Artigo de Periódico
Boundary behaviour of the four-point function in the 3-dimensional Gross–Neveu model
Fecha
2004Registro en:
0370-2693
v. 583, n. 3-4
Autor
Malbouisson, Adolfo Pedro Carvalho
Malbouisson, Jorge Mário Carvalho
Santana, Ademir Eugênio de
Silva, J. C. da
Malbouisson, Adolfo Pedro Carvalho
Malbouisson, Jorge Mário Carvalho
Santana, Ademir Eugênio de
Silva, J. C. da
Institución
Resumen
We consider the N-components 3-dimensional massive Gross–Neveu model compactified in one spatial direction, the system
being constrained to a slab of thickness L. We derive a closed formula for the renormalized L-dependent four-point function at vanishing external momenta in the large-N limit (the effective coupling constant), using bag-model boundary conditions. For
values of the fixed coupling constant in absence of boundaries λ λc 19.16, we obtain small-distance asymptotic freedom
(for L→0) and a singularity for a length L(c) such that 2.07m −1 <L(c) 2.82m −1, m being the fermionic mass. Taking for
m an average of the masses of the quarks composing the proton, we obtain a “confining” length L
(c) p which is comparable with an estimated proton diameter.