Quantum Field Theoretical Approach Research Articles

Schwarzschild Black Hole from Perturbation Theory to All Orders.

Applying the quantum field theoretic perturbiner approach to Einstein gravity, we compute the metric of a Schwarzschild black hole order by order in perturbation theory. Using recursion, this calculation can be carried out in de Donder gauge to all orders in Newton's constant. The result is a geometric series which is convergent outside a disk of finite radius, and it agrees within its region of convergence with the known de Donder gauge metric of a Schwarzschild black hole. It thus provides a first all-order perturbative computation in Einstein gravity with a matter source, and this series converges to the known nonperturbative expression in the expected range of convergence.

Strong fluctuation theory of Tatarskii: quantum field theoretic approach – a critical assessment

In this paper, we carried out a critical investigation of the strong fluctuation theory using a quantum field theoretic approach [Tatarskii VI. The effects of the turbulent atmosphere on wave propagation. Jerusalem: IPST; 1971]. We employed the Dyson and Bethe-Salpeter equations to derive the radiative transfer equation (RTE) for the Green's function of the radiant intensity. We proceeded to obtain estimates of the domain of validity of the RTE. The results thus obtained satisfy both the optical theorem for waves in random media and energy conservation. We also derived the RTE for our problem by employing a recently developed scale-separated asymptotic theory [Bal G., Komorowski T, Ryzhik L. Kinetic limits of waves in random media. Kinet Relat Models. 2010;3:529–644]. Although the RTE obtained by the two approaches are identical, we explain that the applicability regimes, and hence validity conditions are different.

An algebraic quantum field theoretic approach to toric code with gapped boundary

Topologically ordered quantum spin systems have become an area of great interest, as they may provide a fault-tolerant means of quantum computation. One of the simplest examples of such a spin system is Kitaev’s toric code. Naaijkens made mathematically rigorous the treatment of toric code on an infinite planar lattice (the thermodynamic limit), using an operator algebraic approach via algebraic quantum field theory. We adapt his methods to study the case of toric code with gapped boundary. In particular, we recover the condensation results described in Kitaev and Kong and show that the boundary theory is a module tensor category over the bulk, as expected.

Birth process of electron-positron pairs inside supercritical fields

We propose a computational quantum field theoretical approach to obtain a microscopic insight into the creation process of electrons and positrons as well as their subsequent motion inside a supercritical external field with space-time resolution. A machine-learning–based method permits us to address fundamental questions such as where inside the interaction region the particles are being created and what their initial velocity distribution is. It suggests that the particles' most likely birth positions change in time during the dynamics. At early times the particles' birth density is roughly proportional to the square of the force field, but in the long-time and steady state production regime their possible birth locations narrow down significantly. Counterintuitively, this leads for longer times to the occurrence of “birth-free” zones within the field, where particles are no longer created even though the electric field is maximal there. The genetic-programming–based symbolic regression algorithms first learn multiple sequences of partially dressed positronic spatial probability densities as training data and then exploit their features as a function of the dressing strength in order to predict the particles' true distribution in space and momentum.

On-shell approach to neutrino oscillations

In the usual quantum field theoretical approach, neutrino oscillations are studied diagonalising either the mass or matter Hamiltonians. In this paper we analyse the problem from an on-shell amplitude perspective, where Lagrangians or Hamiltonians are not available. We start by studying in detail how flavor enters in the amplitudes and how the PMNS matrix emerges. We then analyse the elastic amplitude of two neutrinos and two charged leptons that induce matter effects and propose a strategy to obtain the known results of the standard oscillation theory without Hamiltonians. Finally, we extend the previously proposed procedure and use the most general elastic 4-point amplitude to study beyond the Standard Model effects on oscillations.

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.

Dirac type relativistic quantum mechanics for massive photons

Constructing a relativistic quantum mechanics (RQM) for a massive photon, without appealing to the quantum field theoretical approach such as the massive Proca model, we find a new theoretical particle solution which allows the massive photon having either positive or negative energy as solutions. In particular, we predict the existence of the so-called anti-photon corresponding to the negative energy solution, similar to the positron in the Dirac RQM for an electron. Note that the anti-photons could be an intense radiation flare of the gamma ray burst. In this RQM for the massive photon, we construct a positive definite probability density and a nontrivial diagonal Hamiltonian, and also discuss a massless photon. Moreover we confirm the covariances of the relativistic equation of motion for the massive photon and the corresponding probability continuity equation under the Lorentz transformation.

