On the simplified path integral on spheres

Abstract We have recently studied a simplified version of the path integral for a particle on a sphere, and more generally on maximally symmetric spaces, and proved that Riemann normal coordinates allow the use of a quadratic kinetic term in the particle action. The emerging linear sigma model conta...

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Bibliographic Details
Main Authors: Fiorenzo Bastianelli, Olindo Corradini
Format: Article
Language:English
Published: SpringerOpen 2017-11-01
Series:European Physical Journal C: Particles and Fields
Online Access:http://link.springer.com/article/10.1140/epjc/s10052-017-5307-6
Description
Summary:Abstract We have recently studied a simplified version of the path integral for a particle on a sphere, and more generally on maximally symmetric spaces, and proved that Riemann normal coordinates allow the use of a quadratic kinetic term in the particle action. The emerging linear sigma model contains a scalar effective potential that reproduces the effects of the curvature. We present here further details of the construction, and extend its perturbative evaluation to orders high enough to read off the type-A trace anomalies of a conformal scalar in dimensions $$d=14$$ d = 14 and $$d=16$$ d = 16 .
ISSN:1434-6044
1434-6052