Field Theory Research Articles

Exact partition function of the Potts model on the Sierpinski gasket and the Hanoi lattice

We present an analytic study of the Potts model partition function on the Sierpinski and Hanoi lattices, which are self-similar lattices of triangular shape with non integer Hausdorff dimension. Both lattices are examples of non-trivial thermodynamics in less than two dimensions, where mean field theory does not apply. We used and explain a method based on ideas of graph theory and renormalization group theory to derive exact equations for appropriate variables that are similar to the restricted partition functions. We benchmark our method with Metropolis Monte Carlo simulations. The analysis of fixed points reveals information of location of the Fisher zeros and we provide a conjecture about the location of zeros in terms of the boundary of the basins of attraction.

Canonical lifts in multisymplectic De Donder–Weyl Hamiltonian field theories

We define canonical lifts of vector fields to the multisymplectic multimomentum bundles of De Donder–Weyl Hamiltonian (first-order) field theories and to the appropriate premultisymplectic embedded constraint submanifolds on which singular field theories are studied. These new canonical lifts are used to study the so-called natural Noether symmetries present in both regular and singular Hamiltonian field theories along with their associated conserved quantities obtained from Noether’s theorem. The Klein–Gordon field, the Polyakov bosonic string, and Einstein–Cartan gravity in 3+1 dimensions are analyzed in depth as applications of these concepts; as a peripheral result obtained in the analysis of the bosonic string, we provide a new geometrical interpretation of the well-known Virasoro constraint.

In-in formalism for the entropy of quantum fields in curved spacetimes

We show how to compute the purity and entanglement entropy for quantum fields in a systematic perturbative expansion. To that end, we generalize the in-in formalism to non-unitary dynamics (i.e. accounting for the presence of an environment) and to the calculation of quantum information measures, which are not observables in the usual sense. This allows us to reduce the problem to one involving standard correlation functions, and to organize their computation in a diagrammatic expansion for which we construct the corresponding Feynman rules. As an illustration, we apply the formalism to a cosmological setting inspired by the effective field theory of inflation. We find that at late times, non-linear loop corrections share the same time behavior as the linear contribution, and only yield a slight redressing of the purity. In particular, when the environment is heavy compared to the Hubble scale, the phenomenon of recoherence previously encountered is robust to the class of non-linear extensions considered. Bridging the gap between perturbative quantum field theory and open quantum systems paves the way to a better understanding of renormalization and resummation in open effective field theories. It also enables a more systematic exploration of quantum information properties in field theoretic settings.

Piloting a co-created local and alternative food network involving professional buyers in Norway: Forces and tensions influencing viability

We can obtain knowledge about how sustainability transitions can take place through experimenting with niche-activities. An alternative food network (AFN) called Green Parallel was co-created through action research in an agri-food living lab and was piloted in 2019 and 2020. The purpose was to contribute to more organic produce in localized food systems and improve communication between producers and professional buyers (e.g. specialty stores, restaurants, chain retails, private and public canteens) in the Vestfold region in Norway. This paper analyses the occurring forces and tensions that support or hinder the viability of the AFN.The methods of data collection were interviews, reflection notes and participants’ notes from the participatory processes. We utilized perspectives from field theory and institutional economy to understand individual behaviors in relation to internal and external forces and tensions in a multi-level perspective (MLP).A strong supportive force was the initial motivation participants in Green Parallel had to collaborate. In addition, we identified seven forces and tensions affecting the viability of Green Parallel. These forces and tensions worked through complex interdependencies within individuals and actor types and across actor types, as well as across internal and external niche spans. The study can inform further development of organic and local agri-food systems.

Schrödinger evolution of a scalar field in Riemannian and pseudo-Riemannian expanding metrics

We study the quantum field theory (QFT) of a scalar field in the Schrödinger picture in the functional formulation. We derive a formula for the evolution kernel in a flat expanding metric. We discuss a transition between Riemannian and pseudo-Riemannian metrics (signature inversion). We express the real time Schrödinger evolution by the Brownian motion. We discuss the Feynman integral for a scalar field in a radiation background. We show that the unitary Schrödinger evolution for positive time can go over for negative time into a dissipative evolution as a consequence of the imaginary value of . The time evolution remains unitary if in the Hamiltonian is replaced by .

