Field theoretical treatment of plasma modes in coupled two-dimensional systems

We investigate an assembly of two-dimensional electron systems, separated spatially but coupled by Coulomb interaction. The acoustic and the optical plasma modes are studied using a field theoretical method. It is found that a certain approximation in treating one class of diagrams gives an effective exchange potential equal to that calculated using the method of Kohn and Sham [1]. For small wave-vector, expressions equivalent to Boltzmann equations are obtained. Numerical results are finally obtained for the dependence of the frequency on wave vector and densities of the electron systems.     

A generalization of the Fermi-Breit equation to non-Coulombic spatial interactions

Starting from the relativistic invariance properties at classical level, we generalize the Darwin equation to the case of non-Coulombic spatial interactions. The relativistic correction terms for vector interactions are derived from a given nonrelativistic potential. We show that, for a Coulombic potential, the results coincide with those obtained in the Coulomb gauge. The results are adapted to the quantum theory obtaining a generalization of the Fermi-Breit equation. An Hermitian interaction operator is constructed. A critical comparison with other possible treatments of the retardation terms is performed also discussing the usual choice of the Coulomb gauge. Special attention is devoted to the construction of a model for quark interaction.     

On the meaning of a non-renormalizable theory of gravitation

The renormalizability of quantum gravity remains an open question while it has been established recently that quantum gravity in the presence of standard sources is non-renormalizable. In view of traditional confusion and ambiguities surrounding non-renormalizable quantum field theories, it has been felt that physical theories must be renormalizable. Recently a new, nonperturbative view of non-renormalizable theories has been suggested that may have relevance for various interactions including gravity and various sources. In a path integral approach to quantum field theory such a view attributes ‘hard cores’ in the space of field histories to non-renormalizable interactions. Just as with more familiar ‘hard cores’, turning off the interaction does not completely remove all effects of the potential. Consequently the interacting theory is not even continuously connected to the usual free theory, but rather to an alternative ‘pseudo-free’ theory that incorporates the vestiges of the ‘hard cores’. Some insight into what is the significance and interpretation of non-renormalizable interactions can be gleaned from exactly soluble models. Application of this philosophy of non-renormalizable interactions is discussed for the gravitational field in interaction with some standard sources.     

On gradient field theories: gradient magnetostatics and gradient elasticity

In this work, the fundamentals of gradient field theories are presented and reviewed. In particular, the theories of gradient magnetostatics and gradient elasticity are investigated and compared. For gradient magnetostatics, non-singular expressions for the magnetic vector gauge potential, the Biot–Savart law, the Lorentz force and the mutual interaction energy of two electric current loops are derived and discussed. For gradient elasticity, non-singular forms of all dislocation key formulas (Burgers equation, Mura equation, Peach–Koehler stress equation, Peach–Koehler force equation, and mutual interaction energy of two dislocation loops) are presented. In addition, similarities between an electric current loop and a dislocation loop are pointed out. The obtained fields for both gradient theories are non-singular due to a straightforward and self-consistent regularization.     

A UV completion of scalar electrodynamics

In previous works, we constructed UV-finite and unitary scalar field theories with an infinite spectrum of propagating modes for arbitrary polynomial interactions. In this paper, we introduce infinitely many massive vector fields into a U(1) gauge theory to construct a theory with UV-finiteness and unitarity.     

Self-Consistent Approximations in Relativistic Plasmas: Quasiparticle Analysis of the Thermodynamic Properties

We generalize the concept of conserving, Φ-derivable, approximations to relativistic field theories. Treating the interaction field as a dynamical degree of freedom, we derive the thermodynamic potential in terms of fully dressed propagators, an approach which allows us to resolve the entropy of a relativistic plasma into contributions from its interacting elementary excitations. We illustrate the derivation for a hot relativistic system governed by electromagnetic interactions.     

New boundary conformal field theories indexed by the simply laced Lie algebras

We consider the field theory of N massless bosons which are free except for an interaction localized on the boundary of their (1+1)-dimensional world. The boundary action is the sum of two pieces: a periodic potential and a coupling to a uniform abelian gauge field. Such models arise in open-string theory and dissipative quantum mechanics, and possibly in edge state tunneling in the fractional quantized Hall effect. We explicitly show that conformal invariance is unbroken for certain special choices of the gauge field and the periodic potential. These special cases are naturally indexed by semi-simple, simply laced Lie algebras. For each such algebra, we have a discrete series of conformally invariant theories where the potential and gauge field are conveniently given in terms of the weight lattice of the algebra. We compute the exact boundary state for these theories, which explicitly shows the group structure. The partition function and correlation functions are easily computed using the boundary state result.     

