New Energy Definition for Higher Curvature Gravities

We propose a novel but natural definition of conserved quantities for gravity models quadratic and higher in curvature. Based on the spatial asymptotics of curvature rather than of metric, it avoids the GR energy machinery's more egregious problems--such as zero energy "theorems" and failure in flat backgrounds -- in this fourth-derivative realm. In D>4, the present expression indeed correctly discriminates between second derivative Gauss-Bonnet and generic, fourth derivative, actions.Comment: 3 pages, Typos fixe

The Dynamics of General Relativity

This article--summarizing the authors' then novel formulation of General Relativity--appeared as Chapter 7 of an often cited compendium edited by L. Witten in 1962, which is now long out of print. Intentionally unretouched, this posting is intended to provide contemporary accessibility to the flavor of the original ideas. Some typographical corrections have been made: footnote and page numbering have changed--but not section nor equation numbering etc. The authors' current institutional affiliations are encoded in: [email protected], [email protected], [email protected] .Comment: 30 pages (LaTeX2e), uses amsfonts, no figure

Quantum Theory of Gravitation: General Formulation and Linearized Theory

The problem of quantizing general relativity using the Schwinger action principle is considered. The advantages of this technique are discussed and the general formulation of the action principle using the Palatini Lagrangian is given. The difficulty in quantizing general relativity is due to the constraint equations. Two types of constraints are distinguished: algebraic constraint equations and differential constraint equations. The former may be dealt with trivially in this formalism. The latter arise due to the presence of function-type ("gauge") group invariances. In order to eliminate these variables one must make use of the group transformations themselves. Thus in general relativity the transformation from the full set of variables to the independent canonical ones is a coordinate transformation. The linearized theory is treated in detail from this viewpoint and the full theory is briefly discussed

The Spin‐Statistics Theorem

A derivation of the connection between spin and statistics is obtained for spin 0, ½, and 1 fields with arbitrary local interactions. The basis used is the Schwinger action principle, whose assumptions are specified; they include neither positive energy spectrum nor TCP invariance. The connection can be obtained without either of these two extra requirements in most cases. The remaining cases are characterized by non‐TCP invariant free Lagrangians and nonpositive definite free‐particle energies. Commutation relations among different fields are also briefly discussed by means of the action principle

Renormalization of Derivative Coupling Theories

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

Note on Uniqueness of Canonical Commutation Relations

It has been pointed out by Wigner that the consistency requirement between the Lagrange and Heisenberg equations of motion does not uniquely determine the canonical commutation relations, at least for one‐dimensional systems. It is shown here that this ambiguity does not arise in local field theory whose basic equal‐time commutators commute with the translation operator

Spontaneous Symmetry Breakdown and the μ−e−γ Interaction

Spontaneous breakdowns of symmetries have been examined for a system of two charged fields of zero bare mass (the "muon" and "electron" fields) interacting minimally with the electromagnetic field. Upon arranging the two fields into an "isotopic" doublet, the Lagrangian is seen to posses SU(2)symmetry. Three possibilities are available: (a) no spontaneous breakdown of the SU(2) symmetry is allowed and the muon-electron system remains a degenerate doublet; (b) a partial breakdown occurs in which a mass splitting develops but the heavier muon remains stable; (c) a complete breakdown occurs in which the muon decays into an electron plus a photon. Using the high-energy scheme of Baker, Johnson, and Willey, approximate solutions for the one-fermion Green's function and vertex function are examined. (The approximation scheme has the advantage that no ad hoc cutoffs need be invoked.) The solutions obtained permit case (b) to occur but not case (c), provided improper Lorentz invariance is imposed. It is shown, at least for the one-fermion Green's function, that no solutions breaking P, C, or T invariance can arise

Quantum Contributions to Cosmological Correlations II: Can These Corrections Become Large?

This is a sequel to a previous detailed study of quantum corrections to cosmological correlations. It was found there that except in special cases these corrections depend on the whole history of inflation, not just on the behavior of fields at horizon exit. It is shown here that at least in perturbation theory these corrections can nevertheless not be proportional to positive powers of the Robertson--Walker scale factor, but only at most to powers of its logarithm, and are therefore never large.Comment: 10 pages. Some explanations and references added. Paper now accepted for publication in Physical Revie