Vector, axial propagation

Global velocity distribution behind flame front. Upward propagation in 5.15% methane/air mixture, (a) vector map, (b) and (c) scalar maps of axial and radial velocity components, respectively. Spots are caused by condensation of water vapor on the glass walls. 

The handedness, or chirality, inherent in foundational electrodynamics at the U(l) level manifests itself clearly in the Beltrami form (903). The chiral nature of the field is inherent in left- and right-handed circular polarization, and the distinction between axial and polar vector is lost. This result is seen in Eq. (901), where , is a tensor form that contains axial and polar components of the potential. This is precisely analogous with the fact that the field tensor F, contains polar (electric) and axial (magnetic) components intermixed. Therefore, in propagating electromagnetic radiation, there is no distinction between polar and axial. In the received view, however, it is almost always asserted that E and A are polar vectors and that is an axial vector. 

In atoms, as noted already, it is adequate to replace the propagator for the massive bosons by a contact function, and the weak interaction reduces to a current-current interaction form. The electron current has vector and axial vector forms and where is the... 

Fig. 7.4 A-C. A model of control of morphogenesis by vectors of auxin wave propagation in the final phase (autolysis) of axial tracheid maturation in secondary xylem of the stem. A Trajectories of vectors of auxin wave propagation (a) in the cambial region and in differentiating secondary tissues as seen in radial (b) and transverse (c) sections. The breakdown of the cytoplasm is initiated when some critical angle (a) between the vector of auxin wave propagation and the cell axis is attained. B and C Vector trajectories associated with a model of regulation of earlywood and latewood differentiation. Ph conducting phloem Ph dividing phloem Cj cambial initial dividing xylem ...

It may seem odd that a spin 1 particle like the W can transform directly into a spin 0 tt in Fig. 14.6(c). The reason for this is rather subtle (Leader, 1968). In a Feynman diagram the propagator of a vector meson off mass shell is really a mixture of spin 1 and spin 0 pieces. Only on mass shell does it reduce to pure spin 1. However, if the vector meson couples to a conserved current (as does the photon) the spin 0 part gives no contribution. The axial part of the current to which the W couples is, of course, not conserved, which explains its ability to transform into the pseudo-scalar ir. On the other hand, according to CVC (see Section 1.2), the W couples to a conserved vector current and thus it cannot transmute into a spin 0 scalar particle. 

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