Stability discussion of metal carbonates in aqueous solution: Reactive force field and density functional theory

The nucleation and precipitation of metal carbonates occupy a crucial position in a wide array of industrial processes, environmental occurrences, and geological formations. Understanding the fundamental mechanisms underlying these processes is paramount for optimizing industrial applications and mitigating environmental impacts. In this study, we embark on an investigation utilizing reactive force field molecular-dynamics simulations to delve deeply into the nucleation and precipitation process of metal carbonates. These simulations provide profound insights into the mechanisms and kinetics governing the process across diverse conditions. Additionally, through density functional theory calculations, we scrutinize the energetic and dynamical stability of highly hydrated amorphous carbonates and hydrate crystals. Our revelations offer illuminating perspectives on the intricate interplay of factors shaping nucleation and precipitation processes, serving as a foundation for future inquiries in this research field.

RE-algebras, quasi-determinants and the full Toda system

In 1991, Gelfand and Retakh embodied the idea of a noncommutative Dieudonne determinant for a generating matrix of RTT algebra, namely, they found a representation of the quantum determinant of RTT algebra in the form of a product of principal quasi-determinants. In this note we construct an analogue of the above statement for the RE-algebra corresponding to the Drinfeld R-matrix for the order n=2,3. Namely, we have found a family of quasi-determinants that are principal with respect to the antidiagonal, commuting among themselves, whose product turns out to be the quantum determinant of this algebra. This family generalizes the construction of integrals of the full Toda system due to Deift et al. for the quantum case of RE-algebras. In our opinion, this result also clarifies the role of RE-algebras as a quantum homogeneous spaces and can be used to construct effective quantum field theories with a boundary.

Multiscale fatigue life prediction model for CFRP laminates considering the mechanical degradation of its constituents and the local stress concentration of the matrix

In the present research, a novel approach for predicting the fatigue life of composites is proposed using a multiscale fatigue model. This model considers two critical physical phenomena that occur in CFRP laminates under tension-tension cyclic loading – the degradation of the physical properties of CFRP constituents and the localized stress concentrations within the matrix. To achieve this, Mori-Tanaka’s mean field theory, a well-known micromechanics model, is employed to consider the deterioration of material properties in various phases, which is dependent on the applied stress level. Localized stress concentration phenomena within the matrix of a composite material are common when CFRP laminate is subjected to cyclic loading. The localized stress concentration on a matrix with different numbers of fibers and orientations using representative volume elements (RVE) is investigated. Two other scales of failure criteria are defined to evaluate its constituent at the material level and ply level at the macroscale. A comparison with fatigue experiment data of AS4/3501-6 composite shows good reliability of the proposed multiscale fatigue model.

A theoretical investigation on equilibrium magnetic properties in nanowire arrays

The paper focuses on the study of an Ising nanowire array composed of core/shell-structured single nanowires placed at the edges of a square lattice. The phase transition temperature, at which a transition occurs in the magnetic properties, is obtained using effective field theory for two interacting individual nanowires. To understand how the interaction affects the magnetic, we defined the exchange interaction (JR) between the single nanowires. This interaction is assigned both positive and negative values to reveal the ferromagnetic and antiferromagnetic characteristics of the system. Our results revealed that the exchange interaction between individual nanowires significantly influences the magnetic properties of the system.

Phenomenology of Horndeski gravity under positivity bounds

A set of conditions that any effective field theory needs to satisfy in order to allow for the existence of a viable UV completion, has recently gained attention in the cosmological context under the name of positivity bounds. In this paper we revisit the derivation of such bounds for Horndeski gravity, highlighting the limitations that come from applying the traditional methodology to a theory of gravity on a cosmological background. We then translate these bounds into a complete set of viability conditions in the language of effective field theory of dark energy. We implement the latter into EFTCAMB and explore the large scale structure phenomenology of Horndeski gravity under positivity bounds. We build a statistically significant sample of viable Horndeski models, and derive the corresponding predictions for the background evolution, in terms of w DE, and the dynamics of linear perturbations, in terms of the phenomenological functions μ and Σ, associated to clustering and weak lensing, respectively. We find that the addition of positivity bounds to the traditional no-ghost and no-gradient conditions considerably tightens the theoretical constraints on all these functions. The most significant feature is a strengthening of the correlation μ ≃ Σ, and a related tight constraint on the luminal speed of gravitational waves c 2 T ≃ 1. In this work we demonstrate the strong potential of positivity bounds in shaping the viable parameter space of scalar-tensor theories. This is certainly promising, but it also highlights the importance of overcoming all issues that still plague a rigorous formulation of the positivity bounds in the cosmological context.

