We show that one-dimensional quantum systems with gapless degrees of freedo
m and open boundary conditions form a universality class of quantum critica
l behavior, which we propose to call ''bounded Luttinger liquids." They sha
re the following properties with ordinary (periodic) Luttinger liquids: the
absence of fermionic quasiparticle excitations, charge-spin separation, an
d anomalous power-law correlations with exponents whose scaling relations a
re parametrized by a single coupling constant per degree of freedom, K-nu.
The values of K-nu are independent of boundary conditions, but the represen
tation of the critical exponents in terms of these K-nu's depends on bounda
ry conditions. We illustrate these scaling relations by exploring general r
ules for boundary critical exponents derived earlier using the Bethe ansatz
solution of the one-dimensional Hubbard model together with boundary confo
rmal held theory, and the theory of Luttinger liquids in finite-size system
s. We apply this theory to the photoemission properties of the organic cond
uctors (TMTSF)(2)X, where TMTSF is tetramethyltetraselenafulvalene, and X =
ClO9, PF6, ReO4, and discuss to what extent the assumption of finite stran
ds with open boundaries at the sample surface can reconcile the experimenta
l results with independent information on the Luttinger-liquid state in the
se materials.