Order In Field Theory Research Articles

A study of the fine-structure constant dependence of radiative capture in Halo-EFT

We study the fine structure constant dependence of the rates of some selected radiative capture reactions within the framework of so-called Halo Effective Field Theory in order to assess the adequacy of some assumptions made on the Coulomb penetrability. We find that this dependence deviates from that implied by a parameterization of the cross sections of this effect via a simple penetration factor. Some features of this fine-structure dependence are discussed, in particular its potential impact on the abundances of the light elements in primordial nucleosynthesis.

A new canonical affine bracket formulation of Hamiltonian classical field theories of first order

It has been a long standing question how to extend, in the finite-dimensional setting, the canonical Poisson bracket formulation from classical mechanics to classical field theories, in a completely general, intrinsic, and canonical way. In this paper, we provide an answer to this question by presenting a new completely canonical bracket formulation of Hamiltonian Classical Field Theories of first order on an arbitrary configuration bundle. It is obtained via the construction of the appropriate field-theoretic analogues of the Hamiltonian vector field and of the space of observables, via the introduction of a suitable canonical Lie algebra structure on the space of currents (the observables in field theories). This Lie algebra structure is shown to have a representation on the affine space of Hamiltonian sections, which yields an affine analogue to the Jacobi identity for our bracket. The construction is analogous to the canonical Poisson formulation of Hamiltonian systems although the nature of our formulation is linear-affine and not bilinear as the standard Poisson bracket. This is consistent with the fact that the space of currents and Hamiltonian sections are respectively, linear and affine. Our setting is illustrated with some examples including Continuum Mechanics and Yang–Mills theory.

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.

3D concrete fracture simulations using an explicit phase field model

Phase field models can effectively capture complicated crack evolution characteristics such as propagation, bifurcating, intersecting and merging. However, the simulation of three-dimensional (3D) quasi-brittle fracture remains a challenge due to large nonlinear equation systems and significant computational costs, which are often intractable by iteration-based implicit approaches, especially in complex mixed-mode fracture. This work presents an efficient explicit phase field model based on the unified phase field theory in order to overcome the above issues. In this model, the displacement field is second-order time dependent while the damage-phase field follows a first-order time dependence with a viscosity term. Efficient explicit central- and forward-difference algorithms for each field are developed by combining VUEL and VUMAT subroutines in the software ABAQUS/Explicit; hence, the convergence issue in the implicit phase field modelling is avoided. Several typical 3D fracture benchmarks with different failure modes are analysed for verification purposes and compared with the available experimental data. The results indicate that the developed model and computational implementation method can simulate complex 3D fracture of brittle/quasi-brittle materials with salient accuracy and efficiency, and are promising to meet the requirements in structural-level engineering practices.

Thick branes via higher order field theory models with exponential and power-law tails

In this work, we obtain exact thick brane models in 4+1 dimensions generated by higher order field theory kinks, inspired by specific potentials for phi ^{10} and phi ^{18} models. We verify that the geodesic equation along the fifth dimension confirms the confining effects of the scalar field on the brane for all of these models. These models provide new solutions with exponential and power-law tails which live in different topological sectors. We show that the resulting branes of specific exponential law models do not possess Z_2-symmetry. Furthermore, we examine the stability of the thick branes, by determining the sign of the w^2 term in the expansion of the potential for the resulting Schrödinger-like equation. It turns out that two of the three models of the phi ^{10} brane are stable, while another contains unstable modes for certain ranges of the model parameters. We also show that the brane solution from the specific phi ^{18} models are stable, while the others involve neutral equilibrium. The asymptotic behaviour of the brane solutions are also discussed.

BRST characterization of the broken phase observables of a confining complex theory

Some time ago we have introduced a route to provide confinement in the sense that particle excitations would appear from condensates of fields that do not have physical asymptotic states. We envisaged this mechanism in an asymmetric vacuum phase of a complex gauge field theory. More recently, we showed how to define a BRST operator to the broken phase of a generic spontaneous broken field theory. Our intention here is to apply these late concepts to the previous complex field theory in order to give a cohomological characterization of those condensed states as actual physical observables of this theory in its broken phase.

