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Category# Quantum field theory

Summary

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. The equation of motion of the particle is determined by minimization of the Lagrangian, a functional of fields associated with the particle. Interactions between particles are described by interaction terms in the Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by Feynman diagrams according to perturbation theory in quantum mechanics.
History of quantum field theory
Quantum field theory emerged from the work of generations of theoretical physicists spanning much of the 20th century. Its development began in the 1920s with the description of interactions between light and electrons, culminating in the first quantum field theory—quantum electrodynamics. A major theoretical obstacle soon followed with the appearance and persistence of various infinities in perturbative calculations, a problem only resolved in the 1950s with the invention of the renormalization procedure. A second major barrier came with QFT's apparent inability to describe the weak and strong interactions, to the point where some theorists called for the abandonment of the field theoretic approach. The development of gauge theory and the completion of the Standard Model in the 1970s led to a renaissance of quantum field theory.
Quantum field theory results from the combination of classical field theory, quantum mechanics, and special relativity. A brief overview of these theoretical precursors follows.
The earliest successful classical field theory is one that emerged from Newton's law of universal gravitation, despite the complete absence of the concept of fields from his 1687 treatise Philosophiæ Naturalis Principia Mathematica.

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PHYS-432: Quantum field theory II

The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions such as Quantum Electrodynamics.

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The course builds on the course QFT1 and QFT2 and develops in parallel to the course on Gauge Theories and the SM.

PHYS-415: Particle physics I

Presentation of particle properties, their symmetries and interactions.
Introduction to quantum electrodynamics and to the Feynman rules.

Perturbation theory

In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In perturbation theory, the solution is expressed as a power series in a small parameter . The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of usually become smaller.

Beta function (physics)

In theoretical physics, specifically quantum field theory, a beta function, β(g), encodes the dependence of a coupling parameter, g, on the energy scale, μ, of a given physical process described by quantum field theory. It is defined as and, because of the underlying renormalization group, it has no explicit dependence on μ, so it only depends on μ implicitly through g. This dependence on the energy scale thus specified is known as the running of the coupling parameter, a fundamental feature of scale-dependence in quantum field theory, and its explicit computation is achievable through a variety of mathematical techniques.

Lamb shift

In physics the Lamb shift, named after Willis Lamb, refers to an anomalous difference in energy between two electron orbitals in a hydrogen atom. The difference was not predicted by theory and it cannot be derived from the Dirac equation, which predicts identical energies. Hence the Lamb shift refers to a deviation from theory seen in the differing energies contained by the 2S1/2 and 2P1/2 orbitals of the hydrogen atom.

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Topics in 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.

Standard Model

The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetic, weak and strong interactions – excluding gravity) in the universe and classifying all known elementary particles. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide, with the current formulation being finalized in the mid-1970s upon experimental confirmation of the existence of quarks.

Quantum electrodynamics

In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction.

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In this thesis, we study systems of active particles interacting via generic torques of different nature. We analyze the phase behavior of these systems, which results from the interplay between self-propulsion, excluded-volume and torques.We tackle the problem from two different perspectives. On the one hand, we derive a continuum field theory that describes a system of self-propelled particles subjected to generic torques. At the mean-field level, the linear stability analysis of the field equations unveils different instabilities of the homogeneous and isotropic state, leading to pattern formation and phase separation.On the other hand, we explore the phase diagrams of collections of aligning active Brownian particles by means of numerical simulations. We specifically focus on understanding what happens to motility-induced phase separation in the presence of different types of velocity alignment interactions. We study Vicsek-like alignment rules as well as dipolar interactions, which can be regarded as an alternative way of introducing effective alignment to the system. We extend the numerical simulations to also explore the phase behavior of mixtures of aligning active particles with different motilities. Here, we report a coupling between the fast and slow species, by which the fast species enhances the slow-species' motility. Finally, we address, at a fundamental level, what are the minimal ingredients leading to the emergence of a polarized phase in systems of aligning active particles. To do so, we propose a Hamiltonian model that could admit a transition to collective motion fulfilling the conservation of total linear momentum and derive a suitable algorithm to properly integrate the equations of motion.

Quantum Field Theory(QFT) as one of the most promising frameworks to study high energy and condensed matter physics, has been mostly developed by perturbative methods. However, perturbative methods can only capture a small island of the space of QFTs.QFT in hyperbolic space can be used to link the conformal bootstrap and massive QFT. Conformal boundary correlators also can be studied by their general properties such as unitarity, crossing symmetry and analicity. On the other hand, by sending the curvature radius to infinity we reach to the flat-space limit in hyperbolic space. This allows us to use conformal bootstrap methods to study massive QFT in one higher dimension and calculate observables like scattering amplitudes or finding bounds on the couplings of theory. The main goal of my research during my Ph.D. would be to study QFTs in hyperbolic space to better understand strongly coupled QFTs.Hamiltonian truncation is a numerical method to study strongly coupled QFTs by imposing a UV cutoff. We use this method to study strongly coupled QFT in hyperbolic space background. For simplicity, we start with scalar field theory in 2-dimensional AdS. We expect to extract the spectrum of our theory as a function of AdS curvature and find the boundary correlation functions.

Magnetic skyrmions are nanometric and non-trivial spin textures with non-zero topological charge. Their robustness against perturbations and the possibility to control them using external stimuli make them ideal candidates for future spintronic applications. In particular the magnetoelectric skyrmion host Cu2OSeO3 holds a lot of promise for low power devices since skyrmions in this compound can be controlled by electric fields alone. Using Lorentz transmission electron microscopy to perform real space and real time biasing experiments on thin lamellas of Cu2OSeO3 in a geometry that is most suitable for technological applications, we observe reproducible creation and annihilation of skyrmions. For a more quantitative analysis, we develop new feature detection algorithms to reliably extract skyrmion positions even in noisy images. We further produce Due to its low pinning, Cu2OSeO3 allows for the formation of large and well-arranged triangular skyrmion lattices. This makes this compound a perfect testbed to study the evolution of skyrmion configurations under external stimuli. Experiments are carried out again using Lorentz transmission electron microscopy on thin lamellas of Cu2OSeO3. We investigate how defects in skyrmion lattices are arranged at grain boundaries and develop algorithms to extract them and to directly visualize their alignment. These defects are at the core of the melting of skyrmion lattices in this system. We show that a controlled magnetic field ramp can induce skyrmion ensembles in Cu2OSeO3 to transition from a two-dimensional solid through a thus far unknown ordered liquid phase called the hexatic phase, to a liquid. We find that this transition is a topological defect-induced two-step process as predicted by the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory. Finally, we go beyond equilibrium phenomena to explore the effect of quenching the system from its liquid phase to its solid phase using different quench rates and find first evidence that our system belongs to the Kibble-Zurek universality class.

Gauge Theories And Modern Particle PhysicsPHYS-432: Quantum field theory II

Covers gauge theories, modern particle physics, the standard model, and field content.

Quantum Chromodynamics Overview

Covers Quantum Chromodynamics, including running coupling constant and confinement of quarks and gluons.

Quarks and Leptons: Spin-1/2 and Dirac Notation

Introduces quarks and leptons, discussing their spin, charge, and notation.