Quantum tunneling as a pseudoparticle solution
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Date
2025-07-03
Authors
Φράγκος, Τρύφωνας
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Abstract
The present dissertation is dedicated to the development of instanton methods as a non-perturbative approach to quantum field theory, presented at an introductory level. Instantons are classical solutions to the equations of motion formulated in imaginary (Euclidean) time and they encode information about quantum tunneling processes between distinct vacuum states. As will be demonstrated early in this work, instantons arise naturally in the path integral formalism, both in quantum mechanics and in quantum field theory, where transition amplitudes are computed by summing over all possible field configuration. The significance of instantons becomes particularly clear in gauge theories, which form the foundation of the Standard Model of particle physics. Their role is especially prominent in quantum chromodynamics (QCD)—the gauge theory describing strong interactions—where instanton contributions capture essential vacuum properties that are inaccessible through any order of perturbation theory. In this sense, instantons provide a powerful window into the deep, topologically non-trivial structure of the QCD vacuum.
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Quantum mechanics, Quantum field theory, Yang-Mills theories