Quantum Field Research Articles

A new approach for solving fractional Kundu-Eckhaus equation and fractional massive Thirring model using controlled Picard’s technique with [formula omitted]-Laplace transform

This paper introduces a novel approach called the Controlled Picard technique along with ρ-Laplace transform for simulating the solutions of the fractional Kundu–Eckhaus equation (FKEE) and time-fractional massive Thirring model (FMTM). Significant applications of these equations can be found in nonlinear optics, weakly dynamic dispersive waves of water, and the study of quantum fields. Our proposed approach merges the Controlled Picard technique with the ρ-Laplace transform, resulting in an elegant framework that effectively solves nonlinear fractional equations without the need for Lagrange multipliers or Adomian polynomials. The inclusion of a small parameter h enhances convergence and is particularly advantageous for nonlinear differential equations. We demonstrate the accuracy and convergence of our method by comparing it with other analytical approaches. In addition, we offer graphical depictions of the numerical results to demonstrate the effectiveness as well as reliability of our suggested methodology. Overall, our approach is highly efficient, accurate, and straightforward to implement.

Numerical simulation of coupled Klein–Gordon–Schrödinger equations: RBF partition of unity

The coupled Klein–Gordon–Schrödinger equations have significant implications in quantum field theory, particle physics, cosmology, and nonlinear dynamics. In this study, we propose an efficient method for numerically simulating this system. The proposed approach involves employing the radial basis function partition of unity for spatial discretization. This method utilizes scaled Lagrange basis functions with polyharmonic spline kernels, taking advantage of the scalability property of the polyharmonic kernel to ensure stability in the approximation process. The resulting spatially discretized system yields a nonlinear time-dependent set of differential equations. To solve this system, we combine an implicit central finite difference scheme with a predictor–corrector procedure to overcome the nonlinearity. In the numerical results section, we assess the efficiency, accuracy, and versatility of the proposed method by conducting several simulations in large domains over extended periods. We present and compare these results with those obtained using alternative methods, demonstrating the effectiveness of the proposed approach in accurately solving the coupled Klein–Gordon–Schrödinger equations.

Crossed product algebras and generalized entropy for subregions

An early result of algebraic quantum field theory is that the algebra of any subregion in a QFT is a von Neumann factor of type III_{1}1, in which entropy cannot be well-defined because such algebras do not admit a trace or density states. However, associated to the algebra is a modular group of automorphisms characterizing the local dynamics of degrees of freedom in the region, and the crossed product of the algebra with its modular group yields a type II_∞∞ factor, in which traces and hence von Neumann entropy can be well-defined. In this work, we generalize recent constructions of the crossed product algebra for the TFD to, in principle, arbitrary spacetime regions in arbitrary QFTs, formally paving the way to the study of entanglement entropy without UV divergences. In contrast to previous works, we emphasize that this construction is independent of gravity. In this sense, the crossed product construction represents a refinement of Haag’s assignment of nets of observable algebras to spacetime regions by providing a natural construction of a type II factor. We present several concrete examples: a QFT in Rindler space, a CFT in an open ball of Minkowski space, and arbitrary boundary subregions in AdS/CFT. In the holographic setting, we provide a novel argument for why the bulk dual must be the entanglement wedge, and discuss the distinction arising from boundary modular flow between causal and entanglement wedges for excited states and disjoint regions.

QED in space–time varying materials

Space–time variation spoils frequency conservation and brings negative frequencies into the picture. In addition, the quantum nature of light comes to the fore in a manner not evident in static systems. Here, we explore the quantum structure of these systems; propose a Hamiltonian; show that, in the Heisenberg picture, quantum field operators evolve according to classical equations; and discuss the uniquely quantum phenomenon of photon-pair creation.

Spin and Susceptibility Effects of Electromagnetic Self-Force in Effective Field Theory.