Addressing energy density functionals in the language of path-integrals I: comparative study of diagrammatic techniques applied to the (0 + 0)-D O(N)-symmetric $$\varphi ^{4}$$-theory

The energy density functional (EDF) method is currently the only microscopic theoretical approach able to tackle the entire nuclear chart. Nevertheless, it suffers from limitations resulting from its empirical character and deteriorating its reliability. This paper is part of a larger program that aims at formulating the EDF approach as an effective field theory (EFT) in order to overcome these limitations. A relevant framework to achieve this is the path-integral formulation of quantum field theory. The latter indeed provides a wide variety of treatments of the many-body problem well suited to deal with non-perturbative interactions and to exploit a Lagrangian resulting from an EFT as a starting point. While developing the formalism in a general setting, we present below a comparative study of such techniques applied to a toy model, i.e. the (0 + 0)-D O(N)-symmetric $$\varphi ^{4}$$ -theory. More specifically, our focus will be on the following diagrammatic techniques: loop expansion, optimized perturbation theory and self-consistent perturbation theory. With these methods, we notably address the spontaneous breakdown of the O(N) symmetry with care especially since spontaneous symmetry breakings play a paramount role in current implementations of the EDF approach.

건축물을 통한 장이론의 적용과 확장

This paper attempted to find its significance by applying and expanding the characteristic elements of field theory to architecture. In particular, attention was paid to the following characteristics of the field theory. It is ‘correlation’ as a perception of relationship and ‘overlapping’ as a multi-layered and three-dimensional tendency. To this end, the text briefly introduced field theory and architecture, and considered the relationship. Subsequently, three types of architecture were considered. It was divided into Unité d'habitation emphasizing internal communication, Bouca Social Housing emphasizing external communication, and Star Apartments emphasizing internal communication and external communication. This architecture is through the study also affects people living there, but other hand, affected also required to verify. Furthermore, the relationship between the field and the architecture was reflected in ‘correlation between subject and field’, ‘overlapping of field’, ‘recognition of change’, ‘humanities exploration to grasp the essence’, and ‘application and expansion in daily life’ and sought to expand the field theory. Ultimately, through this work, it was intended to confirm that essential solutions should be sought based on the correlation, overlap, and relativity of the field theory in order to solve the problems we face or develop into a better environment.

Kink solutions with power law tails

We present a comprehensive review about the various facets of kink solutions with a power law tail, which have received considerable attention during the last few years. This area of research is in its early stages; although several aspects have become clear by now, there are a number of issues which have only been partially understood or not understood at all. We first discuss the aspects which are reasonably well known and then address in some detail the issues which are only partially or not understood at all. We present a wide class of higher (than sixth) order field theory models admitting implicit kink as well as mirror kink solutions where the two tails facing each other have a power law or a power-tower type fall off, whereas the other two ends not facing each other could have either an exponential or a power law tail. The models admitting implicit kink solutions where the two ends facing each other have an exponential tail while the other two ends have a power law tail are also discussed. Moreover, we present several field theory models which admit explicit kink solutions with a power law fall off; we note that in all these polynomial models while the potential V(ϕ) is continuous, its derivative is discontinuous. We also discuss one of the most important and only partially understood issues of the kink–kink and the kink–antikink forces in case the tails facing each other have a power law fall off. Finally, we briefly discuss the kink–antikink collisions at finite velocity and present some open questions.

New Wine Calls For New Wineskins: Entrepreneurship in Times of Crisis

Prior literature has largely focused on the resilience of entrepreneurship in times of crisis, while paying little attention to the roles of individuals, organizations, and communities in driving transformation. The recent COVID-19 pandemic presents a timely setting to further investigate the relationship between entrepreneurship and crises. This paper applies field theory in order to answer the following questions: (1) What characteristics of a crisis trigger entrepreneurship? In what ways does a crisis foster entrepreneurship?; (2) What are the factors that influence the creation and survival of new firms in times of crisis?; and (3) What are the regional characteristics that exist where entrepreneurship is active in times of crisis? After conducting a comprehensive literature review, we found that mere resiliency or a return to the status quo does not guarantee future success. Rather, it is the entrepreneurial actors who possess the skills and power necessary to transform existing fields and foster creative destruction, innovation, and community development. Only then can faster recovery, economic welfare, social welfare, and sustainable value creation be generated. This study contributes to entrepreneurship and crisis related literature by examining how entrepreneurs, firms, and communities can achieve sustainable growth, even in the midst of a crisis.

