Search

All one-loop divergences of the quantized Einstein-Maxwell system are calculated, using dimensional regularization and the background-field method. The resulting counterterms, including photon and graviton ghost contributions, are quadratic in curvatures when evaluated on the mass shell, and cannot be renormalized away by rescaling. Brans-Dicke theory is also nonrenormalizable; source-free Einstein theory with cosmological term is (formally) renormalizable, as are Weyl models.

The one-loop ultraviolet divergences of the quantized coupled Einstein-Yang-Mills fields are evaluated. They are precisely of the same nonrenormalizable form as for a corresponding set of free Maxwell fields together with the usual flat-space Yang-Mills divergences. The two free Yang-Mills field parameters, namely the group dimension and the self-coupling constant, cannot be chosen to make the one-loop divergences renormalizable in the usual sense.

An explicit calculation shows perturbation theory to be arbitrarily good for the deep Euclidean Green's functions of any Yang-Mills theory and of many Yang-Mills theories with fermions. Under the hypothesis that spontaneous symmetry breakdown is of dynamical origin, these symmetric Green's functions are the asymptotic forms of the physically significant spontaneously broken solution, whose coupling could be strong.

The method of functional integrals is applied to the problem of meson theories with derivative couplings. In the static limit, solutions in closed form can be exhibited. The infinities occurring in the theory are found to be removable in terms of Z_2 and mass renormalizations, contrary to the conclusions of perturbation analysis. The divergences occurring here have the form of essential singularities, in contradistinction to the branch-point behavior of the usual "renormalizable" theories. The lack of validity of the perturbation expansion is thereby accounted for. These techniques can be extended to treat the full recoil neutral ps(pv) problem omitting closed loops. The theory is represented in terms of an exponential coupling which permits a nonperturbation series solution for the various propagators. Two infinite renormalizations are again required. The resultant functions are given meaning by analytic continuation procedures which are adapted to the four-dimensional nature of the problem. The form of the effective coupling suggests a rearrangement of the answer in terms of exponentials of the meson propagator. As a result mass operator-like structures can be defined. These explicitly exhibit the transcendental nature of the coupling and generalized equivalence theorems with ps(ps) theory can be generated. In a similar fashion, effective interaction operators for the two-nucleon and meson-nucleon Green's functions are derived. The possible applicability of these quantities to questions of physical interest such as nuclear potentials and multiple meson production is briefly mentioned. In an appendix, a model of beta coupling is discussed in connection with the renormalization question there.

The joint implications of Bjorken and Regge asymptotics are discussed for the structure function of electroproduction. It is suggested that for q^2 → ∞, the function νW2 approaches a constant for large values of p ≡ mν/q^2.

As the result of a study to determine a Reggepole formula with Mandelstam analyticity for the elastic scattering of two unequal-mass particles, we were led to raise the following question: What are the constraints, if any, that follow from assuming that scattering amplitudes satisfy both the Mandelstam representation and the condition of meromorphism in the right-half angular momentum plane? To put it another way, are Mandelstam and l-plane analyticity necessarily consistent in every case? We find that if there is to be consistency, one can conclude directly that the high-energy limit of the Regge-pole position, α(∞), is necessarily negative.

From the physical three-vector Maxwell equations for an electromagnetic (E.M.) field in static gravitation, we examine the artifice of replacing the gravitation by an equivalent medium and we find modified Debye potentials for an E.M. wave in a simple, angularly homogeneous, material medium in a Schwarzs-child gravitational field. The fact that these potentials do not obey the generalized scalar wave equation implies that gravitation scatters the vector E.M. wave and a scalar wave differently. Also, we obtain and solve by perturbation the amplitude and eikonal equations for a high-frequency wave in a weak spherical gravitational field. To the order $\frac{M}{r}$, the state of transverse polarization does not change along a ray path whereas the transverse-field amplitudes are modified by the factor ${e}^{\frac{M}{r}}$ which strengthens the field near the mass. The longitudinal-field amplitude, on the other hand, is modified by ${e}^{\frac{\ensuremath{-}M}{r}}$. These effects, in principle, may provide a further test of classical E.M. theory and general relativity.

