Field Theoretical Approach Research Articles

Statistical field theory for polar fluids.

Using a variational field-theoretic approach, we derive a theory for polar fluids. The theory naturally accounts for the reaction field without resorting to the cavity construct and leads to a simple formula for the dielectric constant in terms of the molecular dipole moment and density. We apply our formula to calculate the dielectric constants of nonpolarizable liquid models for more than a hundred small molecules without using any adjustable parameters. Our formula predicts dielectric constants of these nonpolarizable liquid models more accurately than the Onsager theory and previous field-theoretic dielectric theories, as demonstrated by the closer agreement to the simulation results. The general theory also yields the free energy, which can describe the response of polar fluids under applied electric fields.

Microscopic field-theoretical approach for mixtures of active and passive particles

We consider a phase field crystal modeling approach for mixtures of interacting active and passive particles in two dimensions. The approach allows us to describe generic properties for such heterogeneous systems within a continuum model. We validate the approach by reproducing experimental results, as well as results obtained with agent-based simulations. The approach is valid for the whole spectrum from highly dilute suspensions of passive particles and interacting active particles in a dense background of passive particles. However, we concentrate only on the extreme cases, because for the situation with similar fractions of active and passive particles emerging structures are hard to analyze and experimental results are missing. We analyze in detail enhanced crystallization due to the presence of active particles, how collective migration is affected by a disordered environment, and laning states, which are globally nematic but polar within each lane.

Understanding the effects of symmetric salt on the structure of a planar dipolar polymer brush.

The effects of added salt on a planar dipolar polymer brush immersed in a polar solvent are studied using a field theoretic approach. The field theory developed in this work provides a unified framework for capturing effects of the inhomogeneous dielectric function, translational entropy of ions, crowding due to finite sized ions, ionic size asymmetry, and ion solvation. In this paper, we use the theory to study the effects of ion sizes, their concentration, and ion-solvation on the polymer segment density profiles of a dipolar brush immersed in a solution containing symmetric salt ions. The interplay of crowding effects, translational entropy, and ion solvation is shown to exhibit either an increase or decrease in the brush height. Translational entropy and crowding effects due to finite sizes of the ions tend to cause expansion of the brush as well as uniform distribution of the ions. By contrast, ion-solvation effects, which tend to be stronger for smaller ions, are shown to cause shrinkage of the brush and inhomogeneous distribution of the ions.

Light-front and conformal field theories in two dimensions

Light-front (LF) quantization of massless fields in two spacetime dimensions is a long-standing and much debated problem. Even though the classical wave-equation is well-documented for almost two centuries, either as problems with initial values in spacetime variables or with initial data on characteristics in light-cone variables, the way to a consistent quantization in both types of frames is still a puzzle in many respects. This is in contrast to the most successful Conformal Field Theoretic (CFT) approach in terms of complex variables [Formula: see text], [Formula: see text] pioneered by Belavin, Polyakov and Zamolodchikov in the ’80s. It is shown here that the 2D-massless canonical quantization in both reference frames is completely consistent provided that quantum fields are treated as Operator-Valued Distributions (OPVD) with Partition of Unity (PU) test functions. We recall first that classical fields have to be considered as distributions (e.g. generalized functions in the Russian literature). Then, a necessary condition on the PU test function follows from the required matching of the classical solutions of the massless differential equations in both types of reference frame. Next we use a mathematical formulation for OPVD, developed in the recent past. Specifically, smooth [Formula: see text] fields are introduced through the convolution operation in the distributional context. Due to the specific behavior of the Fourier-transform of the initial test function, this convolution transform has a well-defined integral in the dual space, whatever the initial choice of the reference frame. The relation to the conformal fields method follows immediately from the transition to Euclidean time and leads directly to explicit calculations of a few correlation functions of the scalar field and its energy–momentum tensor. The LF derivation of the Virasoro algebra is then obtained from the [Formula: see text] and [Formula: see text] expansions of the canonical fields as distributional Laplace-transform in these variables. Finally, the popular and problematic Discretized Light Cone Quantization (DLCQ) method is scrutinized with respect to its zero mode and ultraviolet content as encompassed in the continuum OPVD formulation.

