Field Theory Research Articles

Dilaton in a Multicritical 3+epsilon-D Parity Violating Field Theory

Dilaton in a Multicritical 3+epsilon-D Parity Violating Field Theory

Resources of curriculum materials that induce teachers' professional knowledge of the additive conceptual field

Assuming that curriculum materials reverberate the knowledge of teachers, we sought to identify and discuss features of the materials, related to the additive field, which induce professional knowledge in Mathematics. Through a documentary analysis of three 2nd, 3rd and 4th grade Mathematics Teacher's Manuals, the addition and subtraction problems were mapped and analyzed; the texts presenting the material and the units corresponding to the mapped problems were analyzed, as well as the specific guidelines for working with these problems. Considering the Conceptual Fields Theory and the Knowledge of Knowledge of Curriculum Embedded Mathematics as references, we identified a variety of problem classes, as well as guidelines on the different meanings of operations. We observed weaknesses in the approach taken in the 2nd grade Manual corresponding to the addition and subtraction approach, to the detriment of the other Manuals. We noted the absence of explicitly stated information in the three manuals, which may have an impact on the way teachers read and interpret the guidelines, and evaluate the problems, implying the teaching knowledge mobilized or constructed.

Solving conformal defects in 3D conformal field theory using fuzzy sphere regularization

Defects in conformal field theory (CFT) are of significant theoretical and experimental importance. The presence of defects theoretically enriches the structure of the CFT, but at the same time, it makes it more challenging to study, especially in dimensions higher than two. Here, we demonstrate that the recently-developed theoretical scheme, fuzzy (non-commutative) sphere regularization, provides a powerful lens through which one can dissect the defect of 3D CFTs in a transparent way. As a notable example, we study the magnetic line defect of 3D Ising CFT and clearly demonstrate that it flows to a conformal defect fixed point. We have identified 6 low-lying defect primary operators, including the displacement operator, and accurately extract their scaling dimensions through the state-operator correspondence. Moreover, we also compute one-point bulk correlators and two-point bulk-defect correlators, which show great agreement with predictions of defect conformal symmetry, and from which we extract various bulk-defect operator product expansion coefficients. Our work demonstrates that the fuzzy sphere offers a powerful tool for exploring the rich physics in 3D defect CFTs.

Theories and Methods of Consciousness

This work explores the ontological theories, and their methodologies, regarding the origins and nature of consciousness in the multiverse.  The paper critically assesses Mocombe’s consciousness field theory within the larger body of contemporary ontological debates, and their methodologies, regarding the nature, origin, and constitution of consciousness, especially human consciousness, in the world.   

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

AbstractWe 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 $$\mathbb {C}_{\pi } =\mathbb {C}{\setminus } \mathbb {R}_-$$ C π = C \ R - . 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 $$g=|g| e^{\imath \varphi }$$ g = | g | e ı φ on the sector of the Riemann surface with $$|\varphi |<3\pi /2$$ | φ | < 3 π / 2 , 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, $$Z_n(g)$$ Z n ( g ) and $$W_n(g)$$ W n ( g ) , exhibit analytic properties similar to Z(g, N) and W(g, N) and have transseries expansions. The transseries expansion of $$Z_n(g)$$ Z n ( g ) is readily accessible: much like Z(g, N), for any n, $$Z_n(g)$$ Z n ( g ) has a zero- and a one-instanton contribution. The transseries of $$W_n(g)$$ W n ( g ) is obtained using Möbius inversion, and summing these transseries yields the transseries expansion of W(g, N). The transseries of $$W_n(g)$$ W n ( g ) and W(g, N) are markedly different: while W(g, N) displays contributions from arbitrarily many multi-instantons, $$W_n(g)$$ W n ( g ) exhibits contributions of only up to n-instanton sectors.

