Quantum Field Theoretical Model Research Articles

The Small-N Series in the Zero-Dimensional O(N) Model: Constructive Expansions and Transseries

We consider the zero-dimensional quartic O(N) vector model and present a complete study of the partition function Z(g, N) and its logarithm, the free energy W(g, N), seen as functions of the coupling g on a Riemann surface. We are, in particular, interested in the study of the transseries expansions of these quantities. The point of this paper is to recover such results using constructive field theory techniques with the aim to use them in the future for a rigorous analysis of resurgence in genuine quantum field theoretical models in higher dimensions. Using constructive field theory techniques, we prove that both Z(g, N) and W(g, N) are Borel summable functions along all the rays in the cut complex plane Cπ=C\\R-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {C}_{\\pi } =\\mathbb {C}{\\setminus } \\mathbb {R}_-$$\\end{document}. We recover the transseries expansion of Z(g, N) using the intermediate field representation. We furthermore study the small-N expansions of Z(g, N) and W(g, N). For any g=|g|eıφ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g=|g| e^{\\imath \\varphi }$$\\end{document} on the sector of the Riemann surface with |φ|<3π/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\varphi |<3\\pi /2$$\\end{document}, the small-N expansion of Z(g, N) has infinite radius of convergence in N, while the expansion of W(g, N) has a finite radius of convergence in N for g in a subdomain of the same sector. The Taylor coefficients of these expansions, Zn(g)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_n(g)$$\\end{document} and Wn(g)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W_n(g)$$\\end{document}, exhibit analytic properties similar to Z(g, N) and W(g, N) and have transseries expansions. The transseries expansion of Zn(g)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_n(g)$$\\end{document} is readily accessible: much like Z(g, N), for any n, Zn(g)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_n(g)$$\\end{document} has a zero- and a one-instanton contribution. The transseries of Wn(g)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W_n(g)$$\\end{document} is obtained using Möbius inversion, and summing these transseries yields the transseries expansion of W(g, N). The transseries of Wn(g)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W_n(g)$$\\end{document} and W(g, N) are markedly different: while W(g, N) displays contributions from arbitrarily many multi-instantons, Wn(g)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W_n(g)$$\\end{document} exhibits contributions of only up to n-instanton sectors.

Observational constraints on the interacting dark energy — Dark matter (IDM) cosmological models

Particle creation (or annihilation) mechanisms, described by either quantum field theoretical models, or by the thermodynamics of irreversible processes, play an important role in the evolution of the early Universe, like, for example, in the warm inflationary scenario. Following a similar approach, based on the thermodynamics of open systems, in the present work we investigate the consequences of the interaction, decay, and particle generation in a many-component Universe, containing dark energy, dark matter, radiation, and ordinary matter, respectively. In this model, due to the interaction between these components, and of the corresponding thermodynamical properties, the conservation equations of different cosmological constituents are not satisfied individually. We introduce a thermodynamic description of the Universe, in which two novel physical aspects, the particle number balance equations, and the creation pressures, are considered, thus making the cosmological evolution equations thermodynamically consistent. To constrain the free parameters of the model several observational data sets are employed, including the Planck data sets, Riess 2020, BAO, as well as Pantheon data. By using a scaling ansatz for the dark matter to dark energy ratio, and by imposing constraints from Planck+Riess 2020 data, this model predicts an acceptable value for the Hubble parameter, and thus it may provide a solution to the so-called Hubble tension problem, much debated recently.

