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Quantum electrodynamics (QED) provides a highly accurate description of phenomena involving the interaction of atoms with light. We argue that the quantum theory describing the interaction of cold atoms with a vibrating membrane--quantum…
Infrared quantum electrodynamics (IR-QED) acquires a natural geometric interpretation once soft photons are described as adiabatically transported electron-photon clouds. Within this framework, the relevant infrared structure is encoded in…
The purpose of this paper is to construct a quantum field theory suitable for describing quantum electrodynamics and Yang-Mills theory in a form which satisfies the conditions of the Millennium prize offered by the Clay Mathematics…
Non-perturbative solutions to the quantum-field theory is a topic of current and broad interest, especially for the heavy ion and laser physics communities, since they investigate particle production in the presence of strong external…
Unifying quantum theory and gravity remains a fundamental challenge in physics. While most existing literature focuses on the ultraviolet (UV) modifications of quantum theory due to gravity, this work shows that generic infrared (IR)…
We present a study of the IR behaviour of a three-dimensional super-renormalisable quantum field theory (QFT) consisting of a scalar field in the adjoint of $SU(N)$ with a $\varphi^4$ interaction. A bare mass is required for the theory to…
The hypothesis is suggested that the equation for the Dirac free wave field is, in fact, a group-theoretical relation describing propagation of specific microscopic deviations of space geometry from the euclidean one (closed topological…
In theories with long-range forces like QED or perturbative gravity, loop corrections lead to vanishing amplitudes. There are two well-known procedures to address these infrared divergences: dressing of asymptotic states and inclusion of…
We present a controlled mechanical exfoliation technique for bulk 3D topological insulators that yields atomically clean ultrathin flakes, enabling quantum well states (QWS) of Dirac electrons to be clearly resolved. Achieving reliable…
Systems of free particles in a quantum theory based on a Galois field (GFQT) are discussed in detail. In this approach infinities cannot exist, the cosmological constant problem does not arise and one irreducible representation of the…
We review the theory of quantum fields propagating in an arbitrary, classical, globally hyperbolic spacetime. Our review emphasizes the conceptual issues arising in the formulation of the theory and presents known results in a…
Successful applications of a conceptually novel setup of Quantum Field Theory, that accounts for all subtheories of the Standard Model (QED, Electroweak Interaction and Higgs, Yang-Mills and QCD) and beyond (Helicity 2), call for a…
We study soft photon emission during scattering of Faddeev-Kulish charged states in QED, at leading order in perturbation theory. The charged asymptotic particles are accompanied by clouds of an infinite number of soft photons of energy…
We illustrate the mass and charge renormalization procedures in quantum field theory using, as an example, a simple model of interacting electrons and photons. It is shown how addition of infinite renormalization counterterms to the…
The extended algebra of the free electromagnetic fields, including infrared singular fields, and the almost radial gauge, both introduced earlier, are postulated for the construction of the quantum electrodynamics in a Hilbert space (no…
Infrared singularities in massless gauge theories are known since the foundation of quantum field theories. The root of this problem can be tracked back to the very definition of these long-range interacting theories such as QED. It can be…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
We build the fully relativistic quantum field theory related to the asymmetric Dirac fields. These fields are solutions of the asymmetric Dirac equation, a Lorentz covariant Dirac-like equation whose positive and "negative" frequency plane…
We formulate a new concept of asymptotic completeness for two-dimensional massless quantum field theories in the spirit of the theory of particle weights. We show that this concept is more general than the standard particle interpretation…
Scattering in 3+1-dimensional QED is believed to give rise to transitions between different photon vacua. We show that these transitions can be removed by taking into account off-shell modes which correspond to Li\'enard-Wiechert fields of…