Ground states in non-relativistic quantum electrodynamics

The excited states of a charged particle interacting with the quantized electromagnetic field and an external potential all decay, but such a particle should have a true ground state – one that minimizes the energy and satisfies the Schr?dinger equation. We prove quite generally that this state exists for all values of the fine-structure constant and the ultraviolet cutoff. We also show the same thing for a many-particle system under physically natural conditions. Oblatum 21-IX-2000 & 8-IV-2001?Published online: 18 June 2001     

The quantum electrodynamics of relativistic bound states with cutoffs. I

In this note, we consider a Hamiltonian with ultraviolet and infrared cutoffs describing the interaction of relativistic electrons and positrons in a Coulomb potential with transversal photons in Coulomb gauge. We prove that the Hamiltonian is self-adjoint in the Fock space and has a ground state for a sufficiently small coupling constant.     

Ultraviolet-finite quantum electrodynamics

Institute of Nuclear Research, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 79, No. 3, pp. 371–377, June, 1989.     

Topological quantum electrodynamics

It is shown that Dirac's theory of the electron in a Coulomb field is a topological quantum theory.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 11, pp. 1557–1559, November, 1991.     

Finite quantum electrodynamics

It is shown that the ultraviolet divergences encountered in the lowest order perturbation calculations of quantum electrodynamics no longer appear if the theory is expanded so as to include the mu meson, a triplet of heavy axial vector bosons and two heavy polar vector bosons in addition to the electron and photon, and suitably chosen couplings between them are introduced.     

Dual symmetry of quantum electrodynamics

Conclusions Thus, the introduction of a magnetic charge into electrodynamics from the point of view of dual symmetry arguments is not only justified but necessary. In this case one achieves mutual consistency between the symmetry of the Maxwell equations with sources and the free Maxwell equations. However, Maxwell's equations can be symmetrized without introducing a new type of particle (Dirac monopole). Treating the known particles as doubly-charged particles is selfconsistent and does not contradict experimental data if there is a universal ratio of the electric and the magnetic charges for all particles [5, 21–23]; the corresponding single-charge formulation of electrodynamics corresponds to a definite choice of the dual gauge.Our analysis also shows that the charge quantization condition must be present in any Lorentz invariant quantum formulation of the theory of magnetic charge. Logically, one can have magnetically charged particles whose charge does not follow from the charge quantization condition. But there are then no purely electromagnetic causes for introducing such particles.It is appropriate to emphasize that our starting from the Lorentz-invariant S matrix was essentially dictated by the possibility of demonstrating explicitly the mutual consistency of Lorentz invariance and dual invariance of electrodynamics.Finally, we should mention (see also [24]) that, irrespective of the possible role of doubly charged particles in the construction of hadron models [18, 25, 26], such particles necessitate a reformulation of electrodynamics at the classical and the quantum level.Institute of Physics, Academy of Sciences of the Belorussian SSR. Translated from Teoreticheskaya Matematicheskaya Fizika, Vol. 13, No. 2, pp. 200–208, November, 1972.     

Axiomatic method in quantum electrodynamics

Theoretical and Mathematical Physics -     

String-like excitations in quantum electrodynamics

A study is made of the evolution of string-like excitations of the gauge field (exponentials ordered along the contour of integration) in free quantum electrodynamics and in electrodynamics with static sources. It is shown that such excitations are unstable and are transformed after radiation of excess energy into the field of Coulomb sources. These results are compared with calculations in lattice quantum electrodynamics. It is also shown that in this case the strong-coupling method is not suitable for solving the confinement problem.Joint Institute for Nuclear Research, Dubna. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No. 3, pp. 373–385, December, 1993.     

Energy density and flux in nonrelativistic quantum mechanics

A number of mathematical consequences of the Schroedinger equation are given and interpreted as local energy and momentum conservation laws. Several Hamiltonians are treated.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 8, pp. 1090–1095, August, 1992.     

Fiber Hamiltonians in non-relativistic quantum electrodynamics

A translation invariant Hamiltonian H of non-relativistic quantum electrodynamics is studied. This Hamiltonian is decomposed with respect to the total momentum PT: