35 research outputs found
The \beta-function in duality-covariant noncommutative \phi^4-theory
We compute the one-loop \beta-functions describing the renormalisation of the
coupling constant \lambda and the frequency parameter \Omega for the real
four-dimensional duality-covariant noncommutative \phi^4-model, which is
renormalisable to all orders. The contribution from the one-loop four-point
function is reduced by the one-loop wavefunction renormalisation, but the
\beta_\lambda-function remains non-negative. Both \beta_\lambda and
\beta_\Omega vanish at the one-loop level for the duality-invariant model
characterised by \Omega=1. Moreover, \beta_\Omega also vanishes in the limit
\Omega \to 0, which defines the standard noncommutative \phi^4-quantum field
theory. Thus, the limit \Omega \to 0 exists at least at the one-loop level.Comment: 11 pages, LaTe
Noncommutative spin-1/2 representations
In this letter we apply the methods of our previous paper hep-th/0108045 to
noncommutative fermions. We show that the fermions form a spin-1/2
representation of the Lorentz algebra. The covariant splitting of the conformal
transformations into a field-dependent part and a \theta-part implies the
Seiberg-Witten differential equations for the fermions.Comment: 7 pages, LaTe
Space/time noncommutative field theories and causality
As argued previously, amplitudes of quantum field theories on noncommutative
space and time cannot be computed using naive path integral Feynman rules. One
of the proposals is to use the Gell-Mann--Low formula with time-ordering
applied before performing the integrations. We point out that the previously
given prescription should rather be regarded as an interaction point
time-ordering. Causality is explicitly violated inside the region of
interaction. It is nevertheless a consistent procedure, which seems to be
related to the interaction picture of quantum mechanics. In this framework we
compute the one-loop self-energy for a space/time noncommutative \phi^4 theory.
Although in all intermediate steps only three-momenta play a role, the final
result is manifestly Lorentz covariant and agrees with the naive calculation.
Deriving the Feynman rules for general graphs, we show, however, that such a
picture holds for tadpole lines only.Comment: 16 pages, LaTeX, uses feynmf macros, one reference added; ooops,
version 2 was an older one
On divergent 3-vertices in noncommutative SU(2)gauge theory
We analyze divergencies in 2-point and 3-point functions for noncommutative
-expanded SU(2)-gauge theory with massless fermions. We show that,
after field redefinition and renormalization of couplings, one divergent term
remains.Comment: 7 page
IR-Singularities in Noncommutative Perturbative Dynamics?
We analyse the IR-singularities that appear in a noncommutative scalar
quantum field theory on . We demonstrate with the help of the
quadratic one-loop effective action and an appropriate field redefinition that
no IR-singularities exist. No new degrees of freedom are needed to describe the
UV/IR-mixing.Comment: 6 pages, amsLaTe
Noncommutative Lorentz Symmetry and the Origin of the Seiberg-Witten Map
We show that the noncommutative Yang-Mills field forms an irreducible
representation of the (undeformed) Lie algebra of rigid translations, rotations
and dilatations. The noncommutative Yang-Mills action is invariant under
combined conformal transformations of the Yang-Mills field and of the
noncommutativity parameter \theta. The Seiberg-Witten differential equation
results from a covariant splitting of the combined conformal transformations
and can be computed as the missing piece to complete a covariant conformal
transformation to an invariance of the action.Comment: 20 pages, LaTeX. v2: Streamlined proofs and extended discussion of
Lorentz transformation
Noncommutative Induced Gauge Theory
We consider an external gauge potential minimally coupled to a renormalisable
scalar theory on 4-dimensional Moyal space and compute in position space the
one-loop Yang-Mills-type effective theory generated from the integration over
the scalar field. We find that the gauge invariant effective action involves,
beyond the expected noncommutative version of the pure Yang-Mills action,
additional terms that may be interpreted as the gauge theory counterpart of the
harmonic oscillator term, which for the noncommutative -theory on Moyal
space ensures renormalisability. The expression of a possible candidate for a
renormalisable action for a gauge theory defined on Moyal space is conjectured
and discussed.Comment: 20 pages, 6 figure
Non-renormalizability of noncommutative SU(2) gauge theory
We analyze the divergent part of the one-loop effective action for the
noncommutative SU(2) gauge theory coupled to the fermions in the fundamental
representation. We show that the divergencies in the 2-point and the 3-point
functions in the -linear order can be renormalized, while the
divergence in the 4-point fermionic function cannot.Comment: 15 pages, results presented at ESI 2d dilaton gravity worksho
Vacuum configurations for renormalizable non-commutative scalar models
In this paper we find non-trivial vacuum states for the renormalizable
non-commutative model. An associated linear sigma model is then
considered. We further investigate the corresponding spontaneous symmetry
breaking.Comment: 17 page