d-dimensional oscillating scalar field lumps and the dimensionality of space

Gleiser, Marcelo

doi:10.1016/j.physletb.2004.08.064

d-dimensional oscillating scalar field lumps and the dimensionality of space

Marcelo Gleiser
(
- Dartmouth Coll.
)

Aug, 2004

6 pages

Published in:

Phys.Lett.B 600 (2004) 126-132

e-Print:

hep-th/0408221 [hep-th]

DOI:

10.1016/j.physletb.2004.08.064

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Abstract:

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(\phi) = \sum_{n=1}^h\frac{g_n}{n!}\phi^n

. Assuming spherical symmetry and if

V''<0

for a range of values of

\phi(t,r)

, such configurations exist if: i) spatial dimensionality is below an upper-critical dimension

d_c

: ii) their radii are above a certain value

R_{\rm min}

. Both

d_c

and

R_{\rm min}

are uniquely determined by

V(\phi)

. For example, symmetric double-well potentials only sustain such configurations if

d\leq 6

and

R^2\geq d[3(2^{3/2}/3)^d-2]^{-1/2}

. Asymmetries may modify the value of

d_c

. All main analytical results are confirmed numerically. Such objects may offer novel ways to probe the dimensionality of space.

field theory: scalar
space-time: dimension
potential
model: oscillator
energy
time dependence
numerical calculations

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