Searches for violation of Lorentz invariance in top quark pair production using dilepton events in 13 TeV proton-proton collisions

A search for violation of Lorentz invariance in the production of top quark pairs (tt‾) is presented. The measured normalized differential tt‾ production cross section, as a function of the sidereal time, is examined for potential modulations induced by Lorentz-invariance breaking operators in an effective field theory extension of the standard model (SM). The cross section is measured from collision events collected by the CMS detector at a center-of-mass-energy of 13 TeV, corresponding to an integrated luminosity of 77.8 fb−1, and containing one electron and one muon. The results are found to be compatible with zero, in agreement with the SM, and are used to place upper limits at 68% confidence level on the magnitude of the Lorentz-violating couplings ranging from 1–8×10−3. This is the first precision test of the isotropy in special relativity with top quarks at the LHC, restricting further the bounds on such couplings by up to two orders of magnitude with respect to previous searches conducted at the Tevatron.

Dark Dimension and the Effective Field Theory Limit

Dark Dimension and the Effective Field Theory Limit

SQFT: An Autonomous Explanation of the Interactions of Quantum Particles

AbstractSuccessful applications of a conceptually novel setup of Quantum Field Theory, that accounts for all subtheories of the Standard Model (QED, Electroweak Interaction and Higgs, Yang–Mills and QCD) and beyond (Helicity 2), call for a perspective view in a broader conceptual context. The setting is “autonomous” in the sense of being intrinsically quantum. Its principles are: Hilbert space, Poincaré symmetry and causality. Its free quantum fields are obtained from Wigner’s unitary representations of the Poincaré group, with only physical and observable degrees of freedom. A “quantization” of an “underlying” classical theory is not needed. It allows renormalizable perturbation theory with interactions whose detailed structure, and in some cases even the particle content, is predicted by internal consistency. The results confirm and extend observable predictions for the interactions of the Standard Model without assuming a “principle” of gauge invariance.

String theory and the first half of the universe

We perform a detailed study of stringy moduli-driven cosmologies between the end of inflation and the commencement of the Hot Big Bang, including both the background and cosmological perturbations: a period that can cover half the lifetime of the universe on a logarithmic scale. Compared to the standard cosmology, stringy cosmologies with vacua that address the hierarchy problem motivate extended kination, tracker and moduli-dominated epochs involving significantly trans-Planckian field excursions.We analyse the cosmology within the framework of the Large Volume Scenario but explain how analogous cosmological features are expected in other string theory models characterized by final vacua located in the asymptotic regions of moduli space.Conventional effective field theory is unable to control Planck-suppressed operators and so such epochs require a stringy completion for a consistent analysis. Perturbation growth in these stringy cosmologies is substantially enhanced compared to conventional cosmological histories. The transPlanckian field evolution results in radical changes to Standard Model couplings during this history and we outline potential applications to baryogenesis, dark matter and gravitational wave production.

Enhanced power spectra from multi-field inflation

We investigate the enhancement of the power spectra largeenough to produce primordial black holes in models with multiple scalar fields. We present analytic solutions for the perturbations in the case of constant turns without the need for an effective field theory for the first time and clarify the role of the Hubble friction that has been overlooked previously. We derive the criteria for an arbitrary number of fields that can lead to an exponential amplification of the curvature perturbation on subhorizon scales, while leaving the perturbations stable on superhorizon scales. Finally, we apply our results to a three-field generalization of the “ultra-light” scenario and show how the presence of field-space torsion can yield distinct observables compared to the two-field case.

Time-Delay Following Model for Connected and Automated Vehicles Considering Multiple Vehicle Safety Potential Fields

Connected and automated vehicles (CAVs) represent a significant development in the transport industry owing to their intelligent and interconnected features. Potential field theory has been extensively used to model CAV driving behaviour owing to its objectivity, universality, and measurability. However, existing car-following models do not consider the impact of time delays and the influence of information from multiple vehicles ahead and behind. This paper focuses on the driving-safety risks associated with CAVs, aiming to enhance vehicle safety and reliability during travelling. We developed a multi-vehicle car-following model based on safety potential fields (MIDM-SPF), taking into account the characteristics of multi-vehicle connected information and time delays. To enhance the model’s precision, real-world data from urban roads were employed, alongside an improved optimisation algorithm to fine-tune the car-following model. The simulation experiment revealed that MIDM-SPF significantly reduces stop-and-go traffic, thereby improving traffic flow stability in urban areas. Additionally, we validated the stability of our model under varying market penetration rates in large-scale mixed traffic. Our findings indicate that increasing the CAV proportion improves the stability of mixed traffic flows, which has important implications for alleviating traffic congestion and guiding the large-scale implementation of autonomous driving in the future.

