Feynman Diagram Technique Research Articles

Microscopic Theory of Nonlinear Hall Effect in Three-dimensional Magnetic Systems

Abstract The nonlinear Hall effect (NLHE) has been detected in various of condensed matter systems. Unlike linear Hall effect, NLHE may exist in physical systems with broken inversion symmetry in the crystal. On the other hand, real space spin texture may also break inversion symmetry and result in NLHE. In this letter, we employ the Feynman diagrammatic technique to calculate nonlinear Hall conductivity (NLHC) in three-dimensional magnetic systems. The results connect NLHE with the physical quantity of emergent electrodynamics which originates from the magnetic texture. The leading order contribution of NLHC $\chi_{abb}$ is proportional to the emergent toroidal moment $\mathcal{T}_{a}^{e}$ which reflects how the spin textures wind in three dimension.

Nonlocal gluon condensates in QCD sum rules

Nonlocal gluon condensates are vacuum expectations of the product of gluon field strength tensors. Short-distance expansions of two-, three-, and four-gluon condensates are presented up to dimension-8 local operators. We propose a method for calculating the Wilson coefficients based on the presented expansions and the Feynman diagram technique in the background field approach. The method is demonstrated using the glueball current correlators as examples. Methodological aspects of the background field approach are discussed in relation to glueball studies within QCD sum rules. We confirm the results for Operator Product Expansion (OPE) of the two-gluon $0^{\pm +}$ glueball current correlators and calculate additional contributions coming from dimension-6 four-quark condensate and dimension-8 mixed quark-gluon condensates. The OPEs used in QCD sum rules for three-gluon $0^{\pm +}$ glueballs are revisited up to dimension-6 order.

Quantum Field-Theoretical Description of Neutrino Oscillations in a Magnetic Field and the Solar Neutrino Problem

It is shown that the processes of neutrino oscillations in a magnetic field can be consistently described in the framework of a new quantum field-theoretical approach without use of the neutrino flavor states. It is based on the Feynman diagram technique with a modified distance-dependent propagator, which takes into account the geometry of neutrino oscillation experiments. Processes of neutrino oscillations in a magnetic field, where the neutrinos are detected through the weak charged- and neutral-current interaction, have been studied and numerical calculations have been carried out for some specific examples. Implications for the solar neutrinos are briefly discussed, and formulas for the asymptotic values of the normalized probability of solar neutrino oscillation processes are derived, which coincide with the observable ratio of the measurable neutrino flux to that predicted by the standard solar model.

Conversion of electromagnetic and gravitational waves by a charged black hole

In a strong electromagnetic field, gravitational waves are converted into electromagnetic waves of the same frequency, and vice versa. Here, we calculate scattering and conversion cross sections for a planar wave impinging upon a Reissner-Nordstr\"om black hole in electrovacuum, using the partial-wave expansion and numerical methods. We show that, at long wavelengths, the conversion cross section matches that computed by Feynman-diagram techniques, and at short wavelengths, the essential features are captured by a geometric-optics approximation. We demonstrate that the converted flux can exceed the scattered flux at large scattering angles, for highly-charged black holes. In the short-wavelength regime, the conversion effect may be understood in terms of a conversion phase that accumulates along a ray. We compute the scattering angle for which the converted and scattered fluxes are equal, as a function of charge-to-mass ratio; and we show that this scattering angle approaches 90\ifmmode^\circ\else\textdegree\fi{} in the extremal limit.