The classic Abraham-Lorentz-Dirac self-force of pointlike particles is generalized within an effective field theory setup to include linear spin and susceptibility effects described perturbatively, in that setup, by effective couplings in the action. Electromagnetic self-interactions of the pointlike particle are integrated out using the in-in supersymmetric worldline quantum field theory formalism. Divergences are regularized with dimensional regularization, and the resulting equations of motion are in terms only of an external electromagnetic field and the particle degrees of freedom.

Feynman checkers: lattice quantum field theory with real time

Feynman checkers: lattice quantum field theory with real time

Resurgence and self-completion in renormalized gauge theories

Under certain assumptions and independent of the instantons, we show that the logarithm expansion of dimensional regularization in quantum field theory needs a nonperturbative completion to have a renormalization group flow valid at all energies. Then, we show that such nonperturbative completion has the analytic properties of the renormalons, which we find with only a marginal reference to diagrammatic calculations. We demonstrate that renormalon corrections necessarily lead to analyzable functions, namely, resurgent transseries. A detailed analysis of the resurgent properties of the renormalons is provided. The self-consistency of the theory requires these nonperturbative contributions to render the running coupling well defined at any energy, thus with no Landau pole. We illustrate the point within the case of quantum electrodynamics (QED). This way, we explicitly realize the correspondence between the nonperturbative Landau pole scale and the renormalons. What is seen as a Landau pole in perturbation theory is cured by the nonperturbative, resurgent contributions.

Perturbative method for mutual information and thermal entropy of scalar quantum fields

A new approach is presented to compute entropy for massless scalar quantum fields. By perturbing a skewed correlation matrix composed of field operator correlation functions, the mutual information is obtained for disjoint spherical regions of size r at separation R, including an expansion to all orders in r/R. This approach also permits a perturbative expansion for the thermal field entropy difference in the small temperature limit (T ≪ 1/r).

Distinguishing pure and thermal states by Landauer’s principle in open systems

Starting from Polchinski’s thought experiment on how to distinguish between pure and thermal states, we construct a specific system to study the interaction between qubit and cavity quantum field theory (QFT) in order to provide a more operational point of view. Without imposing any restrictions on the initial states of qubit and cavity QFT, we compute the evolution of the system order by order by the perturbation method. We choose Landauer’s principle, an important bound in quantum computation and quantum measurement, as the basis for the determination of the thermal state. By backtracking the initial state form, we obtain the conditions that must be satisfied by the cavity QFT: the expectation value of the annihilation operator should be zero, and the expectation value of the particle number operator should satisfy the Bose–Einstein distribution. We also discuss the difference between the thermal state and a possible alternative to the thermal state: the canonical thermal pure quantum (CTPQ) state.

Towards a quantum field theory description of nonlocal spacetime defects

We propose an ansatz for encoding the physics of nonlocal spacetime defects in the Green’s functions for a scalar field theory defined on a causal set. This allows us to numerically study the effects of nonlocal spacetime defects on the discrete Feynman propagator of the theory defined on the causal set in 1+1 dimensions, and to compare to the defect-free limit. The latter approaches the expected continuum result, on average, when the number of points becomes large. When defects are present, two points with the same invariant spacetime interval can have different propagation amplitudes, depending on whether the propagation is between two ordinary spacetime points, two defects, or a defect and an ordinary point. We show that a coarse-grained description that is only sensitive to the average effect of the defects can be interpreted as a defect-induced mass and wave-function renormalization of the scalar theory.

All about the neutron from lattice QCD

I describe how simulations of lattice QCD using the path integral formulation provide the two basic quantum mechanical properties of QCD, its ground state in which correlation functions are calculated, and Fock state wavefunctions between which matrix elements of operators are calculated. Both constructs are stochastic, so unfortunately one gets no intuitive picture or even qualitative understanding of what they look like, nevertheless they contain and display all the subtleties of the quantum field theory. Today, these simulations provide many quantities that are impacting phenomenology and experiments. I illustrate the methods and the steps in the analysis using, as examples, three observables: the isovector charges of the nucleon, the contribution of the quark’s intrinsic spin to the nucleon spin, and the pion-nucleon sigma term.

