Field theory on a non-commutative plane

Quantenfeldtheorien, die auf Räumen mit nichtkommutierenden Koordinaten definiert sind, finden in den letzten Jahren zunehmend Interesse. Mögliche Anwendungen dieser Modelle gibt es unter anderem in der Stringtheorie, der Phänomenologie der Elementarteilchen und in der Festkörperphysik. In der vorliegenden Arbeit untersuchen wir nichtstörungstheoretisch solche nichtkommutativen Feldtheorien mit Hilfe von Monte-Carlo Simulationen. Wir betrachten eine zweidimensionale reine U(1) Eichfeldtheorie und eine dreidimensionale skalare Feldtheorie. Dazu bilden wir die entsprechenden Gittertheorien auf dimensional reduzierte Modelle ab, die mittels N x N Matrizen formuliert sind. Die 2d Eichtheorie auf dem Gitter ist äquivalent zum twisted Eguchi-Kawai Modell, das wir für N=25 bis 515 simulierten. Wir beobachteten ein deutliches Skalierungsverhalten der Ein- und Zweipunktfunktionen von Wilson-Schleifen sowie von Zweipunktfunktionen von Polyakov-Linien bei großen N. Die Zweipunktfunktionen stimmen mit einer universellen Wellenfunktionsrenormierung überein. Der Doppel-Skalierungslimes bei N gegen unendlich entspricht dem Kontinuumslimes in der nichtkommutativen Gittereichtheorie. Das beobachtete Skalierungsverhalten bei großen N zeigt die nichtstörungstheoretische Renormierbarkeit dieser nichtkommutativen Feldtheorie. Für kleine Flächen gilt das Flächengesetz der Wilson-Schleifen wie in der kommutativen 2d planaren Eichtheorie. Für große Flächen finden wir jedoch stattdessen ein oszillierendes Verhalten. In diesem Bereich wächst die Phase der Wilson-Schleifen linear mit der Fläche. Identifiziert man den Nichtkommutativitätsparameter mit einem inversen Magnetfeld, entspricht dies dem Aharonov-Bohm-Effekt. Als nächstes untersuchen wir das 3d lambda phi^4 Modell mit zwei nichtkommutierenden Dimensionen. Wir analysieren das Phasendiagramm. Unsere Ergebnisse stimmen mit einer Vermutung von Gubser und Sondhi in vier Dimensionen überein. Sie sagen vorher, daß sich der geordnete Bereich in eine uniforme und eine nichtuniforme Phase aufspaltet. Desweiteren zeigen wir Ergebnisse für Korrelatoren und der Dispersionsrelation. In der nichtkommutativen Feldtheorie ist die Lorentz-Symmetrie explizit gebrochen, was zu einer deformierten Dispersionsrelation führt. In der Ein-Schleifen Störungstheorie ergibt sich ein zusätzlicher infrarot divergenter Term. Unsere Daten bestätigen dieses störungstheoretische Ergebnis. Wir bestätigen ebenso eine Beobachtung von Ambjorn und Catterall, daß eine nichtuniforme Phase auch in zwei Dimensionen existiert, obwohl dies eine spontane Brechung der Translationssymmetrie impliziert.In the recent years there is a surge of interest in quantum field theories on spaces with non-commutative coordinates. The potential applications of such models include string theory, particle phenomenology as well as solid state physics. We perform a non-perturbative study of such non-commutative field theories by the means of Monte Carlo simulations. In particular we consider a two dimensional pure U(1) gauge field theory and a three dimensional scalar field theory. To this end we map the corresponding lattice theories on dimensionally reduced models, which are formulated in terms of N x N matrices. The 2d gauge theory on the lattice is equivalent to the twisted Eguchi-Kawai model, which we simulated at N ranging from 25 to 515. We observe a clear large N scaling for the 1- and 2-point function of Wilson loops, as well as the 2-point function of Polyakov lines. The 2-point functions agree with a universal wave function renormalization. The large N double scaling limit corresponds to the continuum limit of non-commutative gauge theory, so the observed large N scaling demonstrates the non-perturbative renormalizability of this non-commutative field theory. The area law for the Wilson loops holds at small physical area as in commutative 2d planar gauge theory, but at large areas we find an oscillating behavior instead. In that regime the phase of the Wilson loop grows linearly with the area. This agrees with the Aharonov-Bohm effect in the presence of a constant magnetic field, identified with the inverse non-commutativity parameter. Next we investigate the 3d lambda phi^4 model with two non-commutative coordinates and explore its phase diagram. Our results agree with a conjecture by Gubser and Sondhi in d=4, who predicted that the ordered regime splits into a uniform phase and a phase dominated by stripe patterns. We further present results for the correlators and the dispersion relation. In non-commutative field theory the Lorentz invariance is explicitly broken, which leads to a deformation of the dispersion relation. In one loop perturbation theory this deformation involves an additional infrared divergent term. Our data agree with this perturbative result. We also confirm the recent observation by Ambjorn and Catterall that stripes occur even in d=2, although they imply the spontaneous breaking of the translation symmetry

