Gravitational anyonization

Journal Article · Thu Aug 15 04:00:00 EDT 1991 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.44.1132· OSTI ID:5184971

Reuter, M ^[1]

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1. Institute of Theoretical Physics, University of Hannover, Appelstrasse 2, D-3000 Hannover 1 (Germany)

The statistics of scalar matter changes when it is coupled to a U(1) gauge field with Chern-Simons dynamics, because all particles carry a magnetic flux and therefore give rise to Aharonov-Bohm phases when they move around each other. We argue that also the dual'' version of the Aharonov-Bohm effect, the Aharonov-Casher effect, can give rise to Berry phases which transmute ordinary particles into anyons. The Aharonov-Casher effect consists of an extra topological phase in the wave function of a magnetic moment moving around an electric charge. Considering (2+1)-dimensional Dirac fermions at low energies, both effects are present, and the fermions are turned into (interacting) anyons even though there is no Chern-Simons term included in the action. We study in detail the gravitational analogue of this mechanism. The post-Newtonian approximation is applied to the gravitational interaction of (2+1)-dimensional particles with spin, and to stringlike matter distributions with internal angular momentum in 3+1 dimensions. The action for gravity is taken to be the pure Einstein-Hilbert term. In the adiabatic limit one finds scrA{center dot}{bold v}-type interactions where scrA is a long-range vortex field. These interactions give rise to various kinds of Berry phases, in particular to the gravitational analogues of the Aharonov-Bohm and the Aharonov-Casher phases. The former occurs when a mass moves around a particle with spin, and the latter arises when a particle with spin moves in the Newtonian scalar potential of a second (spinless) particle. These Berry phases lead to a self-anyonization'' of particles with nonzero spin. The topological term in their effective action has the same structure as the one which obtains when spinless particles are considered, but with a gravitational Chern-Simons term included in the action for the gravitational field.

• OSTI ID: 5184971
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 44:4; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

645204* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- Strong Interactions & Properties
645400 -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
BASIC INTERACTIONS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EQUATIONS
FERMIONS
FIELD THEORIES
FUNCTIONS
GAUGE INVARIANCE
GRAVITATIONAL FIELDS
GRAVITATIONAL INTERACTIONS
INTERACTIONS
INVARIANCE PRINCIPLES
LIE GROUPS
MAGNETIC MOMENTS
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE PROPERTIES
QUANTUM FIELD THEORY
SPIN
SYMMETRY GROUPS
THREE-DIMENSIONAL CALCULATIONS
TOPOLOGY
U GROUPS
U-1 GROUPS
WAVE EQUATIONS
WAVE FUNCTIONS