Quantum Field Theory Approach Research Articles

Boundary algebras of the Kitaev quantum double model

The recent article by Jones et al. [arXiv:2307.12552 (2023)] gave local topological order (LTO) axioms for a quantum spin system, showed they held in Kitaev’s Toric Code and in Levin-Wen string net models, and gave a bulk boundary correspondence to describe bulk excitations in terms of the boundary net of algebras. In this article, we prove the LTO axioms for Kitaev’s Quantum Double model for a finite group G. We identify the boundary nets of algebras with fusion categorical nets associated to (Hilb(G),C[G]) or (Rep(G),CG) depending on whether the boundary cut is rough or smooth, respectively. This allows us to make connections to the work of Ogata [Ann. Henri Poincaré 25, 2353–2387 (2024)] on the type of the cone von Neumann algebras in the algebraic quantum field theory approach to topological superselection sectors. We show that the boundary algebras can also be calculated from a trivial G-symmetry protected topological phase (G-SPT), and that the gauging map preserves the boundary algebras. Finally, we compute the boundary algebras for the (3 + 1)D Quantum Double model associated to an Abelian group.

Correlation Functions Involving Dirac Fields from Homotopy Algebras II: The Interacting Theory

Abstract We extend the formula for correlation functions of free scalar field theories and Dirac field theories in terms of quantum $A_{\infty }$ algebras presented in arXiv:2305.11634 to general scalar-Dirac systems. We obtain the result that the same formula as in the previous paper holds in this case. We show that correlation functions from our formula satisfy the Schwinger–Dyson equations. We therefore confirm that correlation functions from our formula express correlation functions from the ordinary approach of quantum field theory.

Multiple scattering, radiative transfer, and parameter regimes

We have established the radiative transfer regime in a four-parameter space spanned by amplitude and scale of fluctuations, convergence rate, and spatial range. The derivation of radiative transfer equations from wave equations offers a better understanding of the underlying physics in radiative transfer theory. One approach is based on tools borrowed from quantum field theory (QFT) and employs the Dyson and Bethe–Salpeter equations as the foundation. This has allowed us to investigate the small scale fluctuation regime, kl = O ( ε ) . We also investigated this regime using the scale-separated asymptotics approach and found that the conditions on the parameters are the same as in the QFT approach if the convergence rate of the Dyson series is O ( ε 2 ) . Furthermore, we found that there is a multitude of regimes where radiative transfer manifests. We hence infer that for a fixed spatial range, increase in the scale size of fluctuations leads to decrease in the upper bound of variance of permittivity fluctuations along with diminished convergence rate of the Wigner series. Also, for a fixed scale size and convergence rate, the spatial range where radiative transport manifests decreases with increase in strength of fluctuations.

Scalar Casimir effects in a Lorentz violation scenario induced by the presence of constant vectors

In this work, we consider a theoretical model that presents a violation of Lorentz symmetry in the approach of quantum field theory. The theoretical model adopted consists of a real massive scalar quantum field confined in the region between two large parallel plates. The violation of Lorentz symmetry is introduced by a CPT-even, aether-like approach, considering a direct coupling between the derivative of the scalar field with two orthogonal constant vectors. The main objective of this paper is to analyze the modification of the Casimir energy and pressure caused by the anisotropy of space–time as a consequence of these couplings. The confinement of the scalar quantum field between the plates is implemented by imposing boundary conditions on them.

Young’s Electron Experiment Enigma

This paper focuses on a long-standing problem in physics that originated more than two centuries ago. In 1802 Young noticed numerous bright and dark bands formed behind a metal sheet containing a pair of slits, when it was illuminated by candlelight. Advances in understanding the nature of light, the bands could be understood as “light interference patterns.” Nevertheless, in the mid-20th century, another paradox arose when individual electrons fell upon the double slit configuration. It was not clear how individual electrons could create the same banded patterns. Yet the new quantum physics theory was at the peak of physics’ popularity. As a result, a special moniker was created that allowed such idiosyncrasies: “wave-particle duality.” Under its banner, waves could act as particles and vice-versa. This behavior failed “locality,” essentially meaning local reality or relativity, as each electron, considered as an indivisible particle, could not then pass through both slits simultaneously. This paper offers a modern Quantum Field Theory (QFT) approach showing how modern Quantum Field Theory can resolve this electron enigma.