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The O(N) model

The functional renormalization group (FRG) approach is a powerful tool for studies of a large variety of systems, ranging from statistical physics over the theory of the strong interaction to gravity. The practical application of this approach relies on the derivation of so-called flow equations, which describe the change of the quantum effective action under the variation of a coarse-graining parameter. In the present work, we discuss in detail a novel approach to solve such flow equations. This approach relies on the fact that RG equations can be rewritten such that they exhibit similarities with the conservation laws of fluid dynamics. This observation can be exploited in different ways. First of all, we show that this allows to employ powerful numerical techniques developed in the context of fluid dynamics to solve RG equations. In particular, it allows us to reliably treat the emergence of nonanalytic behavior in the RG flow of the effective action as it is expected to occur in studies of, e.g., spontaneous symmetry breaking. Second, the analogy between RG equations and fluid dynamics offers the opportunity to gain novel insights into RG flows and their interpretation in general, including the irreversibility of RG flows. We work out this connection in practice by applying it to zero-dimensional quantum-field theoretical models. The generalization to higher-dimensional models is also discussed. Our findings are expected to help improving future FRG studies of quantum field theories in higher dimensions both on a qualitative and quantitative level.

Infraparticle quantum fields and the formation of photon clouds

A non-perturbative and exactly solvable quantum field theoretical model for a “dressed Dirac field” is presented, that exhibits all the kinematical features of QED: an appropriate delocalization of the charged field as a prerequisite for the global Gauss Law, superselected photon clouds (asymptotic expectation values of the Maxwell field), infraparticle nature of charged particles that cannot be separated from their photon clouds, broken Lorentz symmetry. The model serves as an intermediate leg on a new roadmap towards full QED, formulated as an off-shell theory, i.e., including a perturbative construction of its interacting charged fields. It also fills a gap in recent discussions of the “Infrared Triangle”, and points the way towards a new scattering theory for theories with massless particles of helicity ≥ 1, in which infraparticles can be described at the level of charged fields, rather than just states.

Observational Constraints on the Interacting Dark Energy - Dark Matter (Idm) Model

Particle creation (or annihilation) mechanisms, described by either quantum field theoretical models, or by the thermodynamics of irreversible processes, play an important role in the evolution of the early Universe, like, for example, in the warm inflationary scenario. Following a similar approach, based on the thermodynamics of open systems, in the present work we investigate the consequences of the interaction, decay, and particle generation in a many-component Universe, containing dark energy, dark matter, radiation, and ordinary matter, respectively. In this model, due to the interaction between these components, and of the corresponding thermodynamical properties, the conservation equations of different cosmological constituents are not satisfied individually. We introduce a thermodynamic description of the Universe, in which two novel physical aspects, the particle number balance equations, and the creation pressures, are considered, thus making the cosmological evolution equations thermodynamically consistent. To constrain the free parameters of the model several observational data sets are employed, including the Planck data sets, Riess 2020, BAO, as well as Pantheon data. By using a scaling ansatz for the dark matter to dark energy ratio, and by imposing constraints from Planck+Riess 2020 data, this model predicts an acceptable value for the Hubble parameter, and thus it may provide a solution to the so-called Hubble tension problem, much debated recently.

Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model

Several models of quantum gravity predict the emergence of a minimal length at Planck scale. This is commonly taken into consideration by modifying the Heisenberg uncertainty principle into the generalized uncertainty principle. In this work, we study the implications of a polynomial generalized uncertainty principle on the harmonic oscillator. We revisit both the analytic and algebraic methods, deriving the exact form of the generalized Heisenberg algebra in terms of the new position and momentum operators. We show that the energy spectrum and eigenfunctions are affected in a non-trivial way. Furthermore, a new set of ladder operators is derived which factorize the Hamiltonian exactly. The above formalism is finally exploited to construct a quantum field theoretic toy model based on the generalized uncertainty principle.

Higher loop [formula omitted] function for non-Hermitian PT symmetric [formula omitted] theory

We investigate Non-Hermitian quantum field theoretic model with ιgϕ3 interaction in 6-dimension. Such a model is PT-symmetric for the pseudo scalar field ϕ. We analytically calculate the 2-loop β function and analyze the system using renormalization group technique. Behavior of the system is studied near the different fixed points. Unlike gϕ3 theory in 6-dimension ιgϕ3 theory develops a new non trivial fixed point which is energetically stable. Existence of new non-trivial UV fixed points is also shown for three and four loop β-functions.

