Motion of small bodies in classical field theory
- Enrico Fermi Institute and Department of Physics University of Chicago 5640 S. Ellis Avenue, Chicago, Illinois 60637 (United States)
I show how prior work with R. Wald on geodesic motion in general relativity can be generalized to classical field theories of a metric and other tensor fields on four-dimensional spacetime that (1) are second-order and (2) follow from a diffeomorphism-covariant Lagrangian. The approach is to consider a one-parameter-family of solutions to the field equations satisfying certain assumptions designed to reflect the existence of a body whose size, mass, and various charges are simultaneously scaled to zero. (That such solutions exist places a further restriction on the class of theories to which our results apply.) Assumptions are made only on the spacetime region outside of the body, so that the results apply independent of the body's composition (and, e.g., black holes are allowed). The worldline 'left behind' by the shrinking, disappearing body is interpreted as its lowest-order motion. An equation for this worldline follows from the 'Bianchi identity' for the theory, without use of any properties of the field equations beyond their being second-order. The form of the force law for a theory therefore depends only on the ranks of its various tensor fields; the detailed properties of the field equations are relevant only for determining the charges for a particular body (which are the ''monopoles'' of its exterior fields in a suitable limiting sense). I explicitly derive the force law (and mass-evolution law) in the case of scalar and vector fields, and give the recipe in the higher-rank case. Note that the vector force law is quite complicated, simplifying to the Lorentz force law only in the presence of the Maxwell gauge symmetry. Example applications of the results are the motion of 'chameleon' bodies beyond the Newtonian limit, and the motion of bodies in (classical) non-Abelian gauge theory. I also make some comments on the role that scaling plays in the appearance of universality in the motion of bodies.
- OSTI ID:
- 21409626
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 81, Issue 8; Other Information: DOI: 10.1103/PhysRevD.81.084060; (c) 2010 The American Physical Society; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
BLACK HOLES
FIELD EQUATIONS
FIELD THEORIES
FOUR-DIMENSIONAL CALCULATIONS
GAUGE INVARIANCE
GENERAL RELATIVITY THEORY
LAGRANGIAN FUNCTION
LORENTZ FORCE
MASS
MATHEMATICAL SOLUTIONS
METRICS
MONOPOLES
PARTICLES
SPACE-TIME
TENSOR FIELDS
VECTOR FIELDS
EQUATIONS
FUNCTIONS
INVARIANCE PRINCIPLES
RELATIVITY THEORY