Integrable quantum field theories and conformal field theories from lattice models in the light-cone approach

The light-cone lattice approach to two-dimensional quantum field theories is generalized to a large class of vertex models with any number of possible states per link and any simple Lie group of symmetry. Starting from a given lattice model, different scaling limits are defined leading to conformal field theories or to massive integrable quantum field theories, for which the lattice hamiltonian, momentum and currents are constructed. For a large set of models, the complete mass spectrum is also exhibited. Our approach applies equally well to chiral fermionic theories (like the chiral Gross-Neveu) and to bosonic models like the principal chiral model.     

1D FFLO state in absence of time reversal symmetry breaking

We propose a route to a one-dimensional Fulde-Ferrell-Larkin-Ovchinnikov state in the absence of broken time-reversal symmetry. At present such a state may be encouraged in a clean (no disorder) AlAs quantum wire fabricated using the cleaved edge overgrowth technique. The fabrication technique captures two degenerate nonoverlapping bands separated in momentum-space by half an umklapp vector which leads to four Fermi points. Using field theoretic methods such as abelian bosonization and the renormalization group scheme we treat the important low energy long wavelength fermionic interaction terms for this one dimensional system. Due to the specific bandstructure arrangement of the quantum wire there is a new class of unique umklapp assisted interactions. These umklapp interactions are present at all electronic densities and are not related to the commensurability of the electron gas with the underlying lattice. We show that in the presence of the umklapp interactions and without any external perturbations such as a magnetic or electric field a singlet superconducting ground state is preferred with non-zero center-of-mass momentum for the Cooper pairs. The finite pairing momentum of the Cooper pairs is an indication of a Fulde-Ferrell-Larkin-Ovchinnikov state which is known to lead to inhomogeneous superconductivity.     

Generating functionals for harmonic expectation values of paths with fixed end points: Feynman diagrams for nonpolynomial interactions

We introduce a general class of generating functionals for the calculation of quantum-mechanical expectation values of arbitrary functionals of fluctuating paths with fixed end points in configuration or momentum space. The generating functionals are calculated explicitly for the harmonic oscillator with time-dependent frequency, and used to derive a smearing formula for correlation functions of polynomial and nonpolynomial functions of time-dependent positions and momenta. This formula summarizes the effect of quantum fluctuations, and serves to derive generalized Wick rules and Feynman diagrams for perturbation expansions of nonpolynomial interactions.     

Equation of state of a Fermi gas in the BEC-BCS crossover: a quantum Monte Carlo study

We calculate the equation of state of a two-component Fermi gas with attractive short-range interspecies interactions using the fixed-node diffusion Monte Carlo method. The interaction strength is varied over a wide range by tuning the value a of the s-wave scattering length of the two-body potential. For a>0 and a smaller than the inverse Fermi wave vector our results show a molecular regime with repulsive interactions well described by the dimer-dimer scattering length a(m)=0.6a. The pair correlation functions of parallel and opposite spins are also discussed as a function of the interaction strength.     

Some consequences of infinite mass renormalization

Using a finite form of local field equations some consequences of infinite mass renormalization are studied in a rigorous manner. The method is applied to various models. For pseudoscalar meson-nucleon interaction sufficient conditions are given for the equivalence to a direct Fermi coupling. Confirming a recent result byKroll, Lee, andZumino it is shown that a vector meson field should be proportional to the corresponding current if the bare meson mass is infinite. In the conventional treatment of neutral vector meson theories this causes certain difficulties which are analyzed in detail. In case of two vector fields coupled to the same current it is found that the fields must be proportional provided the bare masses are both infinite. In the Appendix finite local field equations are discussed for the coupling of a neutral vector meson field to the current of a spin 1/2 field.     

Modification of short-range repulsive interactions in ReaxFF reactive force field for Fe-Ni-Al alloy

The short-range repulsive interactions of any force field must be modified to be applicable for high energy atomic collisions because of extremely far from equilibrium state when used in molecular dynamics (MD) simulations. In this work, the short-range repulsive interaction of a reactive force field (ReaxFF), describing Fe-Ni-Al alloy system, is well modified by adding a tabulated function form based on Ziegler-Biersack-Littmark (ZBL) potential. The modified interaction covers three ranges, including short range, smooth range, and primordial range. The short range is totally predominated by ZBL potential. The primordial range means the interactions in this range is the as-is ReaxFF with no changes. The smooth range links the short-range ZBL and primordial-range ReaxFF potentials with a taper function. Both energies and forces are guaranteed to be continuous, and qualified to the consistent requirement in LAMMPS. This modified force field is applicable for simulations of energetic particle bombardments and reproducing point defects' booming and recombination effectively.     

Effect of the lattice alignment on Bloch oscillations of a Bose-Einstein condensate in a square optical lattice

We consider a Bose-Einstein condensate of ultracold atoms loaded into a square optical lattice and subject to a static force. For vanishing atom-atom interactions the atoms perform periodic Bloch oscillations for arbitrary direction of the force. We study stability of these oscillations for non-vanishing interactions, which is shown to depend on an alignment of the force vector with respect to the lattice crystallographic axes. If the force is aligned along any of the axes, the mean field approach can be used to identify the stability conditions. On the contrary, for a misaligned force one has to employ the microscopic approach, which predicts periodic modulation of Bloch oscillations in the limit of a large forcing.     