Fermionic quantum field theories as probabilistic cellular automata

A class of fermionic quantum field theories with interactions is shown to be equivalent to probabilistic cellular automata, namely cellular automata with a probability distribution for the initial states. Probabilistic cellular automata on a one-dimensional lattice are equivalent to two-dimensional quantum field theories for fermions. They can be viewed as generalized Ising models on a square lattice and therefore as classical statistical systems. As quantum field theories they are quantum systems. Thus quantum mechanics emerges from classical statistics. As an explicit example for an interacting fermionic quantum field theory we describe a type of discretized Thirring model as a cellular automaton. The updating rule of the automaton is encoded in the step evolution operator that can be expressed in terms of fermionic annihilation and creation operators. The complex structure of quantum mechanics is associated to particle-hole transformations. The naive continuum limit exhibits Lorentz symmetry. We exploit the equivalence to quantum field theory in order to show how quantum concepts as wave functions, density matrix, noncommuting operators for observables and similarity transformations are convenient and useful concepts for the description of probabilistic cellular automata.

Geometric integration by parts and Lepage equivalents

We compare the integration by parts of contact forms – leading to the definition of the interior Euler operator – with the so-called canonical splittings of variational morphisms. In particular, we discuss the possibility of a generalization of the first method to contact forms of lower degree. We define a suitable Residual operator for this case and, working out an original conjecture by Olga Rossi, we recover the Krupka–Betounes equivalent for first order field theories. A generalization to the second order case is discussed.

Interactions of two and three mesons including higher partial waves from lattice QCD

We study two- and three-meson systems composed either of pions or kaons at maximal isospin using Monte Carlo simulations of lattice QCD. Utilizing the stochastic LapH method, we are able to determine hundreds of two- and three-particle energy levels, in nine different momentum frames, with high precision. We fit these levels using the relativistic finite-volume formalism based on a generic effective field theory in order to determine the parameters of the two- and three-particle K-matrices. We find that the statistical precision of our spectra is sufficient to probe not only the dominant s-wave interactions, but also those in d waves. In particular, we determine for the first time a term in the three-particle K-matrix that contains two-particle d waves. We use three Nf = 2 + 1 CLS ensembles with pion masses of 200, 280, and 340 MeV. This allows us to study the chiral dependence of the scattering observables, and compare to the expectations of chiral perturbation theory.

Scalar and fermion on-shell amplitudes in generalized Higgs effective field theory

Beyond-the-standard-model (BSM) particles should be included in effective field theory in order to compute the scattering amplitudes involving these extra particles. We formulate an extension of Higgs effective field theory which contains an arbitrary number of scalar and fermion fields with arbitrary electric and chromoelectric charges. The BSM Higgs sector is described by using the nonlinear sigma model in a manner consistent with the spontaneous electroweak symmetry breaking. The chiral-order counting rule is arranged consistently with the loop expansion. The leading-order Lagrangian is organized in accord with the chiral-order counting rule. We use a geometrical language to describe the particle interactions. The parametrization redundancy in the effective Lagrangian is resolved by describing the on-shell scattering amplitudes only with the covariant quantities in the scalar/fermion field space. We introduce a useful coordinate (normal coordinate), which simplifies the computations of the on-shell amplitudes significantly. We show that the high-energy behaviors of the scattering amplitudes determine the ``curvature tensors'' in the scalar/fermion field space. The massive spinor--wave function formalism is shown to be useful in the computations of on-shell helicity amplitudes.

Canonical Quantum Gravity, Constructive QFT, and Renormalisation

The canonical approach to quantum gravity has been put on a firm mathematical foundation in the recent decades. Even the quantum dynamics can be rigorously defined, however, due to the tremendously non-polynomial character of the gravitational interaction, the corresponding Wheeler–DeWitt operator-valued distribution suffers from quantisation ambiguities that need to be fixed. In a very recent series of works, we have employed methods from the constructive quantum field theory in order to address those ambiguities. Constructive QFT trades quantum fields for random variables and measures, thereby phrasing the theory in the language of quantum statistical physics. The connection to the canonical formulation is made via Osterwalder–Schrader reconstruction. It is well known in quantum statistics that the corresponding ambiguities in measures can be fixed using renormalisation. The associated renormalisation flow can thus be used to define a canonical renormalisation programme. The purpose of this article was to review and further develop these ideas and to put them into context with closely related earlier and parallel programmes.

