Quantum electron self-interaction in a strong laser field

The quantum state of an electron in a strong laser field is altered if the interaction of the electron with its own electromagnetic field is taken into account. Starting from the Schwinger-Dirac equation, we determine the states of an electron in a plane-wave field with inclusion, at leading order, of its electromagnetic self-interaction. On the one hand, the electron states show a pure quantum contribution to the electron quasimomentum, conceptually different from the conventional classical one arising from the quiver motion of the electron. On the other hand, the electron self-interaction induces a distinct dynamics of the electron spin, whose effects are shown to be measurable in principle with available technology.     

Scalar quantum field theory on fractals

We investigate scale invariant measures over multiple variables for scalar field theories by imitating Wiener’s construction of the measure on the space of functions of one variable. We assign random fields values on the vertices of simple geometric shapes (triangles, squares, tetrahedra) which are subdivided into a finite number of similar shapes. We find several Gaussian measures with anomalous scaling associated with these field variables. A non-Gaussian fixed point arises from the Ising model on a fractal. In the continuum limit, we construct correlation functions that vary as a power of the distance. It is either a positive power (analogous to the Wiener process) or a negative power depending on the subdivision scheme used; however it is an irrational number for all the examples. This suggests that in the continuum limits it corresponds to quantum field theories (random fields) on spaces of fractional dimension.     

Quantum field theory in the infinite temperature limit

The T = ∞ limit for renormalizable 4-dimensional Euclidean QFT is considered. A general argument is presented in three examples: φ³, QED, QCD. Using an expansion of the Green's functions generating functional, it is shown at T = ∞ quantum dynamics generally becomes 3 dimensional. All superficially divergent diagrams survive at T = ∞ and ensure renormalization of effective dynamics. The correction to naive dimensional reduction is studied; appearance of “electric” masses in QED and QCD is shown to be the result of such a correction. A curious symmetry of the generating functional in QED and QCD, its implications and breaking by the thermal corrections of heavy modes are discussed. Presence of the symmetry implies survival of some fermion modes at T = ∞.     

Zero-mass limit in perturbative quantum field theory

A newR-operation which satisfies Bogolubov-Parasiuk and Hepp recurrence and which is infrared and ultra violet convergent graph by graph, is defined in perturbative quantum field theory. This new subtraction scheme is used to achieve the zero-mass limit of a massive field theory.Chargé de recherche CNRS. — Work supported in part by Alexander Von Humboldt fellowship.Work supported in part by Deutsche Forschungsgemeinschaft. — Institut für theoretische Physik, Freie Universität Berlin, Berlin, Federal Republic of Germany, and present address: Radiological Research Laboratory, Columbia University, 630 West 168 St. New York, New York 10032, USA.     

Dual field theory of strong interactions

A dual field theory of strong interactions is derived from a Lagrangian of the Yang-Mills and Higgs fields. The existence of a magnetic monopole of mass 2397 MeV and Dirac chargeg=(137/2)e is incorporated into the theory. Unification of the strong, weak, and electromagnetic forces is shown to converge at the mass of the intermediate vector bosonW ^±. The coupling constants of the strong and weak interactions are derived in terms of the fine-structure constant=1/137.     

Scalar quantum field theory with a complex cubic interaction

In this Letter it is shown that an i phi(3) quantum field theory is a physically acceptable model because the spectrum is positive and the theory is unitary. The demonstration rests on the perturbative construction of a linear operator C, which is needed to define the Hilbert space inner product. The C operator is a new, time-independent observable in PT-symmetric quantum field theory.     

Time-dependent density-functional theory with a self-interaction correction

We discuss an implementation of the self-interaction correction for the local-density approximation to time-dependent density-functional theory. A variational formulation is given, taking care of the necessary constraints. A manageable and transparent propagation scheme using two sets of wave functions is proposed and applied to laser excitation with subsequent ionization of a dimer molecule.     

Magnetic susceptibility of a two-dimensional electron gas in the quantum strong magnetic field limit

It is shown that the peak values of the magnetic susceptibility of a two-dimensional electron gas in the quantum strong magnetic field limit are integral multiples of $\text{μ}{}^2{}_{\mathrm{B}}\text{2π}$.     

Transit-time effects in a strong field inverted lamb dip theory

The inverted Lamb dip theory for a spatially-bounded plane laser beam is presented, valid for arbitrary gas pressure levels and field intensities. Line shape, power-broadening, contribution of transit-time and gas pressure effects to the dip linewidth have been computed and are found to be in perfect agreement with experimental data. In the limit of low pressure and intensity, the dip linewidth is found to depend only on the beam radius and the mean thermal velocity of molecules.     

Hydrodynamic theory of electron transport in a strong magnetic field

The mode coupling contribution to the transverse transport coefficients of a three-dimensional one-component plasma in a strong external magnetic field is calculated. For very strong fields it is found that the tagged particle diffusion rate, the thermal diffusion rate, and the coefficient of viscosity in the plane orthogonal to the field have a Bohm-like B ^–1 behavior. The mode coupling mechanism responsible for such an effect is always one that involves the finite-frequency upper hybrid modes.     

The Thomas-Fermi atom in a strong magnetic field: The weak ionization limit

It is proved that the binding energy, radius and chemical potential of the N-electron Thomas-Fermi atom with the nuclear charge Z in a strong magnetic field at q = 1 − N/Z 1 may be expressed as a power series in q^1/3 and In q. The exact values of the first expansion coefficients are found. A comparison with numerical data shows these expansions to be applicable up to q = 0.2.     

On the large N limit of conformal field theory

Following recent advances in large N matrix mechanics, I discuss here the free (Cuntz) algebraic formulation of the large N limit of two-dimensional conformal field theories of chiral adjoint fermions and bosons. One of the central results is a new affine free algebra which describes a large N limit of affine Lie algebra. Other results include the associated free-algebraic partition functions and characters, a free-algebraic coset construction, free-algebraic construction of , free-algebraic vertex operator constructions in the large N Bose systems, and a provocative new free-algebraic factorization of the ordinary Koba-Nielsen factor.     

Strong-segregation limit of the self-consistent field theory for diblock copolymer melts

The self-consistent field theory (SCFT) introduced by Helfand for diblock copolymer melts is expected to converge to the strong-segregation theory (SST) of Semenov in the asymptotic limit, c \chi N ? \rightarrow ∞ . However, past extrapolations of the lamellar/cylinder and cylinder/sphere phase boundaries, within the standard unit-cell approximation, have cast some doubts on whether or not this is actually true. Here we push the comparison further by extending the SCFT calculations to c \chi N = 512000 , by accounting for exclusion zones in the coronae of the cylindrical and spherical unit cells, and by examining finite-segregation corrections to SST. In doing so, we provide the first compelling evidence that SCFT does indeed reduce to SST.