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A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
The in-plane magnetic field suppresses the quantum coupling between electrons in a double quantum well structure. The microscopical theory of this effect is developed and confirmed experimentally. We have shown that the decrease of the…
A concise survey is given of the general method of reduction in the number of coupling parameters. Theories with several independent couplings are related to a set of theories with a single coupling. The reduced theories may or may not have…
The relation between renormalization and short distance singular divergencies in quantum field theory is studied. As a consequence a finite theory is presented. It is shown that these divergencies are originated by the multiplication of…
Scattering amplitudes in quantum field theory are independent of the field parameterization, which has a natural geometric interpretation as a form of `coordinate invariance.' Amplitudes can be expressed in terms of Riemannian curvature…
A series of informal seminars at graduate-student level on the subject of coupling dependence in quantum field theory, with an elementary introduction to the notion of resurgent function that forms the appropriate framework for the coupling…
Quantum field theory (QFT) describes nature using continuous fields, but physical properties of QFT are usually revealed in terms of measurements of observables at a finite resolution. We describe a multiscale representation of a free…
A structural explanation of the coupling constants in the standard model, i.e the fine structure constant and the Weinberg angle, and of the gauge fixing contributions is given in terms of symmetries and representation theory. The coupling…
With the present trend in experimental particle physics of probing yet shorter distances and with the requirement on the theoretical side of renormalizability, conformal invariance becomes an attractive symmetry for particle interactions.…
I review the theory of renormalization, as applied to weak-coupling perturbation theory in quantum field theories.
For two discrete-level quantum systems in interaction, we follow the displacement in the complex plane of the eigen-energies of the compound system when the spectrum of one of the two systems becomes continuous. These new points are usually…
I study the problem of renormalizing a non-renormalizable theory with a reduced, eventually finite, set of independent couplings. The idea is to look for special relations that express the coefficients of the irrelevant terms as unique…
We develop a new spectroscopic method to quickly and intuitively characterize the coupling of two microwave-photon-coupled semiconductor qubits via a high-impedance resonator. Highly distinctive and unique geometric patterns are revealed as…
We examine resonances for two systems consisting of a particle coupled to a massless boson's field. The field is the free field in the whole space. In the first system, the particle is confined inside a ball. We show that besides the usual…
Quantum gauge theories with finite-dimensional representation spaces are constructed that can have canonical gauge field theories as singular limits. They describe nature as a recursive quantum assembly by iterating Fermi-Dirac…
It is shown how the programme of decoherence can be applied in the context of quantum field theory. To illustrate the role of gauge invariance, we first discuss the charge superselection rule in quantum electrodynamics in some detail. We…
Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For…
The concept of discrepancy plays an important role in the study of uniformity properties of point sets. For sets of random points, the discrepancy is a random variable. We apply techniques from quantum field theory to translate the problem…
A systematic study of recursive renormalization of Feynman amplitudes is carried out both in Euclidean and in Minkowski configuration space. For a massless quantum field theory (QFT) we use the technique of extending associate homogeneous…
The path integral formulation of Quantum Field Theory implies an infinite set of local, Schwinger-Dyson-like relations. Exact renormalization group equations can be cast as a particular instance of these relations. Furthermore, exact scheme…