Quantum Field Theoretical Description Research Articles

Quantum corrections to tunnelling amplitudes of neutral scalar fields

Though theoretical treatments of quantum tunnelling within single-particle quantum mechanics are well-established, at present, there is no quantum field-theoretic description (QFT) of tunnelling. Due to the single-particle nature of quantum mechanics, many-particle effects arising from quantum field theory are not accounted for. Such many-particle effects, including pair-production, have proved to be essential in resolving the Klein-paradox. This work seeks to determine how quantum corrections affect the tunnelling probability through an external field. We investigate a massive neutral scalar field, which interacts with an external field in accordance with relativistic quantum mechanics. To consider QFT corrections, we include another massive quantised neutral scalar field coupling to the original via a cubic interaction. This study formulates an all-order recursive expression for the loop-corrected scalar propagator, which contains only the class of vertex-corrected Feynman diagrams. This equation applies for general external potentials. Though there is no closed-form analytic solution, we also demonstrate how to approximate the QFT corrections if a perturbative coupling to the quantised field is assumed.

Minimal-length quantum field theory: a first-principle approach

Phenomenological models of quantum gravity often consider the existence of some form of minimal length. This feature is commonly described in the context of quantum mechanics and using the corresponding formalism and techniques. Although few attempts at a quantum field-theoretical description of a minimal length has been proposed, they are rather the exception and there is no general agreement on the correct one. Here, using the quantum-mechanical model as a guidance, we propose a first-principle definition of a quantum field theory including a minimal length. Specifically, we propose a two-step procedure, by first describing the quantum-mechanical models as a classical field theory and subsequently quantizing it. We are thus able to provide a foundation for further exploration of the implications of a minimal length in quantum field theory.

Toward a quantum field theoretical description of oscillation effects

Toward a quantum field theoretical description of oscillation effects

Quantum version of transport coefficients in Nambu–Jona-Lasinio model at finite temperature and strong magnetic field

We have estimated parallel and perpendicular components of electrical conductivity and shear viscosity of quark matter at finite magnetic field and temperature by using their one-loop Kubo expressions in the framework of Nambu–Jona-Lasinio (NJL) model. At finite magnetic field, a non-trivial medium dependence of those quantities can be found. Previously these NJL-profiles have been addressed in relaxation time approximation, where cyclotron motion of quarks with medium dependent mass plays the key role. With respect to the earlier estimations, the present work provides further enriched profiles via Kubo framework, where field theoretical descriptions of quark transport with medium dependent mass and (Landau) quantized energy have been identified as the key ingredients. Hence the present study can be considered as the complete quantum field theoretical description of the transport coefficients in the framework of NJL model at finite temperature and magnetic field.

Gravity as a Quantum Field Theory

Classical gravity is understood as the geometry of spacetime, and it seems very different from the other known interactions. In this review, I will instead stress the analogies: Like strong interactions, the low energy effective field theory of gravity is related to a nonlinearly realized symmetry, and like electroweak interactions, it is a gauge theory in Higgs phase, with a massive connection. I will also discuss the possibility of finding a UV complete quantum field theoretic description of all interactions.

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.

Editorial for the Special Issue “Asymptotic Safety in Quantum Gravity”

Asymptotically safe quantum gravity (ASQG) attempts to provide a standard quantum-field theoretic description of quantum spacetime across arbitrarily small length scales [...]

Low-energy effective quantum field theoretic description of excitations about soliton configurations

Solitons are the classical field configurations connecting two trivial vacua. These are also the solutions of classical field equations of motion with particle-like properties. Moreover, they are localized in space, having finite energy, and are stable against decay into radiation. The coherent state description of kink-solitons is discussed in the present article. Further, the relation between topological solitons and occupation numbers corresponding to low momentum excitations are also discussed coherently. The description of the low energy excitations about solitons in quantum field theory is the main theme of this article. Further, a few physical observables, namely some low order correlation functions, are computed up to certain integral forms. Furthermore, we have shown that it is possible to detect the presence of soliton-like classical configurations in many-particle systems from the nature of the one-point function and non-conservation of momentum feature of one-point, two-point and three-point functions in this low-energy effective field theory of these excitations.

Casimir and Casimir-Polder Forces in Graphene Systems: Quantum Field Theoretical Description and Thermodynamics

We review recent results on the low-temperature behaviors of the Casimir-Polder and Casimir free energy an entropy for a polarizable atom interacting with a graphene sheet and for two graphene sheets, respectively. These results are discussed in the wide context of problems arising in the Lifshitz theory of van der Waals and Casimir forces when it is applied to metallic and dielectric bodies. After a brief treatment of different approaches to theoretical description of the electromagnetic response of graphene, we concentrate on the derivation of response function in the framework of thermal quantum field theory in the Matsubara formulation using the polarization tensor in (2 + 1)-dimensional space—time. The asymptotic expressions for the Casimir-Polder and Casimir free energy and entropy at low temperature, obtained with the polarization tensor, are presented for a pristine graphene as well as for graphene sheets possessing some nonzero energy gap Δ and chemical potential μ under different relationships between the values of Δ and μ. Along with reviewing the results obtained in the literature, we present some new findings concerning the case μ≠0, Δ=0. The conclusion is made that the Lifshitz theory of the Casimir and Casimir-Polder forces in graphene systems using the quantum field theoretical description of a pristine graphene, as well as real graphene sheets with Δ>2μ or Δ<2μ, is consistent with the requirements of thermodynamics. The case of graphene with Δ=2μ≠0 leads to an entropic anomaly, but is argued to be physically unrealistic. The way to a resolution of thermodynamic problems in the Lifshitz theory based on the results obtained for graphene is discussed.

