A systematization for one-loop 4D Feynman integrals

We present a strategy for the systematization of manipulations and calculations involving divergent (or not) Feynman integrals, typical of the one-loop perturbative solutions of QFT, where the use of an explicit regularization is avoided. Two types of systematization are adopted. The divergent parts are put in terms of a small number of standard objects, and a set of structure functions for the finite parts is also defined. Some important properties of the finite structures, specially useful in the verification of relations among Green's functions, are identified. We show that, in fundamental (renormalizable) theories, all the finite parts of two-, three- and four-point functions can be written in terms of only three basic functions while the divergent parts require (only) five objects. The final results obtained within the proposed strategy can be easily converted into those corresponding to any specific regularization technique providing an unified point of view for the treatment of divergent Feynman integrals. Examples of physical amplitudes evaluation and their corresponding symmetry relations verification are presented as well as generalizations of our results for the treatment of Green's functions having an arbitrary number of points are considered.

Vacuum Polarization Tensor for QED in the Light Front Gauge

The use of light front coordinates in quantum field theories (QFT) always brought some problems and controversies. In this work we explore some aspects of its formalism with respect to the employment of dimensional regularization in the computation of the photon's self-energy at the one-loop level and how the fermion propagator has an important role in the outcoming results.

Flavor mixing in a Lee-type model

An exactly solvable quantum field theory (QFT) model of Lee type is constructed to study how neutrino flavor eigenstates are created through interactions and how the localization properties of neutrinos follows from the parent particle that decays. The two-particle states formed by the neutrino and the accompanying charged lepton can be calculated exactly as well as their creation probabilities. We can show that the coherent creation of neutrino flavor eigenstates follows from the common negligible contribution of neutrino masses to their creation probabilities. on the other hand, it is shown that it is not possible to associate a well-defined flavor to coherent superpositions of charged leptons.

Decay of accelerated protons and the existence of the Fulling-Davies-Unruh effect

A theoretic-oriented strategy was taken to address the weak decay of uniformly accelerated protons. The decay of uniformly accelerated p+'s was analyzed using standard quantum field theory (QFT). It was shown that the FDU effect is essential to reproduce the proper decay rate in the uniformly accelerated frame.

Sólitons e gravitação

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A novel functional renormalization group framework for gauge theories and gravity

In this thesis we develop further the functional renormalization group (RG) approach to quantum field theory (QFT) based on the effective average action (EAA) and on the exact flow equation that it satisfies. The EAA is a generalization of the standard effective action that interpolates smoothly between the bare action for krightarrowinfty and the standard effective action rnfor krightarrow0. In this way, the problem of performing the functional integral is converted into the problem of integrating the exact flow of the EAA from the UV to the IR. The EAA formalism deals naturally with several different aspects of a QFT. One aspect is related to the discovery of non-Gaussian fixed points of the RG flow that can be used to construct continuum limits. In particular, the EAA framework is a useful setting to search for Asymptotically Safe theories, i.e. theories valid up to arbitrarily high energies. A second aspect in which the EAA reveals its usefulness are non-perturbative calculations. In fact, the exact flow that it satisfies is a valuable starting point for devising new approximation schemes. In the first part of this thesis we review and extend the formalism, in particular we derive the exact RG flow equation for the EAA and the related hierarchy of coupled flow equations for the proper-vertices. We show how standard perturbation theory emerges as a particular way to iteratively solve the flow equation, if the starting point is the bare action. Next, we explore both technical and conceptual issues by means of three different applications of the formalism, to QED, to general non-linear sigma models (NLsigmaM) and to matter fields on curved spacetimes. In the main part of this thesis we construct the EAA for non-abelian gauge theories and for quantum Einstein gravity (QEG), using the background field method to implement the coarse-graining procedure in a gauge invariant way. We propose a new truncation scheme where the EAA is expanded in powers of the curvature or field strength. Crucial to the practical use of this expansion is the development of new techniques to manage functional traces such as the algorithm proposed in this thesis. This allows to project the flow of all terms in the EAA which are analytic in the fields. As an application we show how the low energy effective action for quantum gravity emerges as the result of integrating the RG flow. In any treatment of theories with local symmetries that introduces a reference scale, the question of preserving gauge invariance along the flow emerges as predominant. In the EAA framework this problem is dealt with the use of the background field formalism. This comes at the cost of enlarging the theory space where the EAA lives to the space of functionals of both fluctuation and background fields. In this thesis, we study how the identities dictated by the symmetries are modified by the introduction of the cutoff and we study so called bimetric truncations of the EAA that contain both fluctuation and background couplings. In particular, we confirm the existence of a non-Gaussian fixed point for QEG, that is at the heart of the Asymptotic Safety scenario in quantum gravity; in the enlarged bimetric theory space where the running of the cosmological constant and of Newton's constant is influenced by fluctuation couplings.