Lexico-syntactic analysis of antonyms in some speeches of John Dramani Mahama

Language and politics are intertwined. This is because in order to champion political interest, politicians rely on some powerful linguistic resources to communicate with their audience. Available literature suggests that one of such linguistic resources is antonyms. However, researchers have not paid attention to the use of antonyms in political discourse, especially, in Ghana. On account of this, the present study investigated the lexico-syntactic features of antonyms in some speeches of John Dramani Mahama, a former President of the Republic of Ghana. The study is an interface between cognitive semantics and political discourse which sought to discover the lexico-syntactic features and the functional implications of the antonym pairs used in the speeches of John Dramani Mahama. The study was conducted within the framework of the Lexical Field Theory and the speeches were analysed, using the qualitative research method. Through the use of purposive sampling method, sixteen (16) political speeches of John Dramani Mahama were selected for the analysis. The study relied on Cruse’s (1986) outlined features of antonymy and Murphy’s (2003) theoretical view on context-derived antonymy to identify the antonym pairs in the speeches. The study discovered one hundred and seventy-three (173) antonym pairs in the sixteen (16) selected speeches. The outcome of the study further revealed the noun phrase pair as the largest grammatical category in the selected speeches. The study again showed that John Dramani Mahama usually uses noun antonymic pairs and the coordinated frame X and Y in his political speeches. The study concluded that John Dramani Mahama uses antonyms in his speeches to persuade his audience, establish association, inspire hope and confidence, call for patriotism and hardworking towards national development, and finally, to present his political vision to Ghanaians.

Complete prepotentials of 5d higher rank theories

We generalize recent methods regarding the construction of complete prepotentials of five dimensional SCFTs to two classes of rank-N theories, i.e. the X1,N and the UV fixed point of the SU (N + 1)0 + 2(N + 1)F gauge theories. Their complete prepotentials are consistently constructed starting from their weakly coupled descriptions. The results are verified by employing UV dualities and decoupling of flavors from theories with known complete prepotentials. Applications of these results to the recent investigation of non-supersymmetric conformal field theories from soft supersymmetric breaking deformations are addressed.

Dynamic Multi-Target Self-Organization Hunting Control of Multi-Agent Systems

In this paper, we present a novel coordinated method tailored to address the dynamic multi-target hunting control problem in multi-agent systems, offering significant practical value. Our approach encompasses several key components: initially, we introduce a task allocation model that integrates a fuzzy inference system with a particle swarm optimization algorithm. This hybrid model efficiently allocates hunting tasks for scattered evading targets, effectively transforming the dynamic multi-target hunting problem into multiple dynamic single-target-hunting problems. This transformation enhances the speed and efficacy of task allocation. Subsequently, we propose an attraction/repulsive model grounded in potential field theory. This model facilitates the coordinated hunting of each target by organizing agents into subgroups. Relying solely on relative position and velocity information between agents and targets, our model simplifies computation, while maintaining effectiveness. Furthermore, the coordination of hunting activities for each target is achieved through a series of agent subgroups, guided by our proposed motion model. This systematic approach ensures a cohesive and efficient hunting strategy. Finally, we validate the effectiveness and feasibility of our proposed method through simulation results. These results provide empirical evidence of the method’s efficacy and potential applicability in real-world scenarios.

On the Universal Presence of Mathematics for Incompletely Predictable Problems in Rigorous Proofs for Riemann Hypothesis, Modified Polignac’s and Twin Prime Conjectures

We validly ignore even prime number 2. Based on all arbitrarily large number of even Prime gaps 2, 4, 6, 8, 10...; the complete set and its derived subsets of Odd Primes fully comply with the Prime number theorem for Arithmetic Progressions, and our derived Generic Squeeze theorem and Theorem of Divergent-to-Convergent series conversion for Prime numbers. With these conditions being satisfied by all Odd Primes, we argue Polignac's and Twin prime conjectures are proven to be true when they are usefully treated as Incompletely Predictable Problems. In so doing [and with Riemann hypothesis being a special case], this action also support the generalized Riemann hypothesis formulated for Dirichlet L-function. By broadly applying Hodge conjecture, Grothendieck period conjecture and Pi-Circle conjecture to Dirichlet eta function (proxy function for Riemann zeta function), Riemann hypothesis is separately proven to be true when it is usefully treated as Incompletely Predictable Problem. Crucial connections exist between these Incompletely Predictable Problems and Quantum field theory whereby eligible (sub-)functions and (sub-)algorithms are treated as infinite series.