Space-time-resolved quantum field approach to Klein-tunneling dynamics across a finite barrier

Klein tunneling takes place when a particle scatters on a supercritical barrier that is creating particle antiparticle pairs. The authors, using a space-time resolved relativistic quantum field theory approach, show that the transmitted particle does not tunnel through the barrier but is instead produced by modulations in the pair creation rate.

Loop correction to the scalar Casimir energy density and generation of topological mass due to a helix boundary condition in a scenario with Lorentz violation

In this paper, the effective potential approach in quantum field theory is used in order to investigate self-interaction loop correction to the Casimir energy density and generation of topological mass for both massless and massive real scalar fields. It is assumed that the scalar field obeys a helix boundary condition. In addition, it is also considered a CPT-even aether-type violation of the Lorentz symmetry. In the absence of the Lorentz violation, we obtain analytical expressions for the loop correction to the Casimir energy density and to the mass of the scalar field. The same expressions are also obtained assuming the Lorentz violation in each of the spacetime directions. We also show some graphs that exhibit how the loop correction and the Lorentz violation affect the Casimir energy density and the mass of the scalar field.

All things retarded: radiation-reaction in worldline quantum field theory

We exhibit an initial-value formulation of the worldline quantum field theory (WQFT) approach to the classical two-body problem in general relativity. We show that the Schwinger-Keldysh (in-in) formalism leads to purely retarded propagators in the evaluation of observables in the WQFT. Integration technology for retarded master integrals is introduced at third post-Minkowskian (3PM) order. As an application we compute the complete radiation-reacted impulse and radiated four momentum for the scattering of two non-spinning neutron stars including tidal effects at 3PM order, as well as the leading (2PM) far-field gravitational waveform.

Real-time observables from Euclidean thermal correlation functions

In this work we apply a local quantum field theory approach in order to analyse the connection between real-time observables and Euclidean thermal correlation functions. In particular, using data generated from the functional renormalisation group in the quark-meson model, we demonstrate that in-medium effects can be directly extracted from the spatial momentum dependence of the Euclidean propagators, in contrast to conventional approaches, which rely on the reconstruction from different Matsubara frequencies. As an application, we determine the analytic features that arise from the discrete spectral contribution to the pion correlation function, and calculate the non-perturbative shear viscosity arising from these states.

Covariant coordinate transformations and scalar-field – matter interactions

Abstract We propose a classical Lorentz invariant model of local scalar-field - matter interactions where the zeroth component of the space-time coordinates of a particle is modified by a background Klein–Gordon field. This model is not directly explained in terms of the standard model (SM) because the CPT symmetry is generally broken with a Hermitian Hamiltonian. Our ultimate goal (which is not explored here) is to construct a quantum field theory approach to tackle the matter–antimatter asymmetry problem. To understand the basics of the theory, two examples are discussed only at the quantum mechanical level: (i) a (quantum) harmonic oscillator with the occurrence of negative-energy eigenvalues where the effective energy-masses of the ‘particle and antiparticle’ are not symmetric with respect to the non-physical zero-energy mode of the oscillator; (ii) a Dirac particle in an electromagnetic (EM) linear potential.

Universal leading quantum correction to the Newton potential

The derivation of effective quantum gravity corrections to Newton’s potential is an important step in the whole effective quantum field theory approach. We hereby add new strong arguments in favor of omitting all the diagrams with internal lines of the massive sources, and we also recalculate the corrections to the Newtonian potential using functional methods in an arbitrary parametrization of the quantum fluctuations of the metric. The general proof of the gauge- and parametrization-independence within this approach is also explicitly given. On top of that, we argue that the universality of the result holds regardless of the details of the ultraviolet completion of quantum gravity theory. Indeed, it turns out that the logarithm quantum correction depends only on the low energy spectrum of the theory that is responsible for the analytic properties of loop’s amplitudes.