BCJ-relations in quantum field theory

BCJ-relations have a series of important consequences in Quantum FieldrnTheory and in Gravity. In QFT, one can use BCJ-relations to reduce thernnumber of independent colour-ordered partial amplitudes and to relate nonplanarrnand planar diagrams in loop calculations. In addition, one can usernBCJ-numerators to construct gravity scattering amplitudes through a squaringrn procedure. For these reasons, it is important to nd a prescription tornobtain BCJ-numerators without requiring a diagram by diagram approach.rnIn this thesis, after introducing some basic concepts needed for the discussion,rnI will examine the existing diagrammatic prescriptions to obtainrnBCJ-numerators. Subsequently, I will present an algorithm to construct anrneective Yang-Mills Lagrangian which automatically produces kinematic numeratorsrnsatisfying BCJ-relations. A discussion on the kinematic algebrarnfound through scattering equations will then be presented as a way to xrnnon-uniqueness problems in the algorithm.

A linear O(N) model: a functional renormalization group approach for flat and curved space

In questa tesi sono state applicate le tecniche del gruppo di rinormalizzazione funzionale allo studio della teoria quantistica di campo scalare con simmetria O(N) sia in uno spaziotempo piatto (Euclideo) che nel caso di accoppiamento ad un campo gravitazionale nel paradigma dell'asymptotic safety. Nel primo capitolo vengono esposti in breve alcuni concetti basilari della teoria dei campi in uno spazio euclideo a dimensione arbitraria. Nel secondo capitolo si discute estensivamente il metodo di rinormalizzazione funzionale ideato da Wetterich e si fornisce un primo semplice esempio di applicazione, il modello scalare. Nel terzo capitolo è stato studiato in dettaglio il modello O(N) in uno spaziotempo piatto, ricavando analiticamente le equazioni di evoluzione delle quantità rilevanti del modello. Quindi ci si è specializzati sul caso N infinito. Nel quarto capitolo viene iniziata l'analisi delle equazioni di punto fisso nel limite N infinito, a partire dal caso di dimensione anomala nulla e rinormalizzazione della funzione d'onda costante (approssimazione LPA), già studiato in letteratura. Viene poi considerato il caso NLO nella derivative expansion. Nel quinto capitolo si è introdotto l'accoppiamento non minimale con un campo gravitazionale, la cui natura quantistica è considerata a livello di QFT secondo il paradigma di rinormalizzabilità dell'asymptotic safety. Per questo modello si sono ricavate le equazioni di punto fisso per le principali osservabili e se ne è studiato il comportamento per diversi valori di N.

Algoritmi quantistici e classi di complessità

Solitamente il concetto di difficoltà è piuttosto soggettivo, ma per un matematico questa parola ha un significato diverso: anche con l’aiuto dei più potenti computer può essere impossibile trovare la soluzione di un sudoku, risolvere l’enigma del commesso viaggiatore o scomporre un numero nei suoi fattori primi; in questo senso le classi di complessità computazionale quantificano il concetto di difficoltà secondo le leggi dell’informatica classica. Una macchina quantistica, però, non segue le leggi classiche e costituisce un nuovo punto di vista in una frontiera della ricerca legata alla risoluzione dei celebri problemi del millennio: gli algoritmi quantistici implementano le proprietà straordinarie e misteriose della teoria dei quanti che, quando applicate lucidamente, danno luogo a risultati sorprendenti.

Alternative derivative expansion in Functional RG and application

We give a brief review of the Functional Renormalization method in quantum field theory, which is intrinsically non perturbative, in terms of both the Polchinski equation for the Wilsonian action and the Wetterich equation for the generator of the proper verteces. For the latter case we show a simple application for a theory with one real scalar field within the LPA and LPA' approximations. For the first case, instead, we give a covariant "Hamiltonian" version of the Polchinski equation which consists in doing a Legendre transform of the flow for the corresponding effective Lagrangian replacing arbitrary high order derivative of fields with momenta fields. This approach is suitable for studying new truncations in the derivative expansion. We apply this formulation for a theory with one real scalar field and, as a novel result, derive the flow equations for a theory with N real scalar fields with the O(N) internal symmetry. Within this new approach we analyze numerically the scaling solutions for N=1 in d=3 (critical Ising model), at the leading order in the derivative expansion with an infinite number of couplings, encoded in two functions V(phi) and Z(phi), obtaining an estimate for the quantum anomalous dimension with a 10% accuracy (confronting with Monte Carlo results).