Quantum field theoretical description of the Casimir effect between two real graphene sheets and thermodynamics

The analytic asymptotic expressions for the Casimir free energy and entropy for two parallel graphene sheets possessing nonzero energy gap $\Delta$ and chemical potential $\mu$ are derived at arbitrarily low temperature. Graphene is described in the framework of thermal quantum field theory in the Matsubara formulation by means of the polarization tensor in (2+1)-dimensional space-time. Different asymptotic expressions are found under the conditions $\Delta>2\mu$, $\Delta=2\mu$, and $\Delta<2\mu$ taking into account both the implicit temperature dependence due to a summation over the Matsubara frequencies and the explicit one caused by a dependence of the polarization tensor on temperature as a parameter. It is shown that for both $\Delta>2\mu$ and $\Delta<2\mu$ the Casimir entropy satisfies the third law of thermodynamics (the Nernst heat theorem), whereas for $\Delta=2\mu$ this fundamental requirement is violated. The physical meaning of the discovered anomaly is considered in the context of thermodynamic properties of the Casimir effect between metallic and dielectric bodies.

Extracting the Field Theory Description of a Quantum Many-Body System from Experimental Data

Quantum field theory is a powerful tool to describe the relevant physics governing complex quantum many-body systems. Here we develop a general pathway to extract the irreducible building blocks of quantum field theoretical descriptions and its parameters purely from experimental data. This is accomplished by extracting the one-particle irreducible (1PI) vertices from which one can construct all observables. To match the capabilities of experimental techniques used in quantum simulation experiments, our approach employs a formulation of quantum field theory based on equal-time correlation functions only. We illustrate our procedure by applying it to the quantum sine-Gordon model in thermal equilibrium. The theoretical foundations are illustrated by estimating the irreducible vertices at equal times both analytically and using numerical simulations. We then demonstrate explicitly how to extract these quantities from an experiment where we quantum simulate the sine-Gordon model by two tunnel-coupled superfluids. We extract the full two-point function and the interaction vertex (four-point function) and their variation with momentum, encoding the `running' of the couplings. The measured 1PI vertices are compared to the theoretical estimates, verifying our procedure. Our work opens new ways of addressing fundamental questions in quantum field theory, which are relevant in high-energy and condensed matter physics, and in taking quantum phenomena from fundamental science to practical technology.

Neutrino evolution in dense matter and electromagnetic field

Neutrino evolution in dense matter and electromagnetic field is studied within quantum-field theoretical description on the base of a modification of the Standard Model, where the neutrinos are combined in S U(3)-multiplets. A quantum wave equation for neutrino in matter and electromagnetic field is obtained. In quasi-classical approximation a general method for calculating the probabilities of different spin-flavor transitions of neutrino in constant homogeneous field and moving matter with constant polarization is developed. In two-flavor model the explicit form of the solutions is obtained in constant electromagnetic field taking into account the transition magnetic moments. The obtained spin-flavor transition probabilities are compared to the results for unpolarized moving matter.

Quantum field-theoretical description of neutrino and neutral kaon oscillations

It is shown that the neutrino and neutral kaon oscillation processes can be consistently described in quantum field theory using only plane waves of the mass eigenstates of neutrinos and neutral kaons. To this end, the standard perturbative S-matrix formalism is modified so that it can be used for calculating the amplitudes of the processes passing at finite distances and finite time intervals. The distance-dependent and time-dependent parts of the amplitudes of the neutrino and neutral kaon oscillation processes are calculated and the results turn out to be in accordance with those of the standard quantum mechanical description of these processes based on the notion of neutrino flavor states and neutral kaon states with definite strangeness. However, the physical picture of the phenomena changes radically: now, there are no oscillations of flavor or definite strangeness states, but, instead of it, there is interference of amplitudes due to different virtual mass eigenstates.