Revisit the isospin violating decays of X(3872)

In this work, we revisit the isospin violating decays of $X(3872)$ in a coupled-channel effective field theory. In the molecular scheme, the $X(3872)$ is interpreted as the bound state of ${\overline{D}}^{*0}{D}^{0}/{\overline{D}}^{0}{D}^{*0}$ and ${D}^{*\ensuremath{-}}{D}^{+}/{D}^{\ensuremath{-}}{D}^{*+}$ channels. In a cutoff-independent formalism, we relate the coupling constants of $X(3872)$ with the two channels to the molecular wave function. The isospin violating decays of $X(3872)$ are obtained by two equivalent approaches, which amend some deficiencies about this issue in literature. In the quantum field theory approach, the isospin violating decays arise from the coupling constants of $X(3872)$ to two dimeson channels. In the quantum mechanics approach, the isospin violating is attributed to wave functions at the origin. We illustrate that how to cure the insufficient results in literature. Within the comprehensive analysis, we bridge the isospin violating decays of $X(3872)$ to its inner structure. Our results show that the proportion of the neutral channel in $X(3872)$ is over 80%. As a by-product, we calculate the strong decay width of $X(3872)\ensuremath{\rightarrow}{\overline{D}}^{0}{D}^{0}{\ensuremath{\pi}}^{0}$ and radiative one $X(3872)\ensuremath{\rightarrow}{\overline{D}}^{0}{D}^{0}\ensuremath{\gamma}$. The strong decay width and radiative decay width are about 30 keV and 10 keV, respectively, for the binding energy from $\ensuremath{-}300\text{ }\text{ }\mathrm{keV}$ to $\ensuremath{-}50\text{ }\text{ }\mathrm{keV}$.

Useful model to understand Schwartz’ distributions’ approach to non-renormalizable QFTs

Quantum Field Theory (QFT) is a difficult subject, plagued by puzzling infinities. Its most formidable challenge is the existence of many non-renormalizable QFT theories, for which the number of infinities is itself infinite. We will here appeal to a rather non-conventional QFT approach developed in [J. of Phys. Comm. 2 115029 (2018)] that uses Schwartz’ distribution theory (SDT). This technique avoids the need for counterterms. In the SDT approach to QFT, infinities arise due to the presence of products of distributions with coincident point singularities. In the present study, we will carefully discuss a simple QFT-model devised by Bollini and Giambiagi. Because of its simplicity, it makes easy to appreciate just how it is possible to successfully deal with the issue of non-renormalizability via SDT.

The von Neumann boson-antiboson pair creation quantum entanglement entropy in noncommutative Bianchi I space-time

The noncommutative Bianchi I curved space-time vierbeins and spin connections are derived. Moreover, a general Klein-Gordon equation up to the second order of the noncommutativity θ paramter and its solutions are presented. As an application within the quantum field theory approach using Bogoliubov transformations, the von Neumann boson-antiboson pair creation quantum entanglement entropy is studied. It is shown that its behavior is strongly dependent on the value of the noncommutativity θ parameter, k⊥ modes frequencies and the structure of the curved Bianchi I space-time. various discussions of the obtained numerical results are presented.

