Gravitational anyonization

Journal Article · Thu Aug 15 00:00:00 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), Vol. 44:4; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

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