Phonon transport in disordered alloys: A Multiple-scattering approach

I present a formalism to calculate the configuration-averaged lattice thermal conductivity for substitutional random alloys. The method is based on multiple-scattering approach which can capture the effect of disorder-induced configuration fluctuations on single-particle and two-particle phonon Green functions in random alloys. The randomness of the system is dealt within the augmented space theorem. This is combined with a generalized Feynman diagrammatic technique to extract various useful results in the form of mathematical expressions. I show the structure of all possible scattering diagrams up to the fourth order and subsequently illustrate how to obtain Dyson's equation from a resummation of the diagrammatic series. I also study how disorder scattering affects two-particle Green functions associated with thermal response. It was shown explicitly how the disorder scattering renormalizes both the phonon propagators as well as the heat currents. I derive the relation between these renormalized heat currents and the self-energy of the propagators. I have also studied a different class of scattering diagrams which are not related to the self-energy but rather to the vertex corrections. The configuration-averaging scheme is straightforward to apply to other relevant quantities such as joint density of states, thermal diffusivity, etc., for random alloys. The developed formalism is applied to a realistic ${\mathrm{Au}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}$ binary alloy. The effect of disorder-induced corrections (as compared to the simple virtual crystal approximation) turns out to be appreciable in this alloy. The configuration-averaged lattice thermal conductivity for ${\mathrm{Au}}_{50}{\mathrm{Fe}}_{50}$ shows a quadratic behavior in low-temperature regime ($T\ensuremath{\le}30$ K), which increases smoothly to a $T$-independent saturated value at high $T$. Simulated thermal diffusivity $D(\ensuremath{\nu})$ helps to numerically estimate the mobility $\mathrm{edge}\phantom{\rule{0.28em}{0ex}}({\ensuremath{\nu}}_{c})$ which in turn evaluates the fraction of localized states. $D(\ensuremath{\nu})$ is found to decrease smoothly (almost linearly) in the high-$\ensuremath{\nu}$ range, which when fitted to ${({\ensuremath{\nu}}_{c}\ensuremath{-}\ensuremath{\nu})}^{\ensuremath{\alpha}}$ gives the critical $\mathrm{exponent}\phantom{\rule{0.28em}{0ex}}(\ensuremath{\alpha})$ to be 1.018 for ${\mathrm{Au}}_{50}{\mathrm{Fe}}_{50}$ alloy. This agrees fairly well with the scaling and other theories of Andersen localization.

Nonequilibrium green function technique for analyzing electron transport through single and two levels of interacting quantum dot

The electron transport through nanoelectronic device, fabricated by coupling a QD into two metallic electrodes, is analyzed theoretically using Non-equilibrium Green function formalism. The considered QD has one quantum level with one-site coulomb interaction (two-channel for transportation). The spectra function of this QD is obtained by using Feynman diagram technique for single-level model and the equation of motion method for two-level model. Analytical approximations of electric current through this device are presented at low temperature and at finite temperature. Depending on the analytical approaches, we will analyze the dependency of nano-device current on the QD size, level width, and temperature. Finally, the dependency of current on the applied voltages is analyzed with respect to coulomb-blocked diamonds. The current-applied voltages characteristics help us to understand the behavior of nano-devices that has two channels of transport. We will show where and why the two-channel nano-device shows two and one current steps depending on the chosen value of gate voltage.

NLO impact factor for inclusive photon+dijet production in e+A DIS at small x

We compute the next-to-leading order (NLO) impact factor for inclusive photon $+$dijet production in electron-nucleus (e+A) deeply inelastic scattering (DIS) at small $x$. An important ingredient in our computation is the simple structure of ``shock wave" fermion and gluon propagators. This allows one to employ standard momentum space Feynman diagram techniques for higher order computations in the Regge limit of fixed $Q^2\gg \Lambda_{\rm QCD}^2$ and $x\rightarrow 0$. Our computations in the Color Glass Condensate (CGC) effective field theory include the resummation of all-twist power corrections $Q_s^2/Q^2$, where $Q_s$ is the saturation scale in the nucleus. We discuss the structure of ultraviolet, collinear and soft divergences in the CGC, and extract the leading logs in $x$; the structure of the corresponding rapidity divergences gives a nontrivial first principles derivation of the JIMWLK renormalization group evolution equation for multiparton lightlike Wilson line correlators. Explicit expressions are given for the $x$-independent $O(\alpha_s)$ contributions that constitute the NLO impact factor. These results, combined with extant results on NLO JIMWLK evolution, provide the ingredients to compute the inclusive photon $+$ dijet cross-section at small $x$ to $O(\alpha_s^3 \ln(x))$. First results for the NLO impact factor in inclusive dijet production are recovered in the soft photon limit. A byproduct of our computation is the LO photon+ 3 jet (quark-antiquark-gluon) cross-section.

Two-Species Reaction-Diffusion System: the Effect of Long-Range Spreading

We study fluctuation effects in the two-species reaction-diffusion systemA+B→ Ø andA+A→ (Ø,A). In contrast to the usually assumed ordinary short-range diffusion spreading of the reactants we consider anomalous diffusion due to microscopic long-range hops. In order to describe the latter, we employ the Lévy stochastic ensemble. The probability distribution for the Lévy flights decays inddimensions with the distanceraccording to a power-lawr−d−σ. For anomalous diffusion (including Lévy flights) the critical dimensiondc=σdepends on the control parameterσ, 0<σ ≤ 2. The model is studied in terms of the field theoretic approach based on the Feynman diagrammatic technique and perturbative renormalization group method. We demonstrate the ideas behind theBparticle density calculation.