Emergence of p+ip superconductivity in two-dimensional doped Dirac systems

Searching for $p+ip$ superconducting(SC) state has become a fascinating subject in condensed matter physics, as a dream application awaiting in topological quantum computation. In this paper, we report a theoretical discovery of a $p+ip$ SC ground state (coexisting with ferromagnetic order) in honeycomb lattice Hubbard model with infinite repulsive interaction at low doping($\delta< 0.2$), by using both the state-of-art Grassmann tensor product state(GTPS) approach and a quantum field theory approach. Our discovery suggests a new mechanism for $p+ip$ SC state in generic strongly correlated systems and opens a new door towards experimental realization. The $p+ip$ SC state has an instability towards a potential non-Fermi liquid with a large but finite $U$. However, a small Zeeman field term stabilizes the $p+ip$ SC state. Relevant realistic materials are also proposed.

Ricci curvature and quantum geometry

We describe a few elementary aspects of the circle of ideas associated with a quantum field theory (QFT) approach to Riemannian Geometry, a theme related to how Riemannian structures are generated out of the spectrum of (random or quantum) fluctuations around a background fiducial geometry. In such a scenario, Ricci curvature with its subtle connections to diffusion, optimal transport, Wasserestein geometry and renormalization group, features prominently.

Quantum wave packet approach to oscillation of decay neutrinos

In this paper, we consider the neutrino and anti-neutrino emerging from the Z0 decay and the wave packet quantum mechanical approach is used to obtain the probability of detecting a neutrino of flavor α and the corresponding anti-neutrino of flavor β at the positions L and , respectively. For this purpose, it is essential to construct a bipartite entangled state of neutrino and anti-neutrino wave packets. The result of this calculation is the same as the result obtained before in quantum field theory approach.

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.

Nonequilibrium quantum spin dynamics from two-particle irreducible functional integral techniques in the Schwinger boson representation

We present a non-equilibrium quantum field theory approach to the initial-state dynamics of spin models based on two-particle irreducible (2PI) functional integral techniques. It employs a mapping of spins to Schwinger bosons for arbitrary spin interactions and spin lengths. At next-to-leading order (NLO) in an expansion in the number of field components, a wide range of non-perturbative dynamical phenomena are shown to be captured, including relaxation of magnetizations in a 3D long-range interacting system with quenched disorder, different relaxation behaviour on both sides of a quantum phase transition and the crossover from relaxation to arrest of dynamics in a disordered spin chain previously shown to exhibit many-body-localization. Where applicable, we employ alternative state-of-the-art techniques and find rather good agreement with our 2PI NLO results. As our method can handle large system sizes and converges relatively quickly to its thermodynamic limit, it opens the possibility to study those phenomena in higher dimensions in regimes in which no other efficient methods exist. Furthermore, the approach to classical dynamics can be investigated as the spin length is increased.

Renormalization of viscosity in wavelet-based model of turbulence

Statistical theory of turbulence in viscid incompressible fluid, described by the Navier-Stokes equation driven by random force, is reformulated in terms of scale-dependent fields $\mathbf{u}_a(x)$, defined as wavelet-coefficients of the velocity field $\mathbf{u}$ taken at point $x$ with the resolution $a$. Applying quantum field theory approach of stochastic hydrodynamics to the generating functional of random fields $\mathbf{u}_a(x)$, we have shown the velocity field correlators $\langle \mathbf{u}_{a_1}(x_1)\ldots \mathbf{u}_{a_n}(x_n)\rangle$ to be finite by construction for the random stirring force acting at prescribed large scale $L$. The study is performed in $d=3$ dimension. Since there are no divergences, regularization is not required, and the renormalization group invariance becomes merely a symmetry that relates velocity fluctuations of different scales in terms of the Kolmogorov-Richardson picture of turbulence development. The integration over the scale arguments is performed from the external scale $L$ down to the observation scale $A$, which lies in Kolmogorov range $l \ll A \ll L$. Our oversimplified model is full dissipative: interaction between scales is provided only locally by the gradient vertex $(\mathbf{u}\nabla) \mathbf{u}$, neglecting any effects or parity violation that might be responsible for energy backscatter. The corrections to viscosity and the pair velocity correlator are calculated in one-loop approximation. This gives the dependence of turbulent viscosity on observation scale and describes the scale dependence of the velocity field correlations.