Browsing by Subject "Quantum field theory"
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Item Application of wavelets in few-body problems.(2012-08) Hewawasam, KuraviThis study is an application of wavelet numerical techniques in solving a non-perturbative Yukawa Hamiltonian in light-front quantum field theory. Once the problem is stated in the form of an integral equation, a wavelet basis of a particular scale is used to discretize the problem into a dense matrix. Wavelets are a class of functions with special properties. Daubachies wavelets are a subset of wavelets defined to have vanishing lower order moments, enabling Daubachies 2 and 3 wavelet bases to exactly represent polynomials of degree up to two. These properties make them useful as a basis set for various numerical methods. It was observed that a kernel containing structure in fine scales requires a fine scaling function basis to converge closer to analytical results. Once the kernel matrix is obtained, the wavelet transform followed by an absolute thresholding filters the dense kernel matrix to a sparse matrix. The sparse matrix eigenvalue problem was then solved and compared with the original eigenvalue problem. It was observed that as long as the problem is discretized with a scale fine enough to resolve the features of the kernel, higher levels of filtering would still reproduce eigenvalues that agree with the unfiltered problem.Item Coupled quantum systems in inflationary cosmology.(2010-08) Gumrukcuoglu, Ahmet EmirThe studies presented in this thesis describe applications of quantum field theory in a time dependent background. Two distinct problems are addressed in the framework of inflationary cosmology. The strict predictions of inflation are mostly in agreement with the Cosmic Microwave Background observations. In the recent years, large scale anomalies in the data motivated a series of analyses leading to a detection of broken statistical isotropy. Assuming that this effect is sourced by early time cosmology, I discuss the phenomenology of inflationary models extended to anisotropic backgrounds. Due to lack of rotational invariance, these models generically involve a system of coupled quantum fields. This leads to a tensor-scalar correlation function, which is a characteristic signature of these models. Another open question in cosmology involves the transition from inflation to the Hot Big Bang cosmology. In the presence of supersymmetric flat directions, the formation of the thermal radiation may undergo a dramatic delay, provided that these directions decay only perturbatively. In the scope of a toy model and a realistic example, both involving two flat directions, I discuss the nonperturbative decay that rapidly depletes the flat directions. If realized, this process can dramatically affect the previous assumptions on the thermalization scale. Due to the vast number of degrees of freedom, this problem generically involves coupled quantum fields. The decay of the flat directions gets contributions from both the diagonal (nonadiabatic evolution of frequency eigenvalues) and nondiagonal (nonadiabatic evolution of frequency eigenstates) effects. An additional characteristic effect of coupled quantization is the rotation of light eigenstates to heavy ones, which do not get produced in a diagonal system.Item Topics in generalized symmetries in the continuum and on the lattice(2023-06) Jacobson, TheodoreThis dissertation explores topics in quantum field theory from the perspective of generalized symmetries. Driven by new ideas in condensed matter and high energy physics, the notion of symmetry has been significantly expanded in recent years, giving rise to new insights and constraints on strongly-coupled quantum field theories. In this thesis we focus on the implications of higher-form symmetries for confining gauge theories, and discuss lattice discretizations of continuum quantum field theories where such global symmetries can be analyzed in a concrete setting. In the continuum, we examine the interplay between confinement and 1-form symmetries in gauge theories. We point out that in two spacetime dimensions, theories with 1-form symmetries necessarily have relevant deformations which directly impact confinement. We also show that SU(N) QCD with fundamental quarks has no emergent 1-form symmetry in the large N limit, despite the fact that the theory is confining at large N. On the lattice, we employ a recently-discovered approach known as the modified Villain formulation to discretize abelian Chern-Simons theory. We take particular care to maintain its global structure, symmetries, and 't Hooft anomalies at the lattice level. This thesis also contains an introduction to some basic concepts in generalized symmetries along with illustrative examples.