Contestation in aesthetic fields: Legitimation and legitimacy struggles in outsider art

Legitimation is often theorized as a form of consensus and implicitly treated as an end-state that obtains after the unfolding of a process. Conflict and disagreement are recognized as part of legitimation processes; however, scholarship emphasizes consensus-building over contestation. Moreover, as legitimacy processes are always ongoing and never final, such contestation can persist even in legitimated fields. We bring together Baumann's (2007) general theory of artistic legitimation and field theories (Bourdieu, 1993; Fligstein & McAdam, 2012) in order to develop an approach to artistic legitimacy that accounts for conflict and contestation as much as consensus in legitimacy processes. We use a historical case study to build theory on legitimacy struggles in aesthetic fields. Specifically, we examine the legitimation of Outsider art, an aesthetic field defined as work by artists who produce outside established art worlds and who come from disadvantaged social worlds. Artist William Edmondson serves as an exemplar to ground our discussion of the Outsider field as we focus on resources, opportunity spaces, and legitimating discourses (Baumann, 2007) over time, to produce a multilevel and multifaceted approach to legitimation in aesthetic fields. In this way, our approach calls attention to ongoing legitimacy struggles in legitimated fields. We hypothesize that legitimacy struggles are more common in fields where judgement criteria are ambiguous, multiple players have a stake, and/or where resources are changing.

The Jacobi morphism and the Hessian in higher order field theory; with applications to a Yang–Mills theory on a Minkowskian background

We characterize the second variation of an higher order Lagrangian by a Jacobi morphism and by currents strictly related to the geometric structure of the variational problem. We discuss the relation between the Jacobi morphism and the Hessian at an arbitrary order. Furthermore, we prove that a pair of Jacobi fields always generates a (weakly) conserved current. An explicit example is provided for a Yang–Mills theory on a Minkowskian background.

Logarithmic potential with super-super-exponential kink profiles and tails

We consider a novel one dimensional model of a logarithmic potential which has super-super-exponential kink profiles as well as kink tails. We provide analytic kink solutions of the model—it has 3 kinks, 3 mirror kinks and the corresponding antikinks. While some of the kink tails are super-super-exponential, some others are super-exponential whereas the remaining ones are exponential. The linear stability analysis reveals that there is a gap between the zero mode and the onset of continuum. Finally, we compare this potential and its kink solutions with those of very high order field theories harboring seven degenerate minima and their attendant kink solutions, specifically ϕ14, ϕ16 and ϕ18.

Advantages of the Mathematical Structure of a Dirac Fermion

The mathematical structure of quantum field theories of first order and of second order partial differential equations is analyzed. Relativistic properties of the Lagrangian density and the dimension of its elements are examined. The analysis is restricted to elementary massive particles that are elements of the Standard Model of particle physics. In the case of the first order Dirac equation, the dimensionless 4-vector γµ and the partial 4-derivative ∂µ whose dimension is [L−1],are elements of the mathematical structure of the theory. On the other hand, the mathematical structure of second order quantum equations has no dimensionless 4-vector which is analogous to γµ of the linear equation. It is proved that this deficiency is the root of inherent theoretical inconsistencies of second order quantum equations. Problems of the Klein-Gordon particle, the electroweak theory of the W±, Z particles and the Higgs boson theory are discussed.

Uncertainties in the lightest CP even Higgs boson mass prediction in the minimal supersymmetric standard model: fixed order versus effective field theory prediction

We quantify and examine the uncertainties in predictions of the lightest CP even Higgs boson pole mass M_h in the Minimal Supersymmetric Standard Model ({text {MSSM}}), utilising current spectrum generators and including some three-loop corrections. There are two broadly different approximations being used: effective field theory (EFT) where an effective Standard Model (text {SM}) is used below a supersymmetric mass scale, and a fixed order calculation, where the {text {MSSM}} is matched to text {QCD}times text {QED} at the electroweak scale. The uncertainties on the M_h prediction in each approach are broken down into logarithmic and finite pieces. The inferred values of the stop mass parameters are sensitively dependent upon the precision of the prediction for M_h. The fixed order calculation appears to be more accurate below a supersymmetry (SUSY) mass scale of M_Sapprox 1.2~text {TeV}, whereas above this scale, the EFT calculation is more accurate. We also revisit the range of the lightest stop mass across fine-tuned parameter space that has an appropriate stable vacuum and is compatible with the lightest CP even Higgs boson h being identified with the one discovered at the ATLAS and CMS experiments in 2012; we achieve a maximum value of sim 10^{11} GeV.