Philip B. Yasskin

Non-self-dual gauge fields☆

Abstract The Ward construction is generalized to non-self-dual gauge fields. Reality and currentless conditions are specified.

On the determination of Cauchy surfaces from intrinsic properties

We consider the problem of determining from intrinsic properties whether or not a given spacelike surface is a Cauchy surface. We present three results relevant to this question. First, we derive necessary and sufficient conditions for a compact surface to be a Cauchy surface in a spacetime which admits one. Second, we show that for a non-compact surface it is impossible to determine whether or not it is a Cauchy surface without imposing some restriction on the entire spacetime. Third, we derive conditions for an asymptotically flat surface to be a Cauchy surface by imposing the global condition that it be imbedded in a weakly asymptotically simple and empty spacetime.

Can a macroscopic gyroscope feel torsion

We demonstrate that for a large class of Lagrangian-based torsion theories a macroscopic gyroscope is insensitive to the torsion field: There can be no coupling of the torsion to the gyroscopes angular momentum of rotation. To detect torsion a polarized system with a net elementary particle spin is needed. These conclusions are evident from the conservation laws, which form the basis for deriving the equations of motion.

The well‐posedness of (N=1) classical supergravity

In this paper we investigate whether classical (N=1) supergravity has a well‐posed locally causal Cauchy problem. We define well‐posedness to mean that any choice of initial data (from an appropriate function space) which satisfies the supergravity constraint equations and a set of gauge conditions can be continuously developed into a space‐time solution of the supergravity field equations around the initial surface. Local causality means that the domains of dependence of the evolution equations coincide with those determined by the light cones. We show that when the fields of classical supergravity are treated as formal objects, the field equations are (under certain gauge conditions) equivalent to a coupled system of quasilinear nondiagonal second‐order partial differential equations which is formally nonstrictly hyperbolic (in the sense of Leray–Ohya). Hence, if the fields were numerical valued, there would be an applicable existence theorem leading to well‐posedness. We shall observe that well‐posedne...

The dynamics of the Einstein-Dirac system. I. A principal bundle formulation of the theory and its canonical analysis

Abstract We begin here a mathematical study of the space of globally hyperbolic solutions of the Einstein-Dirac field equations. Our first step is to develop a principal [ O (3, 1)] bundle formulation of the Einstein-Dirac fields (which include the spacetime metric represented as a frame field, and a Dirac anticommuting spinor). This formulation provides an invariant description of the fields, and it is useful for controlling their gauge freedom (represented as bundle automorphisms) and for studying the symmetries of solutions (described via Lie derivatives on the bundle). Our analysis of the field equations follows the program developed by Fischer, Marsden, and Moncrief in their study of the vacuum Einstein field equations. We perform a (3 + 1) decomposition of the fields, we obtain a canonical Hamiltonian formulation of the field equations, we study field perturbations, and finally we relate solution symmetries to the kernel of the evolution operator. Some of the mathematies of bundle theory needed to understand this paper is discussed in the appendixes.

Non-self-dual nonlinear gravitons

Penrose has given a twistor description of all self-dual complex Riemannian space-times. We modify his construction to characterize all complex Riemannian space-times and all complex teleparallel space-times. This construction may be useful in finding non-self-dual solutions to the gravitational field equations (Einsteins or otherwise) without or with sources. It may also lead to a nonperturbative method for computing path integrals. Whereas Penrose shows that a self-dual space-time may be specified by a deformation of projective twistor space (the set of α planes in complex Minkowski space), we find that a Riemannian or teleparallel space-time may be described by a deformation of projective ambitwistor space (the set of null geodesics in complex Minkowski space).

Two kinds of rotation: An argument for torsion

There are now many theories of gravity with a torsion field as well as the usual metric field. One of the arguments for allowing torsion is based upon a gauge theory analogy. The purpose of this paper is to clarify exactly which symmetries are being gauged in this process. The principal observation is that special relativity is invariant under two different kinds of Lorentz transformations. The first type rotate the fields and move them from one point to another in space-time. The second type merely rotate the fields at each point without changing their location. To gauge both types of rotations requires a torsion field as well as a metric field.