Stochastic electrodynamics simulations for collective atom response in optical cavities

We study the collective optical response of an atomic ensemble confined within a single-mode optical cavity by stochastic electrodynamics simulations that include the effects of atomic position correlations, internal level structure, and spatial variations in cavity coupling strength and atom density. In the limit of low light intensity the simulations exactly reproduce the full quantum field-theoretical description for cold stationary atoms and at higher light intensities we introduce semiclassical approximations to atomic saturation that we compare with the exact solution in the case of two atoms. We find that collective subradiant modes of the atoms, with very narrow linewidths, can be coupled to the cavity field by spatial variation of the atomic transition frequency and resolved at low intensities, and show that they can be specifically driven by tailored transverse pumping beams. We show that the cavity optical response, in particular both the subradiant mode profile and the resonance shift of the cavity mode, can be used as a diagnostic tool for the position correlations of the atoms and hence the atomic quantum many-body phase. The quantum effects are found to be most prominent close to the narrow subradiant mode resonances at high light intensities. Although an optical cavity can generally strongly enhance quantum fluctuations via light confinement, we show that the semiclassical approximation to the stochastic electrodynamics model provides at least a qualitative agreement with the exact optical response outside the subradiant mode resonances even in the presence of significant saturation of the atoms.

First Evidence of Running Cosmic Vacuum: Challenging the Concordance Model

Abstract Despite the fact that a rigid -term is a fundamental building block of the concordance ΛCDM model, we show that a large class of cosmological scenarios with dynamical vacuum energy density together with a dynamical gravitational coupling G or a possible non‐conservation of matter, are capable of seriously challenging the traditional phenomenological success of the ΛCDM. In this paper, we discuss these “running vacuum models” (RVMs), in which consists of a nonvanishing constant term and a series of powers of the Hubble rate. Such generic structure is potentially linked to the quantum field theoretical description of the expanding universe. By performing an overall fit to the cosmological observables SN Ia+BAO+H(z)+LSS+BBN+CMB (in which the WMAP9, Planck 2013, and Planck 2015 data are taken into account), we find that the class of RVMs appears significantly more favored than the ΛCDM, namely, at an unprecedented level of . Furthermore, the Akaike and Bayesian information criteria confirm that the dynamical RVMs are strongly preferred compared to the conventional rigid -picture of the cosmic evolution.

From LHC physics to Dirac-Weyl materials

The quantum field theoretical description of particle physics under extreme conditions, namely, at finite temperature, density and in the presence of external magnetic fields, can naturally be extended to describe phenomenology in other branches of physics. In this contribution, I review some aspects of particle physics in the realm of condensed matter physics, particularly graphene and other Dirac-Weyl materials carried out in Mexico. I explore several features of the dynamics of fermions in (2+1)-dimensions which are relevant to heavy ion experiments, but that can be tested in table top experiments.

Erratum: Quantum field theoretical description for the reflectivity of graphene [Phys. Rev. D91, 045037 (2015)

Erratum: Quantum field theoretical description for the reflectivity of graphene [Phys. Rev. D<b>91</b>, 045037 (2015)

Dynamical gap generation in topological insulators

We developed a quantum field theoretical description for the surface states of three-dimensional topological insulators. Within the relativistic quantum field theory formulation, we investigated the dynamics of low-lying surface states in an applied transverse magnetic field. We argued that, by taking into account quantum fluctuations, in three-dimensional topological insulators there is dynamical generation of a gap by a rearrangement of the Dirac sea. By comparing with available experimental data we found that our theoretical results allowed a consistent and coherent description of the Landau level spectrum of the surface low-lying excitations. Finally, we showed that the recently detected zero-Hall plateau at the charge neutral point could be accounted for by chiral edge states residing at the magnetic domain boundaries between the top and bottom surfaces of the three-dimensional topological insulator.

Interacting Dark Matter andq-Deformed Dark Energy Nonminimally Coupled to Gravity

In this paper, we propose a new approach to study the dark sector of the universe by considering the dark energy as an emergingq-deformed bosonic scalar field which is not only interacting with the dark matter, but also nonminimally coupled to gravity, in the framework of standard Einsteinian gravity. In order to analyze the dynamic of the system, we first give the quantum field theoretical description of theq-deformed scalar field dark energy and then construct the action and the dynamical structure of this interacting and nonminimally coupled dark sector. As a second issue, we perform the phase-space analysis of the model to check the reliability of our proposal by searching the stable attractor solutions implying the late-time accelerating expansion phase of the universe.

Extended Supersymmetric Structures in Gapped and Superconducting Graphene

In view of the many quantum field theoretical descriptions of graphene in 2 + 1 dimensions, we present another field theoretical feature of graphene, in the presence of defects. Particularly, we shall be interested in gapped graphene in the presence of a domain wall and also for superconducting graphene in the presence of a vortex. As we explicitly demonstrate, the gapped graphene electrons that are localized on the domain wall are associated with four N = 2 one-dimensional supersymmetries, with each pair combining to form an extended N = 4 supersymmetry with non-trivial topological charges. The case of superconducting graphene is more involved, with the electrons localized on the vortex being associated with n one-dimensional supersymmetries, which in turn combine to form an N = 2n extended supersymmetry with non-trivial topological charges. As we shall prove, all supersymmetries are unbroken, a feature closely related to the number of the localized fermions and also to the exact form of the associated operators. In addition, the corresponding Witten index is invariant under compact and odd perturbations.