David G. Boulware

Classical general relativity derived from quantum gravity

Abstract The existence of long range macroscopic attractive forces between masses implies the existence of a mediating helicity ± 2 particle in special relativistic quantum particle theory. It is shown that this fact alone, without assuming the existence of an underlying tensor field, uniquely determines the long wavelength structure of quantum gravitation to be that of Einsteins theory. This equivalence is shown by deriving, from the Ward identities associated with the graviton propagator, the tree graph structure of the graviton-graviton and graviton-matter interaction and establishing that the classical Einstein action is the generating functional. Some properties of closed loop effects are also exhibited.

Radiation From a Uniformly Accelerated Charge

Abstract The electromagnetic field associated with a uniformly accelerated charge is studied in some detail. The equivalence principle paradox that the co-accelerating observer measures no radiation while a freely falling observer measures the standard radiation of an accelerated charge is resolved by noting that all the radiation goes into the region of space time in-accessible to the co-accelerating observer.

Renormalizeability of massive non-abelian gauge fields - a functional integral approach

Abstract The renormalizeability of massive non-Abelian vector gauge fields is discussed using a functional integral technique. The ideas are first developed for the case of a neutral vector meson coupled to a conserved current, where the renormalizeability holds. The non-Abelian vector field is written as the gauge transform of a four-dimensionally transverse field, and the transverse and gauge variables are then treated separately. It is shown that the renormalizeability depends solely on that of the gauge variables, which are found to be non-renormalizeable; hence, neither is the field theory. The gauge variables alone provide a representation of the σ-model and of Sugawaras theory of currents, which are thus shown to be non renormalizeable theories.

Symmetric space scalar field theory

Some quantum field theories, such as the chiral SU(2) ⊗ SU(2) theory, can have a dynamics invariant under a group G that is realized on a vacuum which is invariant only under a subgroup H of G. These theories may be defined by scalar fields which are coordinates for the coset manifold G/H. They are thus non-polynomial theories on a symmetric space, with the group motions in this space described by a set of Killing vectors. We show how the Lagrange function may be constructed entirely from the Killing vectors. In particular, all physical quantities may be expressed in terms of the currents formed out of the Killing vectors. The current correlation functions do not exhibit the spurious wave function renormalizations which are encountered if ordinary Greens functions are computed. We illustrate the general method by calculating one-loop counter terms in a completely invariant fashion. An Appendix describes in simple terms the general theory of symmetric spaces, which should prove useful in other contexts.

Inconsistency of finite range gravitation

Abstract Gravitational theories with arbitrarily large but finite range either violate basic physical requirements, do not limit to general relativity or both.

LEE-WICK INDEFINITE METRIC QUANTIZATION: A FUNCTIONAL INTEGRAL APPROACH

Abstract In an attempt to study the stability of the Lee-Wick indefinite metric theory, the functional integral for indefinite metric quantum field theories is derived. Theories with an indefinite classical energy may be quantized with either a normal metric and an indefinite energy in Minkowski space or an indefinite metric and a positive energy in euclidean space. However, the functional integral in the latter formulation does not incorporate the Lee-Wick prescription for assuring the unitarity of the positive energy positive metric sector of the theory, hence the stability of the theory cannot be studied non-perturbatively.

Energy and supercharge in higher derivative gravity

Explicit energy expressions are derived, by supergravity embedding, for quadratic curvature actions with or without Einstein terms. Applications include existence of stability domains in R+R^2 models, vanishing of supercharge in conformal supergravity and indefiniteness of the energy in the generic case. The contradiction between the indefiniteness of the energy and its seemingly positive supersymmetric H=ΣQ_α^2 form is traced to the necessarily indefinite Hilbert space of the fermionic sector, which implies H is really a difference of squares.

Quantum field theory in spaces with closed timelike curves

Gott spacetime has closed timelike curves, but no locally anomalous stress energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 2{pi}. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the noncausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the noncausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.

FIELD QUANTIZATION IN THE SCHWARZSCHILD METRIC

Since radiation from a gravitationally collapsed star is thermal and independent of the collapse process, the possibility that the radiation is characteristic of the Schwarzschild metric itself is considered. The scalar field in the maximal analytic extension of the Schwarzschild metric is quantized in order to test this hypothesis. It is found that the radiation is not characteristic of the Schwarzschild metric. (BJG)

CLASSICAL SCHWINGER TERMS.

Schwinger terms must be present in equal time ground state Poisson brackets among currents unless the latter are stationary in that state.