Neutrino Mixing and Oscillations in Quantum Field Theory: A Comprehensive Introduction

We review some of the main results of the quantum field theoretical approach to neutrino mixing and oscillations. We show that the quantum field theoretical framework, where flavor vacuum is defined, permits giving a precise definition of flavor states as eigenstates of (non-conserved) lepton charges. We obtain the exact oscillation formula, which in the relativistic limit reproduces the Pontecorvo oscillation formula and illustrates some of the contradictions arising in the quantum mechanics approximation. We show that the gauge theory structure underlies the neutrino mixing phenomenon and that there exists entanglement between mixed neutrinos. The flavor vacuum is found to be an entangled generalized coherent state of SU(2). We also discuss flavor energy uncertainty relations, which impose a lower bound on the precision of neutrino energy measurements, and we show that the flavor vacuum inescapably emerges in certain classes of models with dynamical symmetry breaking.

Classical observables from coherent-spin amplitudes

The quantum field-theoretic approach to classical observables due to Kosower, Maybee and O’Connell provides a rigorous pathway from on-shell scattering amplitudes to classical perturbation theory. In this paper, we promote this formalism to describe general classical spinning objects by using coherent spin states. Our approach is fully covariant with respect to the massive little group SU(2) and is therefore completely synergistic with the massive spinor-helicity formalism. We apply this approach to classical two-body scattering due gravitational interaction. Starting from the coherent-spin elastic-scattering amplitude, we derive the classical impulse and spin kick observables to first post-Minkowskian order but to all orders in the angular momenta of the massive spinning objects. From the same amplitude, we also extract an effective two-body Hamiltonian, which can be used beyond the scattering setting. As a cross-check, we rederive the classical observables in the center-of-mass frame by integrating the Hamiltonian equations of motion to the leading order in Newton’s constant.

Reactor Antineutrino Anomaly Reanalysis in Context of Inverse-Square Law Violation

We discuss a possibility that the so-called reactor antineutrino anomaly (RAA), which is a deficit of the ν¯e rates in the reactor experiments in comparison to the theoretical expectations, can at least in part be explained by applying a quantum field-theoretical approach to neutrino oscillations, which in particular predicts a small deviation from the classical inverse-square law at short (but still macroscopic) distances between the neutrino source and detector. An extensive statistical analysis of the current reactor data on the integrated ν¯e event rates vs. baseline is performed to examine this speculation. The obtained results are applied to study another long-standing puzzle—gallium neutrino anomaly (GNA), which is a missing νe flux from 37Ar and 51Cr electron-capture decays as measured by the gallium–germanium solar neutrino detectors GALLEX and SAGE.

Quantum Field Theory Beyond the S-Matrix Formalism

Particle transitions passing over finite space and time intervals are self-consistently described within a novel quantum field-theoretical approach based on Feynman diagrams in configuration space. The transition to momentum space is performed following the rules modified so as to consider the geometry of neutral-meson and neutrino oscillation experiments. Using the processes of decay of an unstable scalar particle at a macroscopic distance from the source and of neutral kaon and neutrino oscillations as examples, we demonstrate that their known characteristics are adequately reproduced within the proposed approach.

Neutrinos in curved spacetime: Particle mixing and flavor oscillations

We present a quantum field theoretical approach to the vacuum neutrino oscillations in curved space, we analyze the non--trivial interplay between quantum field mixing and field quantization in curved space and derive new oscillation formulae. We compute the formulae explicitly in the spatially flat FLRW metrics for universes dominated by a cosmological constant and by radiation. We evaluate the transition probabilities in the Schwarzschild black hole metric, and we show that the Hawking radiation affects the oscillations of neutrinos. We show that our results are consistent with those of previous analyses when the quantum mechanical limit is considered.

Gravitons and pions

Both gravitons and pions are described by non-linear and non-renormalizable actions at low energies. These are most usefully treated by effective field theory, which is a full quantum field theoretic approach that relies only on the low energy degrees of freedom and their interactions. The gravitational case is particularly clean because of the masslessness of the graviton and the wide separation of scales. This essay provides an overview of this approach.

