High-Precision Calculations in Strongly Coupled Quantum Field Theory with Next-to-Leading-Order Renormalized Hamiltonian Truncation

Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is an efficient numerical technique to solve strongly coupled QFTs in d=2 spacetime dimensions. Further theoretical developments are needed to increase its accuracy and the range of applicability. With this goal in mind, here we present a new variant of Hamiltonian Truncation which exhibits smaller dependence on the UV cutoff than other existing implementations, and yields more accurate spectra. The key idea for achieving this consists in integrating out exactly a certain class of high energy states, which corresponds to performing renormalization at the cubic order in the interaction strength. We test the new method on the strongly coupled two-dimensional quartic scalar theory. Our work will also be useful for the future goal of extending Hamiltonian Truncation to higher dimensions d >= 3.Comment: 8 pages, 4 figures; v2: published versio

NLO Renormalization in the Hamiltonian Truncation

Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is a numerical technique for solving strongly coupled QFTs, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is limited only by the available computational resources. The renormalization program improves the accuracy by carefully integrating out the high-energy states, instead of truncating them away. In this paper we develop the most accurate ever variant of Hamiltonian Truncation, which implements renormalization at the cubic order in the interaction strength. The novel idea is to interpret the renormalization procedure as a result of integrating out exactly a certain class of high-energy "tail states". We demonstrate the power of the method with high-accuracy computations in the strongly coupled two-dimensional quartic scalar theory, and benchmark it against other existing approaches. Our work will also be useful for the future goal of extending Hamiltonian Truncation to higher spacetime dimensions.Comment: 28pp + appendices, detailed version of arXiv:1706.0612

Human Rights, Environmental Duties: People, Planet & State

All elements of human well-being are ultimately dependent upon a natural environment which provides access to sufficient food and water, promotes both mental and physical health, and ultimately, permits life itself. In seeking the universal achievement of these goods, international human rights law must begin to require States to take strong action to meet the challenges posed by escalating environmental disintegrity. This thesis examines the extent to which the existing international human rights regime provides a means to achieve this. The role of population management as one means of meeting environmental obligations will be discussed, with the goal of demonstrating that the existing law provides a powerful tool both for the advancement of individual rights and for environmental protection. The latter half will consider how the current law incorporates explicit environmental duties, as well as the potential scope for development of these in the future. The debate surrounding the introduction of an 'environmental human right' will be outlined, with the ultimate conclusion that the law as it already exists is more than capable of adequately addressing environmental degradation – all that is required is that it be interpreted and realised in an environmentally cognisant way

Scaling and tuning of EW and Higgs observables

We study deformations of the SM via higher dimensional operators. In particular, we explicitly calculate the one-loop anomalous dimension matrix for 13 bosonic dimension-6 operators relevant for electroweak and Higgs physics. These scaling equations allow us to derive RG-induced bounds, stronger than the direct constraints, on a universal shift of the Higgs couplings and some anomalous triple gauge couplings by assuming no tuning at the scale of new physics, i.e. by requiring that their individual contributions to the running of other severely constrained observables, like the electroweak oblique parameters or $\Gamma(h \rightarrow \gamma\gamma)$, do not exceed their experimental direct bounds. We also study operators involving the Higgs and gluon fields.Comment: v2: 41 pages, 12 tables, 4 figures. Plots of the RG-induced bounds from S and T added, presentation of our approach in sections 2 and 4 improved, a few typos fixed, references added, conclusions and analysis unchanged. Version to appear in JHE

An Investigation in Applying Image Retrieval Techniques to X-Ray Engineering Pictures

Using image retrieval techniques in analysing Non-destructive testing reults is a new challenge in both computing science and engineering applications. Objective of this research is to develop an image retrieval system to analyse X-ray images for welding industry. The content based image retrieval has been used in this investigation, particularly in feature vector paradigm and similarity as well as detailed analysis towards single defects. It is found that X-ray images can be digitally analysed qualitatively and quantitatively easily. It concludes that the use of existing CBIR techniques can provide a platform to quickly develop new image analysis tools

Hamiltonian truncation crafted for UV-divergent QFTs

We develop the theory of Hamiltonian Truncation (HT) to systematically study RG flows that require the renormalization of coupling constants. This is a necessary step towards making HT a fully general method for QFT calculations. We apply this theory to a number of QFTs defined as relevant deformations of d=1+1 CFTs. We investigated three examples of increasing complexity: The deformed Ising, Tricritical-Ising, and non-unitary minimal model M(3,7). The first two examples provide a crosscheck of our methodologies against well established characteristics of these theories. The M(3,7) CFT deformed by its Z2-even operators shows an intricate phase diagram that we clarify. At a boundary of this phase diagram we show that this theory flows, in the IR, to the M(3,5) CFT

Bridging Positivity and S-matrix Bootstrap Bounds

The main objective of this work is to isolate Effective Field Theory scattering amplitudes in the space of non-perturbative two-to-two amplitudes, using the S-matrix Bootstrap. We do so by introducing the notion of Effective Field Theory cutoff in the S-matrix Bootstrap approach. We introduce a number of novel numerical techniques and improvements both for the primal and the linearized dual approach. We perform a detailed comparison of the full unitarity bounds with those obtained using positivity and linearized unitarity. In most cases, the S-matrix Bootstrap bounds are stronger. Moreover, we discuss the notion of Spin Zero and UV dominance along the boundary of the allowed amplitude space by introducing suitable observables. Finally, we show that this construction also leads to novel bounds on operators of dimension less or equal than six.Comment: 40 pages + appendice

Policy change and partisan politics : understanding family policy differentiation in two similar countries

This article looks at how different electoral competition dynamics can result in differentiated party positioning on childcare and family policy. Italy and Spain are compared using a most similar case design. The presence of women in politics,the socioeconomic profiles of the voters of the two main left-wing and right-wing Italian and Spanish parties, and opinions on traditional norms of motherhood explain different policy trajectories and higher incentives for the conservative party in Spain to converge toward the social democratic party in more progressive views of family policy

Gearing up for the next generation of LFV experiments, via on-shell methods

Lepton Flavor Violating (LFV) observables such as $\mu\to e\gamma$, $\mu\to 3e$ and $\mu N \to eN$ are among the best probes for new physics at the TeV scale. In the near future the bounds on these observables will improve by many orders of magnitude. In this work we use the SM EFT to understand the impact of these measurements. The precision reach is such that the interpretation of the bounds requires an analysis of the dimension-six operator mixing up to the two-loop level. Using on-shell amplitude techniques, which make transparent many selection rules, we classify and calculate the different operator mixing chains. At the leading order, on-shell techniques allow to calculate anomalous dimensions of SM EFT operators from the product of tree-level amplitudes, even for two-loop renormalization group mixings. We illustrate the importance of our EFT approach in models with extra vector-like fermions.Comment: 29 page