Singularity avoidance in quantum gravity

The purpose of this work is to investigate the consequences of quantum gravity for the singularity problem. We study the higher-derivative terms that invariably appear in any quantum field theoretical model of gravity, handling them both non-perturbatively and perturbatively. In the former case, by computing the contributions of the additional degrees of freedom to a congruence of geodesics, we show that the appearance of singularities is no longer a necessity. In the latter, which corresponds to treating the quantised general relativity as an effective field theory, we generalise the Hawking-Penrose theorems to include one-loop corrections of both massless matter and graviton fluctuations.

Dynamical generation of field mixing via flavor vacuum condensate

In this paper we study dynamical chiral symmetry breaking of a generic quantum field theoretical model with global chiral flavor symmetry. By purely algebraic means we analyze the vacuum structure for different symmetry breaking schemes and show explicitly how the ensuing non-trivial flavor vacuum condensate characterizes the phenomenon of field mixing. In addition, with the help of Ward-Takahashi identities we demonstrate the emergence of a correct number of Nambu-Goldstone modes in the physical spectrum.

Radiative corrections of order O(αEe/mN) to Sirlin’s radiative corrections of order O(α/π) to the neutron lifetime

We calculate the radiative corrections of order O(alpha E_e/m_N) as next-to-leading order corrections in the large nucleon mass expansion to Sirlin's radiative corrections of order O(alpha/pi) to the neutron lifetime. The calculation is carried out within a quantum field theoretic model of strong low-energy pion--nucleon interactions described by the linear sigma-model (LsM) with chiral SU(2)xSU(2) symmetry and electroweak hadron-hadron, hadron-lepton and lepton-lepton interactions for the electron-lepton family with SU(2)_L x U(1)_Y symmetry of the Standard Electroweak Model (SEM). Such a quantum field theoretic model is some kind a hadronized version of the Standard Model (SM). From a gauge invariant set of the Feynman diagrams with one-photon exchanges we reproduce Sirlin's radiative corrections of order O(alpha/pi), calculated to leading order in the large nucleon mass expansion, and calculate next-to-leading corrections of order O(alpha E_e/m_N). This confirms Sirlin's confidence level of the radiative corrections O(alpha E_e/m_N). The contributions of the LsM are taken in the limit of the infinite mass of the scalar isoscalar sigma-meson. In such a limit the LsM reproduces the results of the current algebra (Weinberg, Phys. Rev. Lett. {\bf 18}, 188 (1967)) in the form of effective chiral Lagrangians of pion-nucleon interactions with non--linear realization of chiral SU(2)xSU(2) symmetry. In such a limit the L$\sigma$M is also equivalent to Gasser-Leutwyler's chiral quantum field theory or chiral perturbation theory (ChPT) with chiral SU(2)xSU(2)symmetry and the exponential parametrization of a pion-field (Ecker, Prog. Part. Nucl. Phys. {\bf 35}, 1 (1995)).

A study of the vector meson ψ(4040)

We investigate the well-known $c\overline c $ vector state ψ(4040) in the frame-work of a quantum field theoretical model. In particular, we study its spectral function and search for the pole(s) in the complex plane. Quite interestingly, the spectral function has a non-standard shape and two poles are present. The role of the meson-meson quantum loops (in particular DD* ones) is crucial and could also explain the not yet conformed “state” Y(4008).

Excited vector mesons: phenomenology and predictions for a yet unknown vector ss state with a mass of about 1.93 GeV

The firm understanding of standard quark-antiquark states (including excited states) is necessary to search for non-conventional mesons with the same quantum numbers. In this work, we study the phenomenology of two nonets of excited vector mesons, which predominantly correspond to radially excited vector mesons with quantum numbers n2S+1LJ = 23S1 and to orbitally excited vector mesons with quantum numbers n2S+1LJ = 13D1. We evaluate the decays of these mesons into two pseudoscalar mesons and into a pseudoscalar and a ground-state vector meson by making use of a relativistic quantum field theoretical model based on flavor symmetry. Moreover, we also study the radiative decays into a photon and a pseudoscalar meson by using vector meson dominance. We compare our results to the PDG and comment on open issues concerning the corresponding measured resonances. Within our approach, we are also able to make predictions for a not-yet discovered ss state in the n2S+1LJ = 13D1 nonet, which has a mass of about 1.93 GeV. This resonance can be searched in the upcoming GlueX and CLAS12 experiments which take place at the Jefferson Lab.