Reconstructed spatial resolution and contrast recovery with Bayesian penalized likelihood reconstruction (Q.Clear) for FDG-PET compared to time-of-flight (TOF) with point spread function (PSF)

BACKGROUND: Bayesian penalized likelihood reconstruction for PET (e.g., GE Q.Clear) aims at improving convergence of lesion activity while ensuring sufficient signal-to-noise ratio (SNR). This study evaluated reconstructed spatial resolution, maximum/peak contrast recovery (CRmax/CRpeak) and SNR of Q.Clear compared to time-of-flight (TOF) OSEM with and without point spread function (PSF) modeling. METHODS: The NEMA IEC Body phantom was scanned five times (3 min scan duration, 30 min between scans, background, 1.5-3.9 kBq/ml F18) with a GE Discovery MI PET/CT (3-ring detector) with spheres filled with 8-, 4-, or 2-fold the background activity concentration (SBR 8:1, 4:1, 2:1). Reconstruction included Q.Clear (beta, 150/300/450), "PSF+TOF4/16" (iterations, 4; subsets, 16; in-plane filter, 2.0 mm), "OSEM+TOF4/16" (identical parameters), "PSF+TOF2/17" (2 it, 17 ss, 2.0 mm filter), "OSEM+TOF2/17" (identical), "PSF+TOF4/8" (4 it, 8 ss, 6.4 mm), and "OSEM+TOF2/8" (2 it, 8 ss, 6.4 mm). Spatial resolution was derived from 3D sphere activity profiles. RC as (sphere activity concentration [AC]/true AC). SNR as (background mean AC/background AC standard deviation). RESULTS: Spatial resolution of Q.Clear150 was significantly better than all conventional algorithms at SBR 8:1 and 4:1 (Wilcoxon, each p < 0.05). At SBR 4:1 and 2:1, the spatial resolution of Q.Clear300/450 was similar or inferior to PSF+TOF4/16 and OSEM+TOF4/16. Small sphere CRpeak generally underestimated true AC, and it was similar for Q.Clear150/300/450 as with PSF+TOF4/16 or PSF+TOF2/17 (i.e., relative differences < 10%). Q.Clear provided similar or higher CRpeak as OSEM+TOF4/16 and OSEM+TOF2/17 resulting in a consistently better tradeoff between CRpeak and SNR with Q.Clear. Compared to PSF+TOF4/8/OSEM+TOF2/8, Q.Clear150/300/450 showed lower SNR but higher CRpeak. CONCLUSIONS: Q.Clear consistently improved reconstructed spatial resolution at high and medium SBR compared to PSF+TOF and OSEM+TOF, but only with beta = 150. However, this is at the cost of inferior SNR with Q.Clear150 compared to Q.Clear300/450 and PSF+TOF4/16/PSF+TOF2/17 while CRpeak for the small spheres did not improve considerably. This suggests that Q.Clear300/450 may be advantageous for the 3-ring detector configuration because the tradeoff between CR and SNR with Q.Clear300/450 was superior to PSF+TOF4/16, OSEM+TOF4/16, and OSEM+TOF2/17. However, it requires validation by systematic evaluation in patients at different activity and acquisition protocols

Nonequilibrium Polaritonics - Nonlinear Effects and Optical Switching

We report a theoretical non-equilibrium description of polaritonics and we propose ultrafast all- optical switching due to highly nonlinear polaritonics. The electronic band structure within gold (Au) nano grains is modified by external laser light. The Au grains are coupled to a single mode photonic waveguide and we derive a strong transmission reduction of switching originating from the establishd quantum interference with a finite lifetime.Comment: 8 pages 8 figure

