Effective potential in curved space and cut-off regularizations

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dimensional versus cut-off renormalization and the nucleon-nucleon interaction

The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon interaction. Both types of renormalizations are performed for attractive divergent one- and two-term separable potentials, a divergent tensor potential, and the sum of a delta function and its derivatives. We allow energy-dependent couplings, and determine the form that these couplings should take if equivalence between the two regularization schemes is to be enforced. We also perform renormalization of an attractive separable potential superposed on an analytic divergent potential.

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.

Quantum Einstein gravity - advancements of heat kernel-based renormalization group studies

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory.rnAs its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained.rnThe constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point.rnFinally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of existing computations, taking the independent running of the Euler topological term into account. Known perturbative results are reproduced in this case from the renormalization group equation, identifying however a unique non-Gaussian fixed point.rn

Thermal Transport and Strong Mass Renormalization in NiCl(2)-4SC(NH(2))(2)

Several quantum paramagnets exhibit magnetic-field-induced quantum phase transitions to an anti-ferromagnetic state that exists for H(c1) <= H <= H(c2). For some of these compounds, there is a significant asymmetry between the low-and high-field transitions. We present specific heat and thermal conductivity measurements in NiCl(2)-4SC(NH(2))(2), together with calculations which show that the asymmetry is caused by a strong mass renormalization due to quantum fluctuations for H <= H(c1) that are absent for H >= H(c2). We argue that the enigmatic lack of asymmetry in thermal conductivity is due to a concomitant renormalization of the impurity scattering.

Nilpotent noncommutativity and renormalization

We analyze renormalizability properties of noncommutative (NC) theories with a bifermionic NC parameter. We introduce a new four-dimensional scalar field model which is renormalizable at all orders of the loop expansion. We show that this model has an infrared stable fixed point (at the one-loop level). We check that the NC QED (which is one-loop renormalizable with a usual NC parameter) remains renormalizable when the NC parameter is bifermionic, at least to the extent of one-loop diagrams with external photon legs. Our general conclusion is that bifermionic noncommutativity improves renormalizability properties of NC theories.

Estimating losses in teleportation schemes using the phenomenological operator approach to dissipation in cavity quantum electrodynamics

In this paper, we estimate the losses during teleportation processes requiring either two high-Q cavities or a single bimodal cavity. The estimates were carried out using the phenomenological operator approach introduced by de Almeida et al. [Phys. Rev. A 62, 033815 (2000)].

HORMONAL RESPONSES TO DIFFERENT RESISTANCE EXERCISE SCHEMES OF SIMILAR TOTAL VOLUME

Uchida, MC, Crewther, BT, Ugrinowitsch, C, Bacurau, RFP, Moriscot, AS, and Aoki, MS. J Strength Cond Res 23(7): 2003-2008, 2009-This study assessed the effect of different resistance exercise scheme (RES) designs of similar total of load lifted on the responses of testosterone, cortisol, and creatine kinase (CK). Twenty-seven healthy males performed 1 of 4 bench press workouts described by the 1 repetition maximum (1RM) load: 4 sets of maximum repetitions at 50%-1RM (50%-1RM RES), 5 sets of maximum repetitions at 75%-1RM (75%-1RM RES), 10 sets of maximum repetitions at 90%-1RM (90%1RM RES), or 8 sets of maximum repetitions at 110%-1RM (110%-1RM RES). Each RES was equated by the total volume of load lifted (repetitions x sets x load). Blood samples, collected pre-exercise (Pre) and post-exercise (Post) at 1 and 24 hours (24 h), were analyzed for total and free testosterone, total cortisol, and CK. In general, testosterone and cortisol showed little change within or between the different RES (p > 0.05), possibly because of the relatively low volume lifted and/ or the small muscle mass activated by the bench press exercise. Cortisol was elevated after the 75%-1RM RES at the Post sample, with this response also exceeding the other RES (p < 0.05). The 24 h CK response was also elevated after the 75%-1RM RES (p < 0.05), thereby suggesting greater training strain for the same volume of load. These results confirm previous recommendations regarding the prescription of resistance exercise and the importance of total volume as a stimulus for activating the endocrine system and achieving long-term adaptation.