Comparison of interferon-gamma release assay versus tuberculin skin test for tuberculosis screening in inflammatory bowel disease

OBJECTIVES: Reactivation of latent tuberculosis (TB) in inflammatory bowel disease (IBD) patients treated with antitumor necrosis factor-alpha medication is a serious problem. Currently, TB screening includes chest x-rays and a tuberculin skin test (TST). The interferon-gamma release assay (IGRA) QuantiFERON-TB Gold In-Tube (QFT-G-IT) shows better specificity for diagnosing TB than the skin test. This study evaluates the two test methods among IBD patients. METHODS: Both TST and IGRA were performed on 212 subjects (114 Crohn's disease, 44 ulcerative colitis, 10 indeterminate colitis, 44 controls). RESULTS: Eighty-one percent of IBD patients were under immunosuppressive therapy; 71% of all subjects were vaccinated with Bacille Calmette Guérin; 18% of IBD patients and 43% of controls tested positive with the skin test (P < 0.0001). Vaccinated controls tested positive more often with the skin test (52%) than did vaccinated IBD patients (23%) (P = 0.011). Significantly fewer immunosuppressed patients tested positive with the skin test than did patients not receiving therapy (P = 0.007); 8% of patients tested positive with the QFT-G-IT test (14/168) compared to 9% (4/44) of controls. Test agreement was significantly higher in the controls (P = 0.044) compared to the IBD group. CONCLUSIONS: Agreement between the two test methods is poor in IBD patients. In contrast to the QFT-G-IT test, the TST is negatively influenced by immunosuppressive medication and vaccination status, and should thus be replaced by the IGRA for TB screening in immunosuppressed patients having IBD.

Tuberculosis in a Swiss army training camp: contact investigation using an Interferon gamma release assay

BACKGROUND: In tuberculosis (TB), the risk of exposure is determined mainly by the proximity to and the hours of direct contact with an infectious patient. We describe the contact investigation after detection of an infectious form of TB in a military camp using an Interferon-g-Release-Assay (IGRA, QuantiFERON-TB Gold In Tube [QTF-GIT]) eight weeks after detection of the index case. INDEX PATIENT: The index patient presented with fever, cough and weight loss in the military hospital six weeks after entering the camp. TB was suspected and anti-tuberculous therapy given immediately. Subsequently, TB was microbiologically confirmed. METHODS: Four exposure groups were formed a priori based on the proximity and the hours of direct contact to the index case. 168 (95.5%) agreed to be investigated: - Group A: sharing the same dormitory (15 persons) - Group B: same platoon, but not sharing the dormitory (20 persons) - Group C: staff and patients of the military hospital (22 persons) - Group D: other three platoons and senior military staff (111 persons). RESULTS: 34 (20.2%) out of 168 contacts tested positive in the QFT-GIT assay. For the exposure groups, the respective QFT-GIT testing results were: group A, 14/15 (93%); group B, 4/20 (20%); group C, 5/22 (22.7%); and group D, 11/111 (9.9%). No secondary TB cases were identified. CONCLUSIONS: In our study, test results show a correlation with the risk of exposure, suggesting that IGRA may be useful for the assessment of TB infection in TB contacts. The high mobility of recruits reduced traceability of contacts. In this context, QFT-GIT allowed for an efficient screening of contacts at a single time point.

Evaluating the potential of IP-10 and MCP-2 as biomarkers for the diagnosis of tuberculosis

The aim of the present study was to evaluate the potential of diagnostic tests based on interferon-gamma inducible protein (IP)-10 and monocyte chemotactic protein (MCP)-2, and compare the performance with the QuantiFERON TB Gold In-Tube (QFT-IT; Cellestis, Carnagie, Australia) test. IP-10 and MCP-2 were determined in supernatants from whole blood stimulated with Mycobacterium tuberculosis-specific antigens. Samples were obtained from 80 patients with culture- and/or PCR-proven tuberculosis (TB), and 124 unexposed healthy controls: 86 high school students and 38 high school staff. IP-10 and MCP-2 test cut-offs were established based on receiver operating characteristic curve analysis. TB patients produced significantly higher levels (median) of IP-10 (2158 pg x mL(-1)) and MCP-2 (379 pg x mL(-1)) compared with interferon (IFN)-gamma (215 pg x mL(-1)). The QFT-IT, IP-10 and MCP-2 tests detected 81, 83 and 71% of the TB patients; 0, 3 and 0% of the high school students and 0, 16 and 3% of the staff, respectively. Agreement between tests was high (>89%). By combining IP-10 and IFN-gamma tests, the detection rate increased among TB patients to 90% without a significant increase in positive responders among the students. In conclusion, interferon-gamma inducible protein-10 and monocyte chemotactic protein-2 responses to Mycobacterium tuberculosis-specific antigens could be used to diagnose infection. Combining interferon-gamma inducible protein-10 and interferon-gamma may be a simple approach to increase the detection rate of the Mycobacterium tuberculosis-specific in vitro tests.