Electromagnetic mass shifts, equal-time commutators (ETC), and their relation are analyzed, using the Jost-Lehmann representation for the forward Compton amplitude. The divergences in δ m are determined by Lorentz scalars associated with the ETC (when these exist). These results are illustrated by models with currents bilinear and linear in canonical fields. Existence of the ETC implies that the Jost-Lehmann representation is unsubtracted.

The Hamiltonian form of the relativistic wave equation for bosons of spin 0 or 1 was first given by Kemmer. The problems associated with the redundant components of the wave function were later resolved by Heitler, who eliminated the redundant components by means of projection operators. We present an alternative treatment which yields essentially the same results as obtained by Heitler, but which retains all components of the wave function. Approved for public release; distribution is unlimited.

Some properties are discussed of the ${\ensuremath{\theta}}^{0}$, a heavy boson that is known to decay by the process ${\ensuremath{\theta}}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}+{\ensuremath{\pi}}^{\ensuremath{-}}$. According to certain schemes proposed for the interpretation of hyperons and $K$ particles, the ${\ensuremath{\theta}}^{0}$ possesses an antiparticle ${\overline{\ensuremath{\theta}}}^{0}$ distinct from itself. Some theoretical implications of this situation are discussed with special reference to charge conjugation invariance. The application of such invariance in familiar instances is surveyed in Sec. I. It is then shown in Sec. II that, within the framework of the tentative schemes under consideration, the ${\ensuremath{\theta}}^{0}$ must be considered as a "particle mixture" exhibiting two distinct lifetimes, that each lifetime is associated with a different set of decay modes, and that no more than half of all ${\ensuremath{\theta}}^{0}'\mathrm{s}$ undergo the familiar decay into two pions. Some experimental consequences of this picture are mentioned.

A Regge-pole formula is derived for the elastic scattering of two unequal-mass particles that combines desirable l-plane analytic properties (i.e., a simple pole at l=α in the right-half l plane) and Mandelstam analyticity. It is verified that such a formula possesses the standard asymptotic Regge behavior u^(α(s)) even in regions where the cosine of the scattering angle of the relevant crossed reaction may be bounded. The simultaneous requirements of I-plane and Mandelstam analyticity enforce important constraints, and the consistency of these constraints is studied. These considerations lead to the appearance of a "background" term proportional asymptotically to u^(α(0)-1) which has no analog in the equal-mass problem. We also conclude that a necessary condition for consistency is α(∞)

No acceptable tensor gravitational theory with arbitrarily long but finite range exists. In linear approximation, the infinite-range limit is a scalar-tensor mixture implying an effective matter-matter coupling different from the strictly infinite-range prediction and contradicted by experiment. Compensation of the scalar requires the admixture of a ghost scalar coupling. In the massive version of the full Einstein theory, (a) there are necessarily six rather than the five tensor degrees of freedom, (b) the energy has no lower bound, (c) the infinite-range limit seems not to exist at all, and (d) lowest-order forces are the same as in the massive linearized theory.

Two generalizations of Sugawara models are discussed. In the first, new interactions are introduced by altering the current commutators but retaining the "free" form of T_(μν), as exemplified by a simple effective π^0 − 2γ interaction, which is compared with the standard triangle-diagram results. The second permits non-quadratic T_(μν), which retain the "algebra" part of the current commutators; these models avoid the Dashen-Frishman parity degeneracy.

In the dual resonance model, introducing a generalized gauge-transformation operator which leaves the vertex functions invariant, we present a general treatment of linear dependences among the vertex functions. We also prove that the two propagators recently discussed in connection with the twisting operator are equal up to our gauge transformation.