Low-Energy Theorem Approach to One-Particle Singularity in QED{2+1}

On the basis a new conjecture, we present a new Lagrangian density and a new quantization method for QED, construct coupling operators and mass operators, derive scattering operators S_{f} and S_{w} which are dependent on each other and supplement new Feynman rules. S_{f} and S_{w} together determine a Fenman integral. Hence all Feynman integrals are convergent and it is unnecessary to introduce regularization and counterterms. That the energy of the vacuum state is equal to ...

This paper constructs exact classical solutions of the equations of QED. These are constructed in 4+2 dimensional space, which fibers over the usual 3+1 dimensional space-time. The solution is stationary and localised about a topological singularity in space time. The electromagnetic field is that of a point electric charge, positioned at the singularity. Away from the singularity, all the conserved currents vanish. The solution comes in 8 varieties, corresponding to any choi...

To our knowledge there are no complete results expressed in terms of eigenfunctions (even not strictly proved mathematically) related to the system of three or more charged quantum particles. For the system of the three such identical particles we suggest the asymptotic formula describing the behavior of eigenfunctions at infinity in configuration space.

In this work, we provide a non-perturbative description of the phenomenon of dynamical mass generation in the case of quantum electrodynamics in $2+1$ dimensions. We will use the Kugo-Ojima-Nakanishi formalism to conclude that the physical Hilbert space of the asymptotic photon field is the same as that of the Maxwell-Chern-Simons.

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 shown that singularities are caused by the massless degrees of freedom (i.e. the photons in the case of QED). In the Bloch-Nordsieck model the absence of the infrared catastrophe can be shown exactly by the complete summation of the radiati...

We consider a spin-$\frac12$ electron in a translation-invariant model of non-relativistic Quantum Electrodynamics (QED). Let $H(\vp,\sig)$ denote the fiber Hamiltonian corresponding to the conserved total momentum $\vp\in\R^3$ of the Pauli electron and the photon field, regularized by a fixed ultraviolet cutoff in the interaction term, and an infrared regularization parametrized by $0<\sig\ll1$ which we ultimately remove by taking $\sig\searrow0$. For $|\vp|<\puppbd$, all $\...

Based on the concept of extended particles recently introduced we perform a Gedankenexperiment accelerating single electrons with photons of suitably low frequency. Accounting for relativistic time dilation due to the acquired velocity and in infinite repetition of single absorption processes it can be shown that the kinetic energy in the infinite limit is equal to m_{e} c^{2}/2. However, the inertial mass of the electron seems enhanced, and it can be established that this en...

We propose a mathematically rigorous construction of the scattering matrix and the interacting fields in models of relativistic perturbative quantum field theory with massless fields and long-range interactions. We consider quantum electrodynamics and a certain model of interacting scalar fields in which the standard definition of the scattering matrix is not applicable because of the infrared problem. We modify the Bogoliubov construction using the ideas of Dollard, Kulish a...

In this work we consider a coupled system of Schwinger-Dyson equations for self-energy and vertex functions in QED_3. Using the concept of a semi-amputated vertex function, we manage to decouple the vertex equation and transform it in the infrared into a non-linear differential equation of Emden-Fowler type. Its solution suggests the following picture: in the absence of infrared cut-offs there is only a trivial infrared fixed-point structure in the theory. However, the presen...

A tentative proposal is demonstrated that there is a natural strategy to get rid of unphysical (UV) infinities in QFTs if one adopts the modern standard point of view that a fundamental theory that is complete and well-defined in all respects underlies the QFTs. This simple strategy works in principle for any interaction model and space-time dimension. It provides a physical rationality behind the UV divergence and the conventional renormalization programs and improves the la...