A New Quantum Field Theory Approach to the Description of Finite-Time Processes

Within the quantum field theory, a new approach to the description of processes taking place at finite space-time intervals is considered. It is based on the Feynman diagram technique in the coordinate representation, in which the transition to the momentum representation is modified in accordance with the existing experimental situation. As a result, the Feynman propagator of particles in the momentum representation changes, while the other Feynman rules remain unchanged. In this approach, wave packets are not used and the initial and final states of particles are described by plane waves, which significantly simplifies the calculations. By example of the decay of an unstable particle and neutrino oscillations, it is shown how the differential probabilities of these processes can be found and that the results obtained agree with the expected ones.

Description of processes passing at finite space-time intervals in the framework of quantum field theory

We consider a novel quantum field-theoretical approach to the description of processes passing at finite space-time intervals based on the Feynman diagram technique in the coordinate representation. The most know phenomena of this type are neutrino and neutral kaon oscillations. The experimental setting of these processes demands that the rules of passing to the momentum representation in the Feynman diagram technique be adjusted in accordance with it, which leads to a modification of the Feynman propagator in the momentum representation. The approach does not make use of wave packets: both initial and final particle states are described by plane waves, which simplifies the calculations considerably. We demonstrate the validity of the formalism by applying it to describing the decay of an unstable particle and neutrino oscillations. It is shown that the considered approach correctly reproduces the known results.

All-order calculations of the energy levels of heavy elements Indium (In) and Tin (Sn)

The energy levels of the heavy elements In, Sn+ and Sn are presented in this article. Dominating corrections beyond the relativistic Hartree-Fock method are included to all orders in the Coulomb interaction using the Feynman diagram technique and the correlation potential method. The configuration interaction technique is combined with the many-body perturbation theory to construct the many-electron wave function for valence electrons and to include core-valence correlations. The good agreement of the results of our calculation with experiment data illustrates the power of the method.

Passive Advection in a Percolation Process: Two-Loop Approximation

The paradigmatic model of the directed percolation process is studied near its second order phase transition between an absorbing and an active state. The model is first expressed in a form of Langevin equation and later rewritten into a field-theoretic formulation. The ensuing response functional is then analyzed employing Feynman diagrammatic technique and perturbative renormalization group method. Percolation process is assumed to occur in external velocity field, which has an additional effect on spreading properties. Kraichnan rapid change ensemble is used for generation of velocity fluctuations. The structure of the fixed points structure is obtained within the two-loop approximation.

Coherence length of neutrino oscillations in a quantum field-theoretical approach

We consider a novel quantum field-theoretical approach to the description of processes passing at finite space-time intervals based on the Feynman diagram technique in the coordinate representation. The most known processes of this type are neutrino and neutral kaon oscillations. The experimental setting of these processes requires one to adjust the rules of passing to the momentum representation in the Feynman diagram technique in accordance with it, which leads to a modification of the Feynman propagator in the momentum representation. The approach does not make use of wave packets, both initial and final particle states are described by plane waves, which simplifies the calculations considerably. We consider neutrino oscillation processes, where the neutrinos are produced in three-particle weak decays of nuclei and detected in the charged-current interaction with nuclei or in the charged- and neutral-current interactions with electrons. Particular examples are considered and it is shown that the momentum spread of the produced neutrinos and the energy dependence of the differential cross section of the detection process result in the suppression of neutrino oscillation, which is characterized by a coherence length specific for a pair of production and detection processes. This coherence length turns out to be much less than the coherence length in the standard quantum-mechanical approach defined by the quantum uncertainty of neutrino momentum.

A combined variational and diagrammatic quantum Monte Carlo approach to the many-electron problem

Two of the most influential ideas developed by Richard Feynman are the Feynman diagram technique and his variational approach. Here we show that combining both, and introducing a diagrammatic quantum Monte Carlo method, results in a powerful and accurate solver to the generic solid state problem, in which a macroscopic number of electrons interact by the long range Coulomb repulsion. We apply it to the quintessential problem of solid state, the uniform electron gas, which is at the heart of the density functional theory success in describing real materials, yet it has not been adequately solved for over 90 years. Our method allows us to calculate numerically exact momentum and frequency resolved spin and charge response functions. This method can be applied to a number of moderately interacting electron systems, including models of realistic metallic and semiconducting solids.