Quantum Field Theory of Neutrino Mixing in Spacetimes with Torsion

In the framework of quantum field theory, we analyze the neutrino oscillations in the presence of a torsion background. We consider the Einstein–Cartan theory and we study the cases of constant torsion and of linearly time-dependent torsion. We derive new neutrino oscillation formulae which depend on the spin orientation. Indeed, the energy splitting induced by the torsion influences oscillation amplitudes and frequencies. This effect is maximal for values of torsion of the same order of the neutrino masses and for very low momenta, and disappears for large values of torsion. Moreover, neutrino oscillation is inhibited for intensities of torsion term much larger than neutrino masses and momentum. The modifications induced by torsion on the CP-asymmetry are also presented. Future experiments, such as PTOLEMY, which have as a goal the analysis of the cosmological background of neutrino (which have very low momenta), can provide insights into the effect shown here.

Observables from classical black hole scattering in Scalar-Tensor theory of gravity from worldline quantum field theory

In this paper, we compute the two observables, impulse and waveform, in a black hole scattering event for the Scalar-Tensor theory of gravity with a generic scalar potential using the techniques of Worldline Quantum Field Theory. We mainly investigate the corrections to the above mentioned observables due to the extra scalar degree of freedom. For the computation of impulse, we consider the most general scenario by making the scalar field massive and then show that each computed diagram has a smooth massless limit. We compute the waveform for scalar and graviton up to 2PM, taking the scalar as massless. Furthermore, we discuss if the scalar has mass and how the radiation integrals get more involved than the massless case. We also arrive at some analytical results using stationary phase approximation. Interestingly, we also show that the λ4φ4 interaction vertex does not contribute to the radiation by showing that the integral has no non-zero finite value.

Comments to Megascopic Quantum Phenomena

We present here the incompleteness of the Copenhagen interpretation regarding the impossibility of explaining the transition from the exact quantum mechanics to the Born-Oppenheimer approximation, where the inaccurate method captures phenomena like spontaneous symmetry breaking, but this is impossible to achieve with exact equations. The solution to this dilemma lies in the revision of quantum field theory which bounds together internal and external (vibrational, translational, and rotational) degrees of freedom in a similar way as the Lorentz transformation deals with space and time. This is the only way how to exactly mathematically justify the corrections beyond the Born-Oppenheimer approximation (Born-Huang ansatz). The consequences are overwhelming: It reveals the wrong BCS theory of superconductivity, derived on the basis of the incomplete quantum field, and all erroneous theories inspired by the BCS one (e.g. Higgs mechanism). Moreover, the second Bohr complementarity emerges from the mechanical wholeness and field fragmentation, opening the door for the megascopic mirror of the microscopic Copenhagen interpretation and for the explanation of megascopic quantum phenomena. Finally, we get an entirely new look at the meaning of physics and chemistry: The first one deals with microscopic and the second one with megascopic phenomena.

Linear graviton as a quantum particle

Wave function of a single linear graviton and its interpretation are proposed. The evolution equation for this function is given. A Hermitian operator with mutually commuting components canonically conjugated to the momentum operator of the linear graviton is found. Second quantization of the linear graviton quantum mechanics as well as quantization of the classical free linear graviton field are investigated.

Large-N Principal Chiral Model in Arbitrary External Fields.

We report the explicit solution for the vacuum state of the two-dimensional SU(N) principal chiral model at large N for an arbitrary set of chemical potentials and any interaction strength, a unique result of such kind for an asymptotically free quantum field theory. The solution matches one-loop perturbative calculation at weak coupling, and in the opposite strong-coupling regime exhibits an emergent spacial dimension from the continuum limit of the SU(N) Dynkin diagram.

Cosmological correlators in massless ϕ4-theory and the method of regions

The calculation of loop corrections to the correlation functions of quantum fields during inflation or in the de Sitter background presents greater challenges than in flat space due to the more complicated form of the mode functions. While in flat space highly sophisticated approaches to Feynman integrals exist, similar tools still remain to be developed for cosmological correlators. However, usually only their late-time limit is of interest. We introduce the method-of-region expansion for cosmological correlators as a tool to extract the late-time limit, and illustrate it with several examples for the interacting, massless, minimally coupled scalar field in de Sitter space. In particular, we consider the in-in correlator 〈ϕ2(η, q)ϕ(η, k1)ϕ(η, k2)〉, whose region structure is relevant to anomalous dimensions and matching coefficients in Soft de Sitter effective theory.

