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Publication# Bootstrapping amplitudes of scalar particles

Abstract

Quantum Field Theories are a central object of interest of modern physics, describing fundamental interactions of matter. However, current methods give limited insight into strongly coupling theories. S-matrix bootstrap program, described in this thesis, aims to provide insight into these strongly coupled theories, by mapping the space of consistent scattering amplitudes that obey properties imposed by unitarity, Lorentz invariance and causality. This thesis aims to outline the basic principles of the program, along with steps to construct numerical S-matrix bootstrap experiment, presents the \texttt{Wolfram Mathematica} library developed by author to automatize parts of the procedure that are shared among experiments, and finally discusses the research on 4d conformal field theories, which, by relevant deformation, can be turned into interacting QFTs, in which bootstrapping the scattering amplitudes allowed finding lower bounds on $a$-anomaly coefficient in the investigated cases.

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Related concepts (34)

Ontological neighbourhood

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Scalar field theory

In theoretical physics, scalar field theory can refer to a relativistically invariant classical or quantum theory of scalar fields. A scalar field is invariant under any Lorentz transformation. The only fundamental scalar quantum field that has been observed in nature is the Higgs field. However, scalar quantum fields feature in the effective field theory descriptions of many physical phenomena. An example is the pion, which is actually a pseudoscalar.

Quantum field theory

In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles.

Bootstrap model

The term "bootstrap model" is used for a class of theories that use very general consistency criteria to determine the form of a quantum theory from some assumptions on the spectrum of particles. It is a form of S-matrix theory. In the 1960s and '70s, the ever-growing list of strongly interacting particles — mesons and baryons — made it clear to physicists that none of these particles is elementary.

Miguel Alexandre Ribeiro Correia

In this thesis we study how physical principles imposed on the S-matrix, such as Lorentz invariance, unitarity, crossing symmetry and analyticity constrain quantum field theories at the nonperturbative level. We start with a pedagogical introduction to the ...

The classical Lagrangian of the Standard Model enjoys the symmetry of the full conformal group if the mass of the Higgs boson is put to zero. This is a hint that conformal symmetry may play a fundamental role in the ultimate theory describing nature. The o ...

In this Letter, we address the question of whether the conformal invariance can be considered as a global symmetry of a theory of fundamental interactions. To describe Nature, this theory must contain a mechanism of spontaneous breaking of the scale symmet ...