Neutrino Oscillation Processes with a Change of Lepton Flavor in Quantum Field-Theoretical Approach

The oscillating probabilities of lepton flavor changing neutrino oscillation processes, where neutrinos are detected by weak charged-current and neutral-current interactions, are calculated in a quantum field-theoretical approach to neutrino oscillations based on a modification of the Feynman propagator in the momentum representation. The approach is most similar to the standard Feynman diagram technique in the momentum representation. It is found that the oscillating distance-dependent probabilities of detecting an electron in experiments with neutrino production in the muonic decay of π+-meson and the detection of the produced neutrino by charged-current and neutral-current interactions exactly coincide with the corresponding probabilities calculated in the standard approach.

Quantum conductivity correction in a two-dimensional disordered pseudospin-1 system

Using the Feynman diagram techniques, we theoretically obtain the quantum conductivity correction for a two-dimensional pseudospin-1 electron system in the presence of long-range diagonal disorder. Theoretical results clearly reveal that the quantum correction depends on the sublattice correlation properties of disorder potential. The sublattice correlated disorder gives rise to normal weak localization, while the sublattice uncorrelated impurity potential leads to the absence of logarithmic term in quantum conductivity correction. Remarkably, those results cannot be understood by conventional symmetry classification. An additional symmetry operator involving internal sublattice degrees of freedom, analogous with the time reversal symmetry operator, enables us to clarify our findings from symmetry consideration.

Quantum Field Theory Description of Processes Passing at Finite Space and Time Intervals

We consider a new approach to the quantum field theory description of processes passing at finite space-time intervals. The formalism is based on the Feynman diagram technique in the coordinate representation supplemented with modified rules for the transition to the momentum representation reflecting specific experimental situations. This effectively implies that only the particle propagators in the momentum representation are modified, while the standard Feynman rules in the momentum representation remain unchanged. No wave packets are used in the approach, i.e., the initial and final states of particles are described by plane waves, which significantly simplifies the calculations. Three processes—neutrino oscillations, unstable particle decay, and neutral kaon oscillations—are used as examples to show that the proposed approach correctly reproduces the well-known results.

HS in flat spacetime: the effective action method

This is the first paper in a series of three dealing with HS theories in flat spacetime. It is divided in three parts. The first part is an elaboration on the method of effective action, initiated in a previous paper. We study the properties of correlators of currents in the free fermion coupled to external higher spin (HS) potentials, and develop techniques for their explicit calculation. In particular we show how they can be calculated via ordinary Feynman diagram techniques. We also introduce the concept of curvedL_infty algebra and show how it can be realized in the context of the fermion model. In part II we compare the results of the scalar model and those of the fermion model (coupled to HS fields). We show that the HS field formulation coming from the scalar model is the ‘square’ of the one ensuing from the fermion model. Finally, in part III, we analyse the possible obstructions that one may meet in constructing the effective action: these are the analogues of anomalies in ordinary gauge theories. We provide explicit and compact formulas of the latter.

Description of processes passing at finite space and time intervals in the framework of QFT

We consider a new approach to the description in the framework of QFT of processes passing at finite space and time intervals. The formalism is based on the Feynman diagram technique in the coordinate representation, in which the rules of passing to the momentum representation are modified in accordance with the experimental setup of neutrino oscillation experiments. In effect, only the propagators of particles in the momentum representation are modified, while all the other standard Feynman rules in the momentum representation remain the same. Since the initial and final particle states are described by plane waves, the approach does not need the use of wave packets, which greatly simplifies the calculations of amplitudes. Taking as examples the processes of displaced pion decay, neutral kaon and neutrino oscillations we show that the approach under consideration correctly reproduces the known standard results.

Quantum field-theoretical descriprion of neutrino oscillations in T2K experiment

We consider neutrino oscillations in the T2K experiment using a new quantum field-theoretical approach to the description of processes passing at finite space-time intervals. It is based on the Feynman diagram technique in the coordinate representation, supplemented by modified rules of passing to the momentum representation. Effectively this leads to the Feynman propagators in the momentum representation being modified, while the rest of the Feynman rules remain unchanged. The approach does not make use ofwave packets, the initial and final particle states are described by plane waves, which essentially simplifies the calculations. The oscillation fading out due to momentum distribution of the initial particles is taken into account. The obtained results reproduce the predictions of the standard description and confirm that the far detector position corresponds to the first minimum for muon production probability and the first maximum for electron production probability.