Decoherence and entropy generation at one loop in the inflationary de Sitter spacetime for Yukawa interaction

Abstract The decoherence mechanism is believed to be possibly connected to the quantum to classical transition of the primordial cosmological perturbations in the early universe. In this paper, we extend our previous analysis on decoherence in a fermion and scalar quantum field theory coupled via the Yukawa interaction in the Minkowski spacetime, to the inflationary de Sitter background. We treat the scalar field as the system and the fermions as the environment, and both the fields are taken to be massless. We utilise a non-equilibrium effective field theory formalism, suitable for open quantum systems such as this. We assume that an observer measures only the Gaussian 2-point correlator for the scalar field, as the simplest realistic scenario. In order to compute the von Neumann entropy generated at late times as a measure of the decoherence, we construct the one loop renormalised Kadanoff-Baym equation, which is the equation of motion satisfied by the 2-point correlators in the closed time path Schwinger-Keldysh formalism. These equations account to the self energy corrections. Using this, we next construct the one loop corrected statistical propagator for the scalar, which is related to its phase space area, to compute the von Neumann entropy. We also compute the variation of the von Neumann entropy with respect to relevant parameters. We note the qualitative similarity between our findings and the scenario where both the system and the environment are scalars. Our result is also qualitatively similar to an earlier one found by using the influence functional technique for a massive Yukawa theory.

Investigating the new perspectives of Caudrey–Dodd–Gibbon equation arising in quantum field theory

The main purpose of the paper is obtaining the analytical results for beta fractional Caudrey–Dodd–Gibbon equation which is used to resolve complex problems in fluid dynamics, chemical kinetics, plasma physics, quantum field theory, crystal dislocations, and nonlinear optics by using auxiliary method. Beta derivative is a useful fractional operator due to satisfying basic properties of integer order derivative and also, allows us using chain rule and wave transform to turn nonlinear fractional partial differential equations into integer order ordinary differential equations. By the way many analytical methods can be applied to these equations. In order to understand the physical features of the solutions, 3D and 2D graphical illustrations are given. Finally, authors expect that the obtained solutions may give a deep insight for the explanation of physical phenomena in the fluid dynamics, chemical kinetics, plasma physics, quantum field theory, crystal dislocations, and nonlinear optics.

What Is the "Hydrogen Bond"? A QFT-QED Perspective.

In this paper we would like to highlight the problems of conceiving the "Hydrogen Bond" (HB) as a real short-range, directional, electrostatic, attractive interaction and to reframe its nature through the non-approximated view of condensed matter offered by a Quantum Electro-Dynamic (QED) perspective. We focus our attention on water, as the paramount case to show the effectiveness of this 40-year-old theoretical background, which represents water as a two-fluid system (where one of the two phases is coherent). The HB turns out to be the result of the electromagnetic field gradient in the coherent phase of water, whose vacuum level is lower than in the non-coherent (gas-like) fraction. In this way, the HB can be properly considered, i.e., no longer as a "dipolar force" between molecules, but as the phenomenological effect of their collective thermodynamic tendency to occupy a lower ground state, compatible with temperature and pressure. This perspective allows to explain many "anomalous" behaviours of water and to understand why the calculated energy associated with the HB should change when considering two molecules (water-dimer), or the liquid state, or the different types of ice. The appearance of a condensed, liquid, phase at room temperature is indeed the consequence of the boson condensation as described in the context of spontaneous symmetry breaking (SSB). For a more realistic and authentic description of water, condensed matter and living systems, the transition from a still semi-classical Quantum Mechanical (QM) view in the first quantization to a Quantum Field Theory (QFT) view embedded in the second quantization is advocated.