Finite-size spectrum of the staggered six-vertex model with antidiagonal boundary conditions

The finite-size spectrum of the critical staggered six-vertex model with antidiagonal boundary conditions is studied. Similar to the case of periodic boundary conditions, we identify three different phases. In two of those, the underlying conformal field theory can be identified to be related to the twisted U(1) Kac-Moody algebra. In contrast, the finite size scaling in the third regime, whose critical behaviour with the (quasi-)periodic BCs is related to the 2d black hole CFTs possessing a non-compact degree of freedom, is more subtle. Here with antidiagonal BCs imposed, the corrections to the scaling of the ground state grow logarithmically with the system size, while the energy gaps appear to close logarithmically. Moreover, we obtain an explicit formula for the Q-operator which is useful for numerical implementation.

Anisotropic damage evolution in solid fractures: A novel phase field approach with multiple failure criteria and directional-dependent structural tensor

This study proposes a novel phase-field fracture model based on unified phase field theory, aiming to overcome current limitations in simulating material complex fracture behaviors. Through this model, analytical solutions for two-dimensional bars subjected to tensile or compressive stresses are provided, enabling the coupling of multiple failure criteria and further proficient simulation of mode-I, mode-II, and mixed mode-I/II fractures, effectively addressing challenges faced in modelling materials with different or complex failure modes under various loading conditions. Furthermore, to account for the strong anisotropic failure behavior of materials, a novel directional-dependent structural tensor is proposed. The tensor correlates fracture energy with crack surface orientation, facilitating precise characterization of material damage evolution with multiple potential crack orientations. This tensor ensures the consistency of phase-field fracture evolution with predefined fracture patterns. The effectiveness of the proposed model is validated through case studies, emphasizing its robustness and superior predictive capability in capturing fracture behavior under various conditions. This research provides a more accurate and universally applicable approach for simulating material failure, particularly for complex or multiple failure mode material failure simulations.

Fitting the DESI BAO data with dark energy driven by the Cohen-Kaplan-Nelson bound

Gravity constrains the range of validity of quantum field theory. As has been pointed out by Cohen, Kaplan, and Nelson (CKN), such effects lead to interdependent ultraviolet (UV) and infrared (IR) cutoffs that may stabilize the dark energy of the universe against quantum corrections, if the IR cutoff is set by the Hubble horizon. As a consequence of the cosmic expansion, this argument implies a time-dependent dark energy density. In this paper we confront this idea with recent data from DESI BAO, Hubble and supernova measurements. We find that the CKN model provides a better fit to the data than the ΛCDM model and can compete with other models of time-dependent dark energy that have been studied so far.

A Neurophysical Hypothesis on the Role of the Intensity of the Electromagnetic Field Generated by the Cerebral Hemispheres in the Determination of Laterality, in Line with Einstein's Unified Field Theory

Abstract Objective: Traditional models of cerebral laterality, focusing primarily on anatomical and functional asymmetries, fall short of explaining the underlying physical dynamics. This study pioneers a novel perspective by hypothesizing that the intensity of the electromagnetic field generated by the cerebral hemispheres plays a crucial role in determining laterality. Inspired by Einstein's unified field theory, we explore this hypothesis through an interdisciplinary approach that merges principles of physics with neurophysiology. Material and Methods: Our research employed an innovative experimental design involving three groups of male Wistar albino rats categorized based on handedness: right-handed, left-handed, and ambidextrous. We utilized electroencephalography (EEG) to measure the electromagnetic field intensity of the cerebral hemispheres, analyzing the data through a lens that combines traditional neuroscientific methods with concepts adapted from field theory. Results: The findings reveal a significant correlation between the intensity of the electromagnetic field in the dominant hemisphere and handedness, with dominant hemispheres displaying higher field intensities. Notably, ambidextrous rats exhibited no significant difference in field intensity between hemispheres, underscoring the potential influence of electromagnetic fields on hemispheric dominance. Conclusion: This study's implications suggest a radical rethinking of how cerebral functions might be influenced by electromagnetic phenomena. The integration of Einstein's unified field theory into the study of cerebral laterality opens new pathways for research. Our findings advocate for a broader, more integrated understanding of brain functionality, highlighting the need for further interdisciplinary research in this nascent field.