The association of intra-therapeutic heterogeneity of somatostatin receptor expression with morphological treatment response in patients undergoing PRRT with [177Lu]-DOTATATE

AIM: Purpose of this study was to evaluate the association of the spatial heterogeneity (asphericity, ASP) in intra-therapeutic SPECT/ CT imaging of somatostatin receptor (SSR) positive metastatic gastroenteropancreatic neuroendocrine neoplasms (GEP-NEN) for morphological treatment response to peptide receptor radionuclide therapy (PRRT). Secondly, we correlated ASP derived form a pre-therapeutic OctreoScan (ASP[In]) and an intra-therapeutic [177Lu]-SPECT/CT (ASP[Lu]). MATERIALS AND METHODS: Data from first therapy cycle [177Lu-DOTA0-Tyr3]octreotate ([177Lu]-DOTATATE)-PRRT was retrospectively analyzed in 33 patients (m = 20; w = 13; median age, 72 [46-88] years). The evaluation of response to PRRT was performed according to RECIST 1.1 in responding lesions [RL (SD, PR, CR), n = 104] and non-responding lesions [NRL (PD), n = 27]. The association of SSR tumor heterogeneity with morphological response was evaluated by Kruskal-Wallis test and receiver operating characteristic curve (ROC). The optimal threshold for separation (RL vs. NRL) was calculated using the Youden-index. Relationship between pre- and intra-therapeutic ASP was determined with Spearman's rank correlation coefficient (ρ) and Bland-Altman plots. RESULTS: A total of 131 lesions (liver: n = 59, lymph nodes: n = 48, bone: n = 19, pancreas: n = 5) were analyzed. Lesions with higher ASP values showed a significantly poorer response to PRRT (PD, median: 11.3, IQR: 8.5-15.5; SD, median: 3.4, IQR: 2.1-4.5; PR, median 1.7, IQR: 0.9-2.8; CR, median: 0.5, IQR: 0.0-1.3); Kruskal-Wallis, p5.45% (sensitivity 96% and specificity 82%). The correlation coefficient of pre- and intra-therapeutic ASP revealed ρ = 0.72 (p <0.01). The mean absolute difference between ASP[In] and ASP[Lu] was -0.04 (95% Limits of Agreement, -6.1-6.0). CONCLUSION: Pre- and intra-therapeutic ASP shows a strong correlation and might be an useful tool for therapy monitoring

PET measured hypoxia and MRI parameters in re-irradiated head and neck squamous cell carcinomas: findings of a prospective pilot study [version 2; peer review: 2 approved]

Background: Tumor hypoxia measured by dedicated tracers like [ 18F]fluoromisonidazole (FMISO) is a well-established prognostic factor in head and neck squamous cell carcinomas (HNSCC) treated with definitive chemoradiation (CRT). However, prevalence and characteristics of positron emission tomography (PET) measured hypoxia in patients with relapse after previous irradiation is missing. Here we report imaging findings of a prospective pilot study in HNSCC patients treated with re-irradiation. Methods: In 8 patients with recurrent HNSCC, diagnosed at a median of 18 months after initial radiotherapy/CRT, [ 18F]fluorodeoxyglucose (FDG)-PET/CT (n=8) and FMISO-PET/MRI (n=7) or FMISO-PET/CT (n=1) were performed. Static FMISO-PET was performed after 180 min. MRI sequences in PET/MRI included diffusion-weighted imaging with apparent diffusion coefficient (ADC) values and contrast enhanced T1w imaging (StarVIBE). Lesions (primary tumor recurrence, 4; cervical lymph node, 1; both, 3) were delineated on FDG-PET and FMISO-PET data using a background-adapted threshold-based method. SUV max and SUV mean in FDG- and FMISO-PET were derived, as well as maximum tumor-to-muscle ratio (TMR max) and hypoxic volume with 1.6-fold muscle SUV mean (HV 1.6) in FMISO-PET. Intensity of lesional contrast enhancement was rated relative to contralateral normal tissue. Average ADC values were derived from a 2D region of interest in the tumor. Results: In FMISO-PET, median TMR max was 1.7 (range: 1.1-1.8). Median HV 1.6 was 0.05 ml (range: 0-7.3 ml). Only in 2/8 patients, HV 1.6 was ≥1.0 ml. In FDG-PET, median SUV max was 9.3 (range: 5.0-20.1). On contrast enhanced imaging four lesions showed decreased and four lesions increased contrast enhancement compared to non-pathologic reference tissue. Median average ADC was 1,060 ×10 6 mm 2/s (range: 840-1,400 ×10 6 mm 2/s). Conclusions: This pilot study implies that hypoxia detectable by FMISO-PET may not be as prevalent as expected among loco-regional recurrent, HPV negative HNSCC. ADC values were only mildly reduced, and contrast enhancement was variable. The results require confirmation in larger sample sizes