The performance of interferon-gamma release assays in tuberculosis patients with type II diabetes

The sensitivity of Interferon-γ release assays for detection of Mycobacterium tuberculosis (MTB) infection or disease is affected by conditions that depress host immunity (such as HIV). It is critical to determine whether these assays are affected by diabetes and related conditions (i.e. hyperglycemia, chronic hyperglycemia, or being overweight/obese) given that immune impairment is thought to underline susceptibility to tuberculosis (TB) in people with diabetes. This is important for tuberculosis control due to the millions of type 2 diabetes patients at risk for tuberculosis worldwide.^ The objective of this study was to identify host characteristics, including diabetes, that may affect the sensitivity of two commercially available Interferon-γ (IFN-γ) release assays (IGRA), the QuantiFERON®-TB Gold (QFT-G) and the T-SPOT®.TB in active TB patients. We further explored whether IFN-γ secretion in response to MTB antigens (ESAT-6 and CFP-10) is associated with diabetes and its defining characteristics (high blood glucose, high HbA1c, high BMI). To achieve these objectives, the sensitivity of QFT-G and T-SPOT. TB assays were evaluated in newly diagnosed, tuberculosis confirmed (by positive smear for acid fast bacilli and/or positive culture for MTB) adults enrolled at Texas and Mexico study sites between March 2006 and April 2009. Univariate and multivariate models were constructed to identify host characteristics associated with IGRA result and level of IFN-γ secretion.^ QFT-G was positive in 68% of tuberculosis patients. Those with diabetes, chronic hyperglycemia or obesity were more likely to have a positive QFT-G result, and to secrete higher levels of IFN-γ in response to the mycobacterial antigens (p<0.05). Previous history of BCG vaccination was the only other host characteristic associated with QFT-G result, whereby a higher proportion of non-BCG vaccinated persons were QFT-G positive, in comparison to vaccinated persons. In a separate group of patients, the T-SPOT.TB was 94% sensitive, with similar performance in all tuberculosis patients, regardless of host characteristics.^ In summary, we have demonstrated the validity of QFT-G and T-SPOT. TB to support the diagnosis of TB in patients with a range of host characteristics, but most notably in patients with diabetes. We also confirmed that TB patients with diabetes and associated characteristics (chronic hyperglycemia or BMI) secreted higher titers of IFN-γ when stimulated with MTB specific antigens, in comparison to patients without these characteristics. Together, these findings suggest that the mechanism by which diabetes increases risk to TB may not be explained by the inability to secrete IFN-γ, a key cytokine for TB control.^

Interferon-gamma release assays for latent tuberculosis infection in child and young adult candidates or recipients of tumor necrosis factor inhibitor therapy

Background. Inhibition of tumor necrosis factor (TNF) is associated with progression of latent tuberculosis infection (LTBI) to active disease. LTBI screening prior to starting TNF inhibitor therapy is recommended. Blood tests, collectively known as interferon-gamma release assays (IGRAs), offer a means other than the tuberculin skin test (TST) of screening for LTBI. However, in the setting of immune compromise, anergy may limit the clinical utility of IGRAs. ^ Methods. A cross-sectional study was conducted in children and young adults ≤ 21 years of age who were cared for at Texas Children's Hospital in Houston, TX, during 2011 and who were candidates for, or were receiving, tumor necrosis factor (TNF)-inhibitor therapy. All subjects answered a risk factor questionnaire and were tested for LTBI by two commercially available IGRAs (QuantiFERON-Gold In-Tube assay and the T-SPOT.TB assay), along with the TST. T-cell phenotypes were evaluated through flow cytometry, both at baseline and after antigen stimulation. ^ Results. Twenty-eight subjects were enrolled. All were TST negative and none were IGRA positive. Results were negative for the 27 subjects who were tested with QuantiFERON-Gold In-Tube. However, 26% of subjects demonstrated anergy in the T-SPOT.T. Patients with T-SPOT. TB anergy had lower quantitative IFN-γ responses to mitogen in the QFT assay—the mean IFN-γ level to mitogen in patients without T-SPOT.TB anergy was 9.84 IU/ml compared to 6.91 IU/ml in patients with T-SPOT.TB anergy (P = 0.046). Age and use of TNF inhibitors, corticosteroids, or methotrexate use were not significantly associated with T-SPOT.TB anergy. Antigen stimulation revealed depressed expression of intracellular IFN-γ in subjects with T-SPOT. TB anergy. ^ Conclusions. The frequency of anergy in this population is higher than would be expected from studies in adults. There appears to be inappropriate IFN-γ responses to antigen in subjects with T-SPOT. TB anergy. This immune defect was detected by the T-SPOT. TB assay but not by the QuantiFERON-Gold In-Tube assay. Further data are needed to clarify the utility of IGRAs in this population.^