15,872 research outputs found
QFT with Twisted Poincar\'e Invariance and the Moyal Product
We study the consequences of twisting the Poincare invariance in a quantum
field theory. First, we construct a Fock space compatible with the twisting and
the corresponding creation and annihilation operators. Then, we show that a
covariant field linear in creation and annihilation operators does not exist.
Relaxing the linearity condition, a covariant field can be determined. We show
that it is related to the untwisted field by a unitary transformation and the
resulting n-point functions coincide with the untwisted ones. We also show that
invariance under the twisted symmetry can be realized using the covariant field
with the usual product or by a non-covariant field with a Moyal product. The
resulting S-matrix elements are shown to coincide with the untwisted ones up to
a momenta dependent phase.Comment: 11 pages, references adde
Finite-size scaling and the deconfinement transition in gauge theories
We introduce a new method for determining the critical indices of the
deconfinement transition in gauge theories. The method is based on the finite
size scaling behavior of the expectation value of simple lattice operators,
such as the plaquette. We test the method for the case of SU(3) pure gauge
theory in (2+1) dimensions and obtain a precise determination of the critical
index , in agreement with the prediction of the Svetitsky-Yaffe
conjecture.Comment: 6 pages. Several comments and one reference added, results unchange
Finite-size scaling and deconfinement transition: the case of 4D SU(2) pure gauge theory
A recently introduced method for determining the critical indices of the
deconfinement transition in gauge theories, already tested for the case of 3D
SU(3) pure gauge theory, is applied here to 4D SU(2) pure gauge theory. The
method is inspired by universality and based on the finite size scaling
behavior of the expectation value of simple lattice operators, such as the
plaquette. We obtain an accurate determination of the critical index , in
agreement with the prediction of the Svetitsky-Yaffe conjecture.Comment: 11 pages, 3 eps figure
q-Deformed quaternions and su(2) instantons
We have recently introduced the notion of a q-quaternion bialgebra and shown
its strict link with the SO_q(4)-covariant quantum Euclidean space R_q^4.
Adopting the available differential geometric tools on the latter and the
quaternion language we have formulated and found solutions of the
(anti)selfduality equation [instantons and multi-instantons] of a would-be
deformed su(2) Yang-Mills theory on this quantum space. The solutions depend on
some noncommuting parameters, indicating that the moduli space of a complete
theory should be a noncommutative manifold. We summarize these results and add
an explicit comparison between the two SO_q(4)-covariant differential calculi
on R_q^4 and the two 4-dimensional bicovariant differential calculi on the bi-
(resp. Hopf) algebras M_q(2),GL_q(2),SU_q(2), showing that they essentially
coincide.Comment: Latex file, 18 page
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