Simple Model of Nonlinear Spin Waves in Graphene Structures

A series of theoretical and experimental works is known which investigated the magnetic properties of graphene structures. This is due, among other things, to the prospects of using graphene as a material for the needs of the future nanoelectronics and spintronics. In particular, it is known about the presence of ferromagnetic properties at temperatures up to 200 C and above in a single-layer graphene films that are free from impurities. Previously there was proposed a quantum field theoretical model describing the possible mechanism of ferromagnetism in graphene as a result of spontaneous breaking of spin symmetry of the surface density of valence electrons. The possible spatial configurations of the localized spin density were described. In this paper we investigate such spatially localized nonlinear spin configurations of the valence electron density on the graphene surface such as kinks, and their interactions, as well as quasibound metastable states of the interacting kinks and antikinks, that are breathers. The spectrum of such breathers is investigated. It is shown that under certain conditions, this spectrum has a discrete sector, which, in turn, allows us to speak about the possibility of coherent quantum generation of spin waves in graphene structures, which is important in terms of practical applications in nanoelectronics and spintronics.

Light meson gas in the QCD vacuum and oscillating universe

We have developed a phenomenological effective quantum-field theoretical model describing the “hadron gas” of the lightest pseudoscalar mesons, scalar σ-meson and σ-vacuum, i.e. the expectation value of the σ-field, at finite temperatures. The corresponding thermodynamic approach was formulated in terms of the generating functional derived from the effective Lagrangian providing the basic thermodynamic information about the “meson plasma + QCD condensate” system. This formalism enables us to study the QCD transition from the hadron phase with direct implications for cosmological evolution. Using the hypothesis about a positively-definite QCD vacuum contribution stochastically produced in early universe, we show that the universe could undergo a series of oscillations during the QCD epoch before resuming unbounded expansion.

Wigner law for matrices with dependent entries—a perturbative approach

We show that Wigner semi-circle law holds for Hermitian matrices with dependent entries, provided the deviation of the cumulants from the normalised Gaussian case obeys a simple power law bound in the size of the matrix. To establish this result, we use replicas interpreted as a zero-dimensional quantum field theoretical model whose effective potential obey a renormalisation group equation.

Computational approach for calculating bound states in quantum field theory

We propose a nonperturbative approach to calculate bound-state energies and wave functions for quantum field theoretical models. It is based on the direct diagonalization of the corresponding quantum field theoretical Hamiltonian in an effectively discretized and truncated Hilbert space. We illustrate this approach for a Yukawa-like interaction between fermions and bosons in one spatial dimension and show where it agrees with the traditional method based on the potential picture and where it deviates due to recoil and radiative corrections. This method permits us also to obtain some insight into the spatial characteristics of the distribution of the fermions in the ground state, such as the bremsstrahlung-induced widening.

Gauge invariant formulation of3γdecay of particle-antiparticle bound states

We construct the gauge invariant three-photon decay amplitude of particle-antiparticle bound states modeled by the Dyson-Schwinger and Bethe-Salpeter equations. Application to the quark-antiquark ($q\overline{q}$) bound states is emphasized. An essential aspect of our formulation is that it applies to any underlying quantum field theoretic model of the $q\overline{q}$ system, and not just to models, like exact QCD, where the quark self-energy $\mathrm{\ensuremath{\Sigma}}$ couples to the electromagnetic field solely via dressed quark propagators. In this way, applications to effective field theories and other QCD motivated models are envisioned. The three-photon decay amplitude is constructed by attaching currents to all possible places in the Feynman diagrams contributing to the dressed quark propagator. The gauge invariance of our construction is thus a direct consequence of respecting the underlying structure of the quantum field theory determining the dynamics. In the resultant expression for the three-photon decay amplitude, all the basic ingredients consisting of the bound-state wave function, the final-state interaction $q\overline{q}$ $t$ matrix, the dressed quark propagator, and dressed quark currents, are determined by a universal Bethe-Salpeter kernel.

