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...
| Main Authors: | , |
|---|---|
| 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 |
| _version_ | 1819198417368252416 |
|---|---|
| author | Fiorenzo Bastianelli Olindo Corradini |
| author_facet | Fiorenzo Bastianelli Olindo Corradini |
| author_sort | Fiorenzo Bastianelli |
| collection | DOAJ |
| description | 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 . |
| first_indexed | 2024-12-23T03:00:07Z |
| format | Article |
| id | doaj.art-816fe92dd815466596a54ecc30024837 |
| institution | Directory Open Access Journal |
| issn | 1434-6044 1434-6052 |
| language | English |
| last_indexed | 2024-12-23T03:00:07Z |
| publishDate | 2017-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-816fe92dd815466596a54ecc300248372022-12-21T18:02:27ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522017-11-01771111210.1140/epjc/s10052-017-5307-6On the simplified path integral on spheresFiorenzo Bastianelli0Olindo Corradini1Dipartimento di Fisica ed Astronomia, Università di BolognaDipartimento di Scienze Fisiche, Informatiche e Matematiche, Università degli Studi di Modena e Reggio EmiliaAbstract 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 .http://link.springer.com/article/10.1140/epjc/s10052-017-5307-6 |
| spellingShingle | Fiorenzo Bastianelli Olindo Corradini On the simplified path integral on spheres European Physical Journal C: Particles and Fields |
| title | On the simplified path integral on spheres |
| title_full | On the simplified path integral on spheres |
| title_fullStr | On the simplified path integral on spheres |
| title_full_unstemmed | On the simplified path integral on spheres |
| title_short | On the simplified path integral on spheres |
| title_sort | on the simplified path integral on spheres |
| url | http://link.springer.com/article/10.1140/epjc/s10052-017-5307-6 |
| work_keys_str_mv | AT fiorenzobastianelli onthesimplifiedpathintegralonspheres AT olindocorradini onthesimplifiedpathintegralonspheres |