Space-time-resolved Breit-Wheeler process for a model system

We study the creation process of an electron-positron pair as a result of the collision between two incoming photons with full spatial and temporal resolution. The dynamics of the four involved particles is described by a simplified model based on a Yukawa Hamiltonian in one spatial dimension. This quantum field theoretical approach permits us to go beyond the usual external field approximation and to study the depletion of the two colliding photon wave packets due to the back reaction of the created electron-positron pair. If the spatial extension of the incoming photons is sufficiently narrow, we predict an interesting blueshift with regard to the optimum incoming photon momentum that can maximize the pair-creation yield close to the threshold momentum.

The variety of approaches to the problem of the derivation of Dirac equation

Purpose. The Dirac equation is one of the fundamental equations of modern theoretical physics. It is in service more than 90 years (1928–2018). The application today is much wider than the areas of quantum mechanics, quantum field theory, atomic and nuclear physics, solid state physics. The successful derivation of some equation of mathematical physics is the first step to successful application. In such process the essence of the corresponding model of nature, the mathematical principles and the physical foundations are visualized. Here we deal with the different approaches to the problem of the Dirac equation derivation. Methods. The quantum-mechanical, quantum field-theoretical, group-theoretical, algebraic, symmetrical, statistical, stochastical and numerical approaches are used. Results. The 26 different ways of the Dirac equation derivation are presented. The various physical principles and mathematical formalisms are used. Three original approaches of the authors to the problem are given. They are (i) the generalization of H. Sallhofer derivation, (ii) the obtaining of the massless Dirac equation from the Maxwell equations in maximally symmetrical form, (iii) the derivation of the Dirac equation with nonzero mass from the relativistic quantum mechanics of the fermion-antifermion spin s = 1/2 doublet. In some sense the role of the Dirac equation today is demonstrated. Conclusions. The original investigation of the problem of the Dirac equation derivation is presented. The different approaches, which are based on the various mathematical and physical principles, are considered (26 methods). Therole of the scientists from Uzhhorod is shown. The importance of place of the Dirac equation in modern theoretical physics is discussed.

Spectral density, Levinson's theorem, and the extra term in the second virial coefficient for the one-dimensional δ -function potential

In contrast with the 3D result, the Beth-Uhlenbeck (BU) formula in 1D contains an extra -1/2 term. The origin of this -1/2 term is explained using a spectral density approach. To be explicit, a delta-function potential is used to show that the correction term arises from a pole of the density of states at zero energy. The spectral density method shows that this term is actually an artifact of the non-normalizability of the scattering states and an infrared cutoff regularization scheme has to be used to get the correct result in 1D. The formal derivation of the BU formula would miss this term since it ignores the effects of the boundary terms. While the result is shown for the delta-function potential, the method and result are valid for more general potentials. Additionally, the 1D Levinson's theorem can be extracted from the spectral density method using the asymptotic form of general potentials. The importance of the result lies in the fact that all these correction terms in 1D have a universal source: a pole at zero energy. Similar calculations using quantum field theoretical approaches (without explicit infrared cutoff regularization schemes) also show the same subtleties with the correction term originating from the zero energy scattering states (appendix A).

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.

X(3872) as virtual companion pole of the charm–anticharm state χc1(2P)

We study the spectral function of the axial-vector charmonium state [Formula: see text] coupled to [Formula: see text] mesons, by employing a quantum field theoretical approach: a pronounced enhancement close to the [Formula: see text] threshold, to be identified with the [Formula: see text], emerges. In the complex plane we find two poles: a pole for the broad seed state [Formula: see text], and — in the easiest scenario — a virtual pole for the [Formula: see text]. Thus, our approach describes both the seed state and the dynamically generated [Formula: see text] simultaneously. In particular, it explains the most prominent, both molecular-like and quarkonium-like, features of the [Formula: see text]: its very small width (the decay into [Formula: see text] is predicted to be about 0.5 MeV), the enhanced radiative decay into [Formula: see text] with respect to [Formula: see text], and the isospin breaking decay into [Formula: see text] (thanks to [Formula: see text] loops mediating this decay channel). At the same time, we aim to determine the pole position and the properties of the charmonium seed state: quite interestingly, even if a pole is always present, it is possible that there is no peak corresponding to this state in the spectral function, thus potentially explaining why the corresponding resonance could not yet be seen in experiments.

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.

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.