potential A<3) is not zero in 0(3) electrodynamics from first principles, which, as shown in this section, are supported empirically with precision. 

Optical activity is one of the best known, but least understood, phenomena of organic chemistry. It is observed as the ability of certain substances to interact with linearly polarized light by rotating the plane of polarization. Linear polarization means that the electromagnetic radiation vectors oscillate in fixed orthogonal planes that intersect along the propagation vector. 

Some specific studies on the measurement of heat losses and indoor temperatures in buildings deserve attention. In his review of the relative importance of thermal comfort in buildings, McIntyre considered that the mean radiant temperature was the most important parameter, followed closely by the "radiation vector," which is defined as the net radiant flux density vector at a given point and measures the asymmetry of the thermal radiation field in a room (97). Benzinger et al. characterized the mean radiant temperature, and asymmetric radiation fields, using a scanning plane radiometer, which maps the plane radiant temperature in a given space indoors (98). 

In addition, the high-order perturbation is ignored in the electromagnetic-radiation vector. Considering these perturbations, the dipole... 

The radiation pattern is defined as a mathematical function or a graphical representation of the far field (ie, for r 2D IX, with D being the largest dimension of the antenna) radiation properties of the antenna, as a function of the direction of departure of the electromagnetic (EM) wave. A radiation pattern can represent several quantities, such as gain, directivity, electric field, or radiation vector. Consequently, the terms gain pattern, electric field pattern, or radiation vector pattern are used, respectively. 

Everywhere outside the (smallest) sphere circumscribing the particle it is appropriate to expand the scattered field in terms of radiating vector spherical... 

The surface fields ei i and hi i are the tangential components of the electric and magnetic fields in the domain bounded by the closed surfaces Sx and 52. Taking into account the completeness property of the system of regular and radiating vector spherical wave functions on two enclosing surfaces... 

To compute the T matrix of the two-particles system and to derive a scattered-field expansion centered at the origin O of the global coordinate system we use the Stratton-Chu representation theorem for the scattered field Eg in Dg. In the exterior of a sphere enclosing the particles, the expansion of the approximate scattered field in terms of radiating vector spherical wave functions reads as... 

To derive the expression of the reflection matrix we use the integral representations for the radiating vector spherical wave functions... 

Returning to the scattering problem of a particle near an arbitrary infinite surface, we see that our analysis is complete if, according to Step 1, we are able to represent the plane electromagnetic wave and the radiating vector spherical wave functions and as integrals over vector plane waves. 

The superscript T stands for the regular vector spherical wave functions while the superscript 3 stands for the radiating vector spherical wave functions. It is useful to note that for n = m = 0, we have mI q = = 0. Mi, ,... 

Passing to the radiating vector spherical wave functions we consider the integral representation (B.28) and the relation r = ro + ri. For ri > ro, this representation can written as... 

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