Spinning particles in scalar-tensor gravity.pdf

a r X i v : 0 7 1 1 .2 5 7 3 v 2 [ g r - q c ] 2 0 N o v 2 0 0 7 Spinning particles in scalar-tensor gravity D.A. Burton?, R.W. Tucker? C.H. Wang? February 2, 2008 Abstract We develop a new model of a spinning particle in Brans-Dicke space- time using a metric-compatible connection with torsion. The particle’s spin vector is shown to be Fermi-parallel (by the Levi-Civita connection) along its worldline (an autoparallel of the metric-compatible connection) when neglecting spin-curvature coupling. 1 Introduction Scalar fields are replete in string-inspired low-energy effective theories and oc- cupy a prominent position in modern particle physics and cosmology. The most widely accepted implementations of mass generation and inflation employ scalar fields and it is not unreasonable to suggest that they should play a role on large scales. Indeed, a number of authors have suggested that Einsteinian gravity (General Relativity), a purely metric-based theory, is incomplete and should be augmented by a scalar component; one of the simplest examples of such a theory was proposed by Brans and Dicke [1]. Their theory was originally formulated as an action principle whose degrees of freedom are the spacetime metric and the Brans-Dicke scalar field ?. It was later shown [2] that Brans-Dicke the- ory could also be obtained from an action whose independent variables are a metric-compatible connection ?, an orthonormal frame field and ?. Unlike the Levi-Civita connection ?? of Einsteinian gravity, whose torsion vanishes identi- cally, the field equations for ? yield a non-trivial torsion tensor in terms of ?. Although the action principle in [2] differs from that introduced by Brans and Dicke, the standard Brans-Dicke equations of motion are recovered when ? is expressed in terms of ?? and ?. In Einsteinian and Brans-Dicke gravity, electrically neutral spinless particles are postulated to follows autoparallels of ?? (geodesics). However, the most natural connection in Brans