SALIVARY HORMONE AND IMMUNE RESPONSES TO THREE RESISTANCE EXERCISE SCHEMES IN ELITE FEMALE ATHLETES

Nunes, JA, Crewther, BT, Ugrinowitsch, C, Tricoli, V, Viveiros, L, de Rose Jr, D, and Aoki, MS. Salivary hormone and immune responses to three resistance exercise schemes in elite female athletes J Strength Cond Res 25(8): 2322-2327, 2011-This study examined the salivary hormone and immune responses of elite female athletes to 3 different resistance exercise schemes. Fourteen female basketball players each performed an endurance scheme (ES-4 sets of 12 reps, 60% of 1 repetition maximum (1RM) load, 1-minute rest periods), a strength-hypertrophy scheme (SHS-1 set of 5RM, 1 set of 4RM, 1 set of 3RM, 1 set of 2RM, and 1set of 1RM with 3-minute rest periods, followed by 3 sets of 10RM with 2-minute rest periods) and a power scheme (PS-3 sets of 10 reps, 50% 1RM load, 3-minute rest periods) using the same exercises (bench press, squat, and biceps curl). Saliva samples were collected at 07:30 hours, pre-exercise (Pre) at 09:30 hours, postexercise (Post), and at 17:30 hours. Matching samples were also taken on a nonexercising control day. The samples were analyzed for testosterone, cortisol (C), and immunoglobulin A concentrations. The total volume of load lifted differed among the 3 schemes (SHS > ES > PS, p < 0.05). Postexercise C concentrations increased after all schemes, compared to control values (p < 0.05). In the SHS, the postexercise C response was also greater than pre-exercise data (p < 0.05). The current findings confirm that high-volume resistance exercise schemes can stimulate greater C secretion because of higher metabolic demand. In terms of practical applications, acute changes in C may be used to evaluate the metabolic demands of different resistance exercise schemes, or as a tool for monitoring training strain.

Online Mammographic Images Database for Development and Comparison of CAD Schemes

Considering the difficulties in finding good-quality images for the development and test of computer-aided diagnosis (CAD), this paper presents a public online mammographic images database free for all interested viewers and aimed to help develop and evaluate CAD schemes. The digitalization of the mammographic images is made with suitable contrast and spatial resolution for processing purposes. The broad recuperation system allows the user to search for different images, exams, or patient characteristics. Comparison with other databases currently available has shown that the presented database has a sufficient number of images, is of high quality, and is the only one to include a functional search system.

A Geometric Approach for Turbo Decoding of Reed-Solomon Codes in QAM Modulation Schemes

This work studies the turbo decoding of Reed-Solomon codes in QAM modulation schemes for additive white Gaussian noise channels (AWGN) by using a geometric approach. Considering the relations between the Galois field elements of the Reed-Solomon code and the symbols combined with their geometric dispositions in the QAM constellation, a turbo decoding algorithm, based on the work of Chase and Pyndiah, is developed. Simulation results show that the performance achieved is similar to the one obtained with the pragmatic approach with binary decomposition and analysis.

Strain-dependent fluid flow defined through rock mass classification schemes

Strain-dependent hydraulic conductivities are uniquely defined by an environmental factor, representing applied normal and shear strains, combined with intrinsic material parameters representing mass and component deformation moduli, initial conductivities, and mass structure. The components representing mass moduli and structure are defined in terms of RQD (rock quality designation) and RMR (rock mass rating) to represent the response of a whole spectrum of rock masses, varying from highly fractured (crushed) rock to intact rock. These two empirical parameters determine the hydraulic response of a fractured medium to the induced-deformations The constitutive relations are verified against available published data and applied to study one-dimensional, strain-dependent fluid flow. Analytical results indicate that both normal and shear strains exert a significant influence on the processes of fluid flow and that the magnitude of this influence is regulated by the values of RQD and RMR.

Two-link approximation schemes for loss networks with linear structure and trunk reservation

Loss networks have long been used to model various types of telecommunication network, including circuit-switched networks. Such networks often use admission controls, such as trunk reservation, to optimize revenue or stabilize the behaviour of the network. Unfortunately, an exact analysis of such networks is not usually possible, and reduced-load approximations such as the Erlang Fixed Point (EFP) approximation have been widely used. The performance of these approximations is typically very good for networks without controls, under several regimes. There is evidence, however, that in networks with controls, these approximations will in general perform less well. We propose an extension to the EFP approximation that gives marked improvement for a simple ring-shaped network with trunk reservation. It is based on the idea of considering pairs of links together, thus making greater allowance for dependencies between neighbouring links than does the EFP approximation, which only considers links in isolation.