Details
| Original language | English |
|---|---|
| Article number | 137564 |
| Number of pages | 10 |
| Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |
| Volume | 835 |
| Early online date | 14 Nov 2022 |
| Publication status | Published - 10 Dec 2022 |
Abstract
We find a two-parameter family of solutions of the Yang–Mills equations for gauge group SO(1,3) on Minkowski space by foliating different parts of it with non-compact coset spaces with SO(1,3) isometry. The interior of the lightcone is foliated with hyperbolic space H3≅SO(1,3)/SO(3), while the exterior of the lightcone employs de Sitter space dS≅3SO(1,3)/SO(1,2). The lightcone itself is parametrized by SO(1,3)/ISO(2) in a nilpotent fashion. Equivariant reduction of the SO(1,3) Yang–Mills system on the first two coset spaces yields a mechanical system with inverted double-well potential and the foliation parameter serving as an evolution parameter. Its known analytic solutions are periodic or runaway except for the kink. On the lightcone, only the vacuum solution remains. The constructed Yang–Mills field strength is singular across the lightcone and of infinite action due to the noncompact cosets. Its energy-momentum tensor takes a very simple form, with energy density of opposite signs inside and outside the lightcone.
Keywords
- Equivariant reduction, Non-compact coset spaces, Yang–Mills solutions
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, Vol. 835, 137564, 10.12.2022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Yang–Mills solutions on Minkowski space via non-compact coset spaces
AU - Kumar, Kaushlendra
AU - Lechtenfeld, Olaf
AU - Picanço Costa, Gabriel
AU - Röhrig, Jona
N1 - Funding Information: K.K. thanks Deutscher Akademischer Austauschdienst (DAAD) for the doctoral research grant 57381412 .
PY - 2022/12/10
Y1 - 2022/12/10
N2 - We find a two-parameter family of solutions of the Yang–Mills equations for gauge group SO(1,3) on Minkowski space by foliating different parts of it with non-compact coset spaces with SO(1,3) isometry. The interior of the lightcone is foliated with hyperbolic space H3≅SO(1,3)/SO(3), while the exterior of the lightcone employs de Sitter space dS≅3SO(1,3)/SO(1,2). The lightcone itself is parametrized by SO(1,3)/ISO(2) in a nilpotent fashion. Equivariant reduction of the SO(1,3) Yang–Mills system on the first two coset spaces yields a mechanical system with inverted double-well potential and the foliation parameter serving as an evolution parameter. Its known analytic solutions are periodic or runaway except for the kink. On the lightcone, only the vacuum solution remains. The constructed Yang–Mills field strength is singular across the lightcone and of infinite action due to the noncompact cosets. Its energy-momentum tensor takes a very simple form, with energy density of opposite signs inside and outside the lightcone.
AB - We find a two-parameter family of solutions of the Yang–Mills equations for gauge group SO(1,3) on Minkowski space by foliating different parts of it with non-compact coset spaces with SO(1,3) isometry. The interior of the lightcone is foliated with hyperbolic space H3≅SO(1,3)/SO(3), while the exterior of the lightcone employs de Sitter space dS≅3SO(1,3)/SO(1,2). The lightcone itself is parametrized by SO(1,3)/ISO(2) in a nilpotent fashion. Equivariant reduction of the SO(1,3) Yang–Mills system on the first two coset spaces yields a mechanical system with inverted double-well potential and the foliation parameter serving as an evolution parameter. Its known analytic solutions are periodic or runaway except for the kink. On the lightcone, only the vacuum solution remains. The constructed Yang–Mills field strength is singular across the lightcone and of infinite action due to the noncompact cosets. Its energy-momentum tensor takes a very simple form, with energy density of opposite signs inside and outside the lightcone.
KW - Equivariant reduction
KW - Non-compact coset spaces
KW - Yang–Mills solutions
UR - http://www.scopus.com/inward/record.url?scp=85141989498&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2206.12009
DO - 10.48550/arXiv.2206.12009
M3 - Article
AN - SCOPUS:85141989498
VL - 835
JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
SN - 0370-2693
M1 - 137564
ER -