2004/08/28 by Marcelo Gleiser
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Combinatorics #Cosmology and Gravitation Theories #Curse of dimensionality #Dimension (graph theory) #Field (mathematics) #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Parameterized complexity #Physics #Pure mathematics #Quantum Electrodynamics and Casimir Effect #Scalar (mathematics) #Scalar field #Space (punctuation) #Upper and lower bounds #hep-th
paper · pdf · doi:10.1016/j.physletb.2004.08.064
published as Phys.Lett. B600 (2004) 126-132 · In press, Physics Letters B. 6 pages, 2 Postscript figures, uses revtex4.sty
arxiv created 2004/08/28 · openalex publication_date 2004/09/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Extremely long-lived, time-dependent, spatially-bound scalar field configurations are shown to exist in d spatial dimensions for a wide class of polynomial interactions parameterized as V(ϕ)=∑n=1hgnn!ϕn. Assuming spherical symmetry and if V″<0 for a range of values of ϕ(t,r), such configurations exist if: (i) spatial dimensionality is below an upper-critical dimension dc; (ii) their radii are above a certain value Rmin. Both dc and Rmin are uniquely determined by V(ϕ). For example, symmetric double-well potentials only sustain such configurations if d⩽6 and R2⩾d[3(23/2/3)d−2]−1/2. Asymmetries may modify the value of dc. All main analytical results are confirmed numerically. Such objects may offer novel ways to probe the dimensionality of space.