Masculinity, sexual citizenship and religion in post-apartheid South Africa: a field-theoretical approach

ABSTRACTWith regard to notions of legitimate masculinity, Black South African men are torn between two antithetical discourses: one organized around liberal notions of rights and freedoms and driven by secular civil society, the other grounded in the values of ‘traditional’ masculinity. In this article, I draw on Bourdieu’s theory of social fields as well as recent ethnographic work in Cape Town and substitute this dichotomy with a fourfold matrix of liberal, traditional, youth gang-oriented and religiously based masculinities. Employing a relational methodology, the article explores how Pentecostal men in Cape Town’s townships position themselves within this field of masculinities and the shifting implications of this positioning for the politics of sexual citizenship. I argue that Pentecostal masculinity is not a stable and fixed configuration of gendered attitudes, values and performances, but a set of cultural distinctions that shift with the problem-space these distinctions address as well as the values they are meant to articulate.

Bourdieu’s capital and insurgent group resilience:a field-theoretic approach to the polisario front

ABSTRACTThe conflict between the rebel group, the Polisario Front, and the Kingdom of Morocco is nearing its 43rd year. Though under-reported, the conflict itself garners attention for the resilience – some would say tenacity – of the ethnically Sahrawi Polisario Front. Despite shifting regional and international politics and the nearly 150,000 Sahrawi refugees waiting in nearby Algerian camps, the rebel group has survived. What explains its resilience? This article uses Bourdieu’s ‘forms of capital’ to understand the Polisario Front’s persistence. Based on field research in Algeria, Western Sahara, and the United States, it finds that social, cultural, symbolic, and economic capital may provide an explanation.

Scratching a 50-year itch with elongated rods

ABSTRACTThe classical Oseen–Frank theory of liquid crystal elasticity is based on the experimentally verified fact that there are three independent modes of distortion, each with its associated elastic constant. On the other hand, the arguably more first-principles order parameter-based Landau–de Gennes theory only involves two independent elastic modes. The resulting ‘elastic constants problem’ has led to a considerable amount of vexation among theorists. In a series of papers at the turn of the century, Fukuda en Yokoyama suggested that the resolution of this problem could be found in the proper treatment of non-local effects in the ideal part of the free energy. They used an ingenious, but technically complex, technique based on a field-theoretic approach to semi-flexible polymers. Here we revisit their idea but now in the more accessible framework of density functional theory of rigid particles. Our work recovers their main results for rod-like particles, in that generically an ordered assembly of non-interacting rods has three independent elastic constants associated to it that all scale as the square of the length of the particles and obey the inequalities . We also consider the case of disc-like particles, and then find in line with expectations that .

Electrostatic field theoretic approach to analyze the partial discharge phenomenon pertaining to insulation degradation

This paper elucidates the application of electrostatic field theory to analyze partial discharge due to the void formation inside the insulating material. Formation of voids leads to accumulation of static charges leading to capacitance build-up. The most probable cause of insulation failure is due to the subjection of high voltage. Prolonged high voltage poses a threat and leads to insulation failure. Failures occur in the tip gap between the conductor and insulating material’s inner periphery. Probable causes of such failures are corona discharge, surface discharge and treeing, leading to formation of Lichtenberger figures in the material and cavity discharge. This paper presents a way of fabricating the inner lining of the insulator with a semiconductor layer obeying avalanche breakdown at breakdown voltage or voltages at which partial discharge is likely to occur. With the onset of high voltage which can cause a discharge, the semiconductor experiences avalanche breakdown giving out a single photon ejection by Geiger mode (principle). A superior prevention method of using Teflon for insulation instead of XLPE/PILC has been suggested and simulated using COMSOL. Detection using Avalanche photo-detector(LiDAR) may enable us to track the probable location of the occurrence of partial discharge and isolate the system.

Coherent states field theory in supramolecular polymer physics.