Higher Time-Derivative Theories from Space–Time Interchanged Integrable Field Theories

We compare a relativistic and a nonrelativistic version of Ostrogradsky’s method for higher-time derivative theories extended to scalar field theories and consider as an alternative a multi-field variant. We apply the schemes to space–time rotated modified Korteweg–de Vries systems and, exploiting their integrability, to Hamiltonian systems built from space–time rotated inverse Legendre transformed higher-order charges of these systems. We derive the equal-time Poisson bracket structures of these theories, establish the integrability of the latter theories by means of the Painlevé test and construct exact analytical period benign solutions in terms of Jacobi elliptic functions to the classical equations of motion. The classical energies of these partially complex solutions are real when they respect a certain modified CPT-symmetry and complex when this symmetry is broken. The higher-order Cauchy and initial-boundary value problem are addressed analytically and numerically. Finally, we provide the explicit quantization of the simplest mKdV system, exhibiting the usual conundrum of having the choice between having to deal with either a theory that includes non-normalizable states or spectra that are unbounded from below. In our non-Hermitian system, the choice is dictated by the correct sign in the decay width.

The Spectral Condition, Plane Waves, and Harmonic Analysis in de Sitter and Anti-de Sitter Quantum Field Theories

We review the role of the spectral condition as a characteristic of Minkowski, de Sitter, and anti-de Sitter quantum field theories. We also discuss the role of plane waves that are compatible with the relevant analyticity domains linked to the spectral condition(s) and discuss harmonic analysis in terms of them.

An Efficient and Accurate SCF Algorithm for Block Copolymer Films and Brushes Using Adaptive Discretizations

Self-consistent field (SCF) theory serves as a robust tool for unraveling the intricate behavior exhibited by soft polymeric materials. However, the accuracy and efficiency of SCF calculations are crucially dependent on the numerical methods employed for system discretization and equation-solving. Here, we introduce a simple three dimensional SCF algorithm that uses real-space methods and adaptive discretization, offering improved accuracy and efficiency for simulating polymeric systems at surfaces. Our algorithm’s efficacy is demonstrated through simulations of two distinct polymeric systems, namely, block copolymer (BCP) films and polymer brushes. By enhancing spatial resolution in regions influenced by external forces and employing finer contour discretization at grafting chain ends, we achieve significantly more accurate results at very little additional cost, enabling the study of 3D polymeric systems that were previously computationally challenging. To facilitate the widespread use of the algorithm, we have made our 1D-3D SCF code publicly available.

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.

What Makes Us See Someone as a Leader? A Field Theory Approach

ABSTRACT We propose that what seems to be uniquely common to individuals perceived as leaders is that they all either meaningfully challenge the status quo or meaningfully resist challenge to the status quo over a sustained period of time. While we note that a relationship between leadership and challenge to the status quo has been alluded to in the literature, especially regarding (but not restricted to) charismatic leadership, a deeper theoretical development has been missing, particularly addressing the context of the social setting in which challenge may occur as opposed to a leader-centric view. Moreover, we observe that a commensurate connection between resistance to challenge and leadership is relatively unobserved and unexplored. We develop our argument drawing on Lewin’s field theory and propose a theoretical explanation of how leadership emerges in the perception of others consequent to the sustained invocation and interaction of situational social forces, specifically meaningful challenge, or resistance to challenge, of the status quo. The theory lends itself to empirical study. MAD statement While the field of change management recognizes the connection between Lewin’s field theory, the process of change and his classic experiments on leadership, it has missed field theory’s connection to the perception of leadership acts and, more specifically, how leadership emerges in the perception of others. We draw on Lewin’s theory to explore the process of leadership emergence. We focus on forces that challenge (and thus attempt to change) the status quo, as well as those that resist challenge (and thus resist change) to the status quo. Our paper makes a difference in extending leadership theory and practice by providing a more robust understanding of the challenge concept and its relationship to perception of leadership, with a detailed discussion about how challenging the status quo works in its social context. We also shed new light on resistance to challenge as a dimension of leadership, wherein leaders oppose change and strive to preserve the status quo. In particular, we explore the missing connection between Lewin’s field theory and leadership emergence. Moreover, we show how Lewin’s field approach can be used to empirically study the forces at work in leadership emergence.