Quantitative assessment of the asphericity of pretherapeutic FDG uptake as an independent predictor of outcome in NSCLC

Background The aim of the present study was to evaluate the predictive value of a novel quantitative measure for the spatial heterogeneity of FDG uptake, the asphericity (ASP) in patients with non-small cell lung cancer (NSCLC). Methods FDG-PET/CT had been performed in 60 patients (15 women, 45 men; median age, 65.5 years) with newly diagnosed NSCLC prior to therapy. The FDG-PET image of the primary tumor was segmented using the ROVER 3D segmentation tool based on thresholding at the volume-reproducing intensity threshold after subtraction of local background. ASP was defined as the relative deviation of the tumor’s shape from a sphere. Univariate and multivariate Cox regression as well as Kaplan-Meier (KM) analysis and log-rank test with respect to overall (OAS) and progression-free survival (PFS) were performed for clinical variables, SUVmax/mean, metabolically active tumor volume (MTV), total lesion glycolysis (TLG), ASP and “solidity”, another measure of shape irregularity. Results ASP, solidity and “primary surgical treatment” were significant independent predictors of PFS in multivariate Cox regression with binarized parameters (HR, 3.66; p < 0.001, HR, 2.11; p = 0.05 and HR, 2.09; p = 0.05), ASP and “primary surgical treatment” of OAS (HR, 3.19; p = 0.02 and HR, 3.78; p = 0.01, respectively). None of the other semi-quantitative PET parameters showed significant predictive value with respect to OAS or PFS. Kaplan-Meier analysis revealed a probability of 2-year PFS of 52% in patients with low ASP compared to 12% in patients with high ASP (p < 0.001). Furthermore, it showed a higher OAS rate in the case of low versus high ASP (1-year-OAS, 91% vs. 67%: p = 0.02). Conclusions The novel parameter asphericity of pretherapeutic FDG uptake seems to provide better prognostic value for PFS and OAS in NCSLC compared to SUV, metabolic tumor volume, total lesion glycolysis and solidity

On the relation between non-commutative field theories at theta = infinity and large N matrix field theories

It is well-known that non-commutative (NC) field theories at theta = infinity are ``equivalent'' to large N matrix field theories to all orders in perturbation theory, due to the dominance of planar diagrams. By formulating a NC field theory on the lattice non-perturbatively and mapping it onto a twisted reduced model, we point out that the above equivalence does not hold if the translational symmetry of the NC field theory is broken spontaneously. As an example we discuss NC scalar field theory, where such a spontaneous symmetry breakdown has been confirmed by Monte Carlo simulations.Comment: 12 pages, LaTe

Earthquake research in China

A visit to China of an American seismological delegation, which took place October 5 to November 5, 1974, is covered in this report. The Americans were sponsored by the Committee on Scholarly Communication with the People's Republic of China (CSCPRC), and the hosts in China were the Scientific and Technical Association and the State Seismological Bureau. The CSCPRC is sponsored jointly by the National Academy of Sciences, the Social Science Research Council, and the American Council of Learned Societies. The visit had its origins in an invitation extended in January 1973 by Carl Kisslinger, as President of the Seismological Society of America, to the Chinese Academy of Sciences to send representatives to a Symposium on Earthquake Prediction Research. Although the Chinese declined to participate, this invitation was one step towards a reciprocal exchange of seismologists between the United States and the People's Republic of China. Several months after Kisslinger's letter the CSCPRC visited Peking. Their purpose was to arrange an exchange program with the Chinese Scientific and Technical Association. Prompted by Kisslinger, the committee's proposals for American delegations included seismology. Not only was this particular exchange accepted, but the Chinese in turn suggested that a Chinese seismology group visit the United States