Coarse-graining approach for dilepton production at energies available at the CERN Super Proton Synchrotron

Coarse-grained output from transport calculations is used to determine thermal dilepton emission rates by applying medium-modified spectral functions from thermal quantum field theoretical models. By averaging over an ensemble of events generated with the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) transport model, we extract the local thermodynamic properties at each time step of the calculation. With an equation of state the temperature $T$ and chemical potential ${\ensuremath{\mu}}_{\mathrm{B}}$ can be determined. The approach goes beyond simplified fireball models of the bulk-medium evolution by treating the full (3+1)-dimensional expansion of the system with realistic time and density profiles. For the calculation of thermal dilepton rates we use the in-medium spectral function of the $\ensuremath{\rho}$ meson developed by Rapp and Wambach and consider thermal quark-gluon plasma (QGP) and multipion contributions as well. The approach is applied to the evaluation of dimuon production in In+In collisions at top CERN Super Proton Synchrotron (SPS) energy. Comparison to the experimental results of the NA60 experiment shows good agreement of this ansatz. We find that the experimentally observed low-mass dilepton excess in the mass region from 0.2 to 0.6 GeV can be explained by a broadening of the $\ensuremath{\rho}$ spectral function with a small mass shift. In contrast, the intermediate-mass region $(M&gt;1.5$ GeV) is dominated by a contribution from the quark-gluon plasma. These findings agree with previous calculations with fireball parametrizations. This agreement, in spite of differences in the reaction dynamics between both approaches, indicates that the time-integrated dilepton spectra are not very sensitive to details of the space-time evolution of the collision.

Transport, Aharonov–Bohm, and Topological Effects in Graphene Molecular Junctions and Graphene Nanorings

The unique ultrarelativistic, massless, nature of electron states in two-dimensional extended graphene sheets, brought about by the honeycomb lattice arrangement of carbon atoms in two dimensions, provides ingress to explorations of fundamental physical phenomena in graphene nanostructures. Here, we explore the emergence of new behavior of electrons in atomically precise segmented graphene nanoribbons (GNRs) and graphene rings with the use of tight-binding calculations, nonequilibrium Green’s function transport theory, and a newly developed Dirac continuum model that absorbs the valence-to-conductance energy gaps as position-dependent masses, including topological-in-origin mass barriers at the contacts between segments. Through transport investigations in variable-width segmented GNRs with armchair, zigzag, and mixed edge terminations, we uncover development of new Fabry–Pérot-like interference patterns in segmented GNRs, a crossover from the ultrarelativistic massless regime, characteristic of extended graphene systems, to a massive relativistic behavior in narrow armchair GNRs, and the emergence of nonrelativistic behavior in zigzag-terminated GNRs. Evaluation of the electronic states in a polygonal graphene nanoring under the influence of an applied magnetic field in the Aharonov–Bohm regime and their analysis with the use of a relativistic quantum field theoretical model unveils development of a topological-in-origin zero-energy soliton state and charge fractionization. These results provide a unifying framework for analysis of electronic states, coherent transport phenomena, and the interpretation of forthcoming experiments in segmented GNRs and polygonal rings.

Holism and nonseparability by analogy

This paper explores the issues of holism and nonseparability in relativistic quantum field theory (QFT) by focusing on an analog of the typical model featuring in many discussions of holism and nonseparability in nonrelativistic quantum mechanics. It is argued that the quantum field theoretic model does exhibit holism in a metaphysical sense and that there are plausible grounds to view QFT holistic in an epistemological sense. However, the complexities arising from the fact that quantum fields have infinite degrees of freedom prohibit the exploitation of the elaborated analogy toward demonstrating that the QFT model exhibits the kind of state nonseparability familiar from ordinary quantum mechanics. Still, it is argued that the QFT model does satisfy a rather weak epistemological criterion for state nonseparability.