Irrelevant and marginal deformed BMS field theories

In this study, we investigate various deformations within the framework of Bondi-van der Burg-Metzner-Sachs invariant field theory (BMSFT). Specifically, we explore the impact of Bondi-van der Burg-Metzner-Sachs (BMS) symmetry on the theory by introducing key deformations, namely, TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document}, JTμ, and TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{T\\overline{T}} $$\\end{document} deformations. In the context of generic seed theories possessing BMS symmetry, we derive the first-order correction of correlation functions using the systematic application of BMS symmetry ward identities. However, it is worth noting that higher-order corrections are intricately dependent on the specific characteristics of the seed theories. To illustrate our findings, we select the BMS free scalar and free fermion as representative seed theories. We then proceed to analytically determine the deformed action by solving the nontrivial flow equations. Additionally, we extend our analysis to include second-order deformations within these deformed theories.

Effective cuscuton theory

Cuscuton field theory is an extension of general relativity that does not introduce additional propagating degrees of freedom, or violate relativistic causality. We construct a general geometric description of the cuscuton field theory by introducing curvature corrections to both the volume (potential) and the surface (kinetic) terms in the original cuscuton action. Our assumptions involve a stack of spacelike branes, separated by 4-dimensional bulks. We conjecture that the cuscuton, initially a discrete field, becomes continuous in the limit, there are many such transitions. From this we derive an effective action for the cuscuton theory and show that at the quadratic level our theory propagates only the two tensorial degrees of freedom.

Stress tensors of 3d Carroll CFTs

We discuss kinematical features of conformal Carroll field theories in three dimensions (3d). Conformal extension of Carroll algebra is infinite dimensional even in 3d unlike its relativistic counterpart, and hence 3d Carroll CFTs share similarities with 2d CFT. We provide a construction for the conserved charges for Carrollian CFTs and an expression for stress tensor OPEs consistent with the algebra of charges. We discuss a free field model where these symmetries are realised and explicitly compute the OPEs verifying our construction. In addition we comment on the possibility of extending the conformal symmetries to diffeomorphisms of spatial slice for these Carrollian theories.

Quantum Field Theory for Multipolar Composite Bosons with Mass Defect and Relativistic Corrections

Quantum Field Theory for Multipolar Composite Bosons with Mass Defect and Relativistic Corrections

A trace inequality for Euclidean gravitational path integrals (and a new positive action conjecture)

The AdS/CFT correspondence states that certain conformal field theories are equivalent to string theories in a higher-dimensional anti-de Sitter space. One aspect of the correspondence is an equivalence of density matrices or, if one ignores normalizations, of positive operators. On the CFT side of the correspondence, any two positive operators A, B will satisfy the trace inequality Tr(AB) ≤ Tr(A)Tr(B). This relation holds on any Hilbert space H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{H} $$\\end{document} and is deeply associated with the fact that the algebra B(H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{H} $$\\end{document}) of bounded operators on H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{H} $$\\end{document} is a type I von Neumann factor. Holographic bulk theories must thus satisfy a corresponding condition, which we investigate below. In particular, we argue that the Euclidean gravitational path integral respects this inequality at all orders in the semi-classical expansion and with arbitrary higher-derivative corrections. The argument relies on a conjectured property of the classical gravitational action, which in particular implies a positive action conjecture for quantum gravity wavefunctions. We prove this conjecture for Jackiw-Teitelboim gravity and we also motivate it for more general theories.

Feynman Diagrams beyond Physics: From Biology to Economy

Feynman diagrams represent one of the most powerful and fascinating tools developed in theoretical physics in the last century. Introduced within the framework of quantum electrodynamics as a suitable method for computing the amplitude of a physical process, they rapidly became a fundamental mathematical object in quantum field theory. However, their abstract nature seems to suggest a wider usage, which actually exceeds the physical context. Indeed, as mathematical objects, they could simply be considered graphs that depict not only physical quantities but also biological or economic entities. We survey the analytical and algebraic properties of such diagrams to understand their utility in several areas of science, eventually providing some examples of recent applications.