Outgoing Field Research Articles

Physical symmetries in a theory of several scalar real fields

Let us consider a theory ofn scalar, real, local, Poincare covariant quantum fields forming an irreducible set and giving rise to one particle states belonging to the same mass different from zero. The vacuum is unique. It is shown under fairly weak assumptions that every Poincare and TCP invariant symmetry of the theory, implemented unitarily, which mapps localized elements of the field algebra into operators almost local with respect to the former (such a symmetry we call a physical one) can be defined uniquely in terms of the incoming or outgoing fields and ann-dimensional (real) orthogonal matrix. The symmetry commutes with the scattering matrix. Incidentally we show also that the symmetry groups are compact. A special case of these symmetries are the internal symmetries and symmetries induced by locally conserved currents local with respect to the basic fields and transforming under the same representation of the Poincare group. We may make linear combinations out the original fields resulting in complex fields and its complex conjugate in a suitable way. The inspection of the representations of the groupsSO(n) and their subgroups sheds some light on the s.c. generalized Carruthers Theorem concerning the self- and pair-conjugate multiplets.

The thermal radiation field emitted by anistropically scattering cloudy planetary atmospheres

The Mie theory is used to compute particle albedos ω 0 , phase functions p(cos θ), and extinction cross sections χ E for a variety of particle-size distribution functions and complex indexes of refraction n ̃ = n ⇔k . It is found that ω 0 and χ E are quite dependent on n ̃ , but that the shape of p(cos θ) is not. It is concluded that because of the way in which these parameters enter the equation of radiative transfer, it is impossible to deduce uniquely the complex index of refraction of cloud materials by observing cloudy atmospheres over a single wavelength interval in the thermal infrared. Next, two methods-the method of discrete ordinates and an exact method— are used to investigate the outgoing thermal radiation field at the top of cloudy atmospheres as a function of the scattering and thermal properties of the atmosphere. Both isothermal and uniformly mixed convective atmospheres are considered in some detail. For limb-darkening observations over a single wavelength interval it is concluded that (1) the optical thickness τ1 can be fairly well determined except for the special set of cases {1.5≲ τ1⪡∞; ω 0>0.4} ; (2) the particle albedo ω 0 can be determined only for the cases 1.5≲ τ1≲4, and only if ω 0≲0.4 ; and (3) no information is available regarding either the particle sizes or the shape of p(cos θ) under any circumstances. On the other hand it is found that the outgoing flux at the top of the atmosphere is sensitive to almost all the relevant single-scattering parameters, implying that observations of the limb function at several independent wavelengths would be extremely useful. In particular it may be possible to obtain some information about the wavelength variation of n ̃ , especially if 1.5≲ τ1≲4and ω 0≲0.4 over most of the spectral range of interest. This is turn would be of extreme importance in connection with the chemical identification of the relevant particulate medium.

A criterion for the free character of fields II

Abstract The clothed particle formalism is shown to be of no practical use as it leads either to an incomplete current or to a non-local field theory which violates not only the locality condition but also the Yang-Feldman equation. A short proof is given of the statement that neither the current nor the Heisenberg field can be expressed as a polynomial (in a generalized sense) in the incoming (or outgoing) fields. This statement is based on the assertion of O.W. Greenberg that the outgoing field cannot be expressed as a polynomial with respect to the incoming fields unless both fields coincide.

Covariant formalism of a field with indefinite metric

The structure of a relativistic field which contains "ghost" (zero norm) states is investigated. Restrictions are made for the case of free fields, which can be thought of as asymptotic parts of a more complicated theory. According to the interpretation the in- or out-going fields may be eliminated from the physical results. If explicit calculations are to be made in any more concrete theory, it is easier to handle dipole ghosts than exponential ghosts. (B.O.G.)