8 research outputs found
One-loop structure of the U(1) gauge model on the truncated Heisenberg space
We calculate divergent one-loop corrections to the propagators of the U(1)
gauge theory on the truncated Heisenberg space, which is one of the extensions
of the Grosse-Wulkenhaar model. The model is purely geometric, based on the
Yang-Mills action; the corresponding gauge-fixed theory is BRST invariant. We
quantize perturbatively and, along with the usual wave-function and mass
renormalizations, we find divergent nonlocal terms of the and
type. We discuss the meaning of these terms and possible
improvements of the model.Comment: 29 page
Properties of classical and quantum field theory on a curved noncommutative space
Posle kratakog istorijskog prikaza razvoja nekomutativne
geometrije i upoznavaa sa osnovnim osobinama i proble-
mima kvantnih teorija po a formulisanih na nekomutativ-
nim prostorima dat je uvod u tetradni formalizam u ne-
komutativnoj diferencijalnoj geometriji. Razmotrili smo
osnovne osobine ranije definisane modifikovane Hajzenber-
gove algebre i opisali konstrukciju diferencijalne geome-
trije na ovom nekomutativnom prostoru. Ovo je uraeno ko-
rixeem tetradnog formalizma. Uvodna razmatraa za-
vrxavamo navoeem prethodnog rezultata, gde je pokazana
ekvivalencija Grose-Vulkenharovog modela i skalarne teo-
rije na zakriv enom nekomutativnom prostoru.
U nastavku predstav amo formulaciju i analizu Dirako-
vog dejstva na modifikovanoj Hajzenbergovoj algebri. Kon-
kretno, razmotrena je neminimalna interakcija sa pozadin-
skim gravitacionim po em. Renormalizabilni model je do-
bijen dimenzionom redukcijom na Hajzenbergovu algebru. Us-
postav ena je ekvivalencija sa Vi-Turnerovim modelom koji
je nekomutativna ekstenzija Gros-Nevoovog modela. Ovaj re-
zultat je indikacija da je interakcija sa torzijom i kri-
vinom neophodan (i dovo an) uslov za renormalizabilnost
skalarnih i spinorskih teorija na zakriv enom nekomuta-
tivnom prostoru.
U posledem delu, predstavili smo rezultate raquna di-
vergentnih kvantnih korekcija propagatora na nivou jedne
pet e, za gradijentno U(1) po e na modifikovanom Hajzen-
bergovom prostoru. Ova teorija je ranije formulisana i
predstav a jednu ekstenziju Grose-Vulkenharovog modela za
gradijentno po e. Model je qisto geometrijski, zasnovan na
Jang-Milsovom dejstvu i BRST invarijantan. Nakon per-
turbativne kvantizacije oko trivijalnog vakuuma, nalazimo
divergentne nelokalne qlanove oblika 1 i 2 . Napo-
sletku analiziramo znaqee ovih qlanova i mogunosti za
popravku modelaIn the first part we shortly review the historical development of the noncommutative
geometry. After presenting some of the main features and problems
of the wide class of quantum field theories on noncommutative spaces,
we give a brief introduction of the frame formalism in the noncommutative
differential geometry. Introducing the earlier defined truncated Heisenbera
algebra, we review the construction of differential geometric objects on it
using the frame formalism. We complete the introduction by citing the previously
shown equivalence of the Grosse-Wulkenhaar model with the scalar
theory coupled to the curvature of the truncated Heisenberg space.
Further, we present our construction and analysis of the Dirac action on
the truncated Heisenberg algebra. In particular, the nonminimal couplings
to the background gravitational field via torsion was considered. By the
dimensional reduction to the Heisenberg algebra we obtained the renormalizable
Vignes-Tourneret model which is an extension of the noncommutative
Gross-Neveu model. This result indicates that, as on the commutative
curved backgrounds, nonminimal couplings with torsion and curvature are
necessary (and sufficient) for renormalisability of scalar and spinor theories
on the curved noncommutative spaces.
In the last part, we present our calculation of the divergent one-loop corrections
to the propagators of the U(1) gauge theory on the truncated Heisenberg
space, which is one of the gauge extensions of the Grosse-Wulkenhaar
model. The model is purely geometric, based on the Yang-Mills action; the
corresponding gauge-fixed theory is BRST invariant and has trivial classical
vacuum. We quantize perturbatively around this vacuum and, along with
the usual wave-function and mass renormalizations, we find divergent nonlocal
terms of the and type. We discuss the meaning of these
terms and possible improvements of the model
Fractal analysis tools for early assessment of liver inflammation induced by chronic consumption of linseed, palm and sunflower oils
Objective: Inflammation is a biological response of tissue to harmful stimuli. A high-fat diet was linked to low-grade chronic liver inflammation, which can further lead to more severe health conditions. It is crucial to assess the intensity of inflammation and structural tissue changes to reduce the subjective judgment by the examiner. We propose fractal-based methods for early-stage low-degree liver inflammation grading. Methods: We have randomly divided 40 C57BL/6 female mice into four groups (control, linseed oil, palm oil, sunflower oil). After 100 days, animals were euthanized, and liver tissue collected for analyses. We performed calculations of fractal dimension, fractal lacunarity, multifractal spectra, local fractal dimension, and particle metrics, applicable to tissue segmentation and grading. Results: Pathohistological analysis of some liver tissue showed a low-grade inflammatory infiltrate around the portal vein of experimental groups subjected to different high-fat diets. Differences in fractal dimension and lacunarity of the inflamed tissue were, in most cases, statistically significant between the high-fat diet groups. Both the observed intensity and area of inflammation were lowest for the sunflower oil. The results of standard fractal analysis, local fractal analysis, and particle analysis were in an excellent agreement. Conclusions: This study demonstrated the efficiency of the fractal analysis based tools in the quantification of complexity and early-stage structural changes in inflamed liver tissue, which could potentially be used in the diagnostic workup of inflammation in the liver. The presented methods could be implemented within a wider scope computer-aided diagnostics system in a very straightforward manner