10 research outputs found
Renormalization Group Invariant Constraints among Coupling Constants in a Noncommutative Geometry Model
We study constraints among coupling constants of the standard model obtained
in the noncommutative geometry (NCG) method. First, we analyze the evolution of
the Higgs boson mass under the renormalization group by adopting the idea of
\'Alvarez et al. For this analysis we derive two certain constraints by
modifying Connes's way of constructing the standard model. Next, we find
renormalization group invariant (RGI) constraints in the NCG method. We also
consider the relation between the condition that a constraint among coupling
constants of a model becomes RGI and the condition that the model becomes
multiplicative renormalizable by using a simple example.Comment: 22 pages, Latex file, 2 figures available upon request to
[email protected], important changes are made, This is the last
version which will appear in Prog. Theor. Phys. {\bf 100} (1998) as
"Constraints among Coupling Constants in Noncommutative Geometry Models
Lorentz Invariance And Unitarity Problem In Non-Commutative Field Theory
It is shown that the one-loop two-point amplitude in {\it Lorentz-invariant}
non-commutative (NC) theory is finite after subtraction in the
commutative limit and satisfies the usual cutting rule, thereby eliminating the
unitarity problem in Lorentz-non-invariant NC field theory in the approximation
considered.Comment: 14 page
Lorentz-Invariant Non-Commutative Space-Time Based On DFR Algebra
It is argued that the familiar algebra of the non-commutative space-time with
-number is inconsistent from a theoretical point of view.
Consistent algebras are obtained by promoting to an
anti-symmetric tensor operator . The simplest among them
is Doplicher-Fredenhagen-Roberts (DFR) algebra in which the triple commutator
among the coordinate operators is assumed to vanish. This allows us to define
the Lorentz-covariant operator fields on the DFR algebra as operators diagonal
in the 6-dimensional -space of the hermitian operators,
. It is shown that we then recover Carlson-Carone-Zobin
(CCZ) formulation of the Lorentz-invariant non-commutative gauge theory with no
need of compactification of the extra 6 dimensions. It is also pointed out that
a general argument concerning the normalizability of the weight function in the
Lorentz metric leads to a division of the -space into two disjoint
spaces not connected by any Lorentz transformation so that the CCZ covariant
moment formula holds true in each space, separately. A non-commutative
generalization of Connes' two-sheeted Minkowski space-time is also proposed.
Two simple models of quantum field theory are reformulated on
obtained in the commutative limit.Comment: LaTeX file, 27 page