The gravitational interaction of conical strings

Up to now calculations of the interaction of cosmic strings have neglected gravity. We consider the purely gravitational interactions that occur at large distances, using the conical line singularity for the gravitational field of a string. We construct spaces with multiple intersecting conical strings, that are exactly consistent with General Relativity, and which can be covered in a single Minkowski coordinate patch, using a Regge calculus type construction. We show that after two such strings pass through each other they remain connected by another string, and we derive the branching rules which govern the junction of three strings. These rules apply to conical type strings in any smoothly curved background, whether they are straight or curved, moving or stationary, and they show that, at the junction, the three strings must be as coplanar as is possible in such a space. For these results to be matched onto the short range results of Field Theory calculations, it is suggested that gravitational radiation must be introduced. This would mean that gravitation is not negligible in these interactions.     

Instabilities in a two-dimensional polar-filament-motor system

The dynamical interaction between filaments and motor proteins is known for their propensity to self-organize into spatio-temporal patterns. Since the filaments are polar in the sense that motors define a direction of motion on them, the system can display a spatially homogeneous polar-filament orientation. We show that the latter anisotropic state itself may become unstable with respect to inhomogeneous fluctuations. This scenario shares similarities with instabilities in planarly aligned nematic liquid crystals: in both cases the wave vector of the instability may be oriented either parallel or oblique to the polarity axis. However, the encountered instabilities here are long-wave instead of short-wave and the destabilizing modes are drifting ones due to the polar symmetry. Additionally a nonpropagating transverse instability is possible. The stability diagrams related to the various wave vector orientations relative to the polarity axis are determined and discussed for a specific model of motor-filament interactions.     

An Alternative to the Gauge Theoretic Setting

The standard formulation of quantum gauge theories results from the Lagrangian (functional integral) quantization of classical gauge theories. A more intrinsic quantum theoretical access in the spirit of Wigner’s representation theory shows that there is a fundamental clash between the pointlike localization of zero mass (vector, tensor) potentials and the Hilbert space (positivity, unitarity) structure of QT. The quantization approach has no other way than to stay with pointlike localization and sacrifice the Hilbert space whereas the approach built on the intrinsic quantum concept of modular localization keeps the Hilbert space and trades the conflict creating pointlike generation with the tightest consistent localization: semiinfinite spacelike string localization. Whereas these potentials in the presence of interactions stay quite close to associated pointlike field strengths, the interacting matter fields to which they are coupled bear the brunt of the nonlocal aspect in that they are string-generated in a way which cannot be undone by any differentiation.     

Ab initio calculation of hyperfine and superhyperfine interactions for shallow donors in semiconductors

For the shallow group V donors in Si we show that the hyperfine interaction for the donor nucleus and the superhyperfine interactions for the first five shells of Si ligands can be quite accurately calculated using the local spin-density approximation of the density-functional theory. We treat the impurity problem in a Green's function approach. Since we have to truncate the long-ranged part of the defect potential, we do not obtain a localized gap state. Instead we identify the resonance above the conduction band with the paramagnetic defect state. We show that the hf and shf interactions thus obtained are at least as accurate as those obtained from one-electron theories with fitting parameters. Application of this first principles method to other shallow donors could be an essential help in defect identification.     

Space-time resolved approach for interacting quantum field theories

An alternative approach to the usual perturbative S-matrix evaluation of quantum field theories is presented which is nonperturbative and provides full space-time resolution. We study the dynamical development of the force between two fermion wave packets for the Yukawa system. The spatial distribution of the virtual bosons that act as mediators of the force can be analyzed along with the fermionic densities. Using a potential function for the fermion-fermion interaction is a good approximation to the field theoretical calculations when the Fock space is restricted to only one boson, but in the full quantum field theory the fermion-fermion force is enhanced by higher-order multiboson processes. Furthermore, the normally attractive fermion-fermion Yukawa force can, in principle, be manipulated to even be repulsive if the momentum modes available to the virtual bosons are restricted.     

Nonlinear equations of the gravitational field in the special theory of relativity

It is proposed that the nonlinearity of the field be taken into account with the help of a method which essentially consists of the fact that the structure of the Lagrangian, expressed in terms of the potential of the field and its derivatives, is not known a priori, but is obtained from a solution of the self-action equation in phase space in which the Lagrangian is the unknown. This equation has a solution and the Lagrangian turns out to be a nonpolynomial function with respect to the field potential. The gravitational field equations following from the variational principle have a similar structure to the equations of general relativity and coincide with them in the linear approximation. The equations of other fields taking into account gravitation, as well as the equation of motion of a test particle in a gravitational field, are constructed.