In 1970, Edwards and Freed presented an elegant representation of interacting branched polymers that resembles the coherent states (CS) formulation of second-quantized field theory. This CS polymer field theory has been largely overlooked during the intervening period in favor of more conventional "auxiliary field" (AF) interacting polymer representations that form the basis of modern self-consistent field theory (SCFT) and field-theoretic simulation approaches. Here we argue that the CS representation provides a simpler and computationally more efficient framework than the AF approach for broad classes of reversibly bonding polymers encountered in supramolecular polymer science. The CS formalism is reviewed, initially for a simple homopolymer solution, and then extended to supramolecular polymers capable of forming reversible linkages and networks. In the context of the Edwards model of a non-reacting homopolymer solution and one and two-component models of telechelic reacting polymers, we discuss the structure of CS mean-field theory, including the equivalence to SCFT, and show how weak-amplitude expansions (random phase approximations) can be readily developed without explicit enumeration of all reaction products in a mixture. We further illustrate how to analyze CS field theories beyond SCFT at the level of Gaussian field fluctuations and provide a perspective on direct numerical simulations using a recently developed complex Langevin technique.

Neutrino oscillation processes in a quantum-field-theoretical approach

It is shown that neutrino oscillation processes can be consistently described in the framework of quantum field theory. Namely, the oscillating electron survival probabilities in experiments with neutrino detection by charged-current and neutral-current interactions are calculated in the quantum field-theoretical approach to neutrino oscillations based on a modification of the Feynman propagator. The approach is most similar to the standard Feynman diagram technique in the momentum representation. It is found that the oscillating distance-dependent probabilities of detecting an electron in experiments with neutrino detection by charged-current and neutral-current interactions exactly coincide with the corresponding probabilities calculated in the standard approach.

On the Renormalization Group Explanation of Universality

It is commonly claimed that the universality of critical phenomena is explained through particular applications of the renormalization group (RG). This article has three aims: to clarify the structure of the explanation of universality, to discuss the physics of such RG explanations, and to examine the extent to which universality is thus explained. The derivation of critical exponents proceeds via a real-space or a field-theoretic approach to the RG. Building on work by Mainwood, this article argues that these approaches ought to be distinguished: while the field-theoretic approach explains universality, the real-space approach fails to provide an adequate explanation.

What is the Right Theory for Anderson Localization of Light? An Experimental Test.

Anderson localization of light is traditionally described in analogy to electrons in a random potential. Within this description, the random potential depends on the wavelength of the incident light. For transverse Anderson localization, this leads to the prediction that the distribution of localization lengths-and, hence, its average-strongly depends on the wavelength. In an alternative description, in terms of a spatially fluctuating electric modulus, this is not the case. Here, we report on an experimentum crucis in order to investigate the validity of the two conflicting theories using optical samples exhibiting transverse Anderson localization. We do not find any dependence of the observed average localization radii on the light wavelength. We conclude that the modulus-type description is the correct one and not the potential-type one. We corroborate this by showing that in the derivation of the traditional potential-type theory, a term in the wave equation has been tacitly neglected. In our new modulus-type theory, the wave equation is exact. We check the consistency of the new theory with our data using the nonlinear sigma model. We comment on the consequences for the general case of three-dimensional disorder.

Cell Growth Rate Dictates the Onset of Glass to Fluid-Like Transition and Long Time Super-Diffusion in an Evolving Cell Colony

Collective migration dominates many phenomena, from cell movement in living systems to abiotic self-propelling particles. Focusing on the early stages of tumor evolution, we enunciate the principles involved in cell dynamics and highlight their implications in understanding similar behavior in seemingly unrelated soft glassy materials and possibly chemokine-induced migration of CD8$^{+}$ T cells. We performed simulations of tumor invasion using a minimal three dimensional model, accounting for cell elasticity and adhesive cell-cell interactions as well as cell birth and death to establish that cell growth rate-dependent tumor expansion results in the emergence of distinct topological niches. Cells at the periphery move with higher velocity perpendicular to the tumor boundary, while motion of interior cells is slower and isotropic. The mean square displacement, $\Delta(t)$, of cells exhibits glassy behavior at times comparable to the cell cycle time, while exhibiting super-diffusive behavior, $\Delta (t) \approx t^{\alpha}$ ($\alpha > 1$), at longer times. We derive the value of $\alpha \approx 1.33$ using a field theoretic approach based on stochastic quantization. In the process we establish the universality of super-diffusion in a class of seemingly unrelated non-equilibrium systems. Super diffusion at long times arises only if there is an imbalance between cell birth and death rates. Our findings for the collective migration, which also suggests that tumor evolution occurs in a polarized manner, are in quantitative agreement with {\it in vitro} experiments. Although set in the context of tumor invasion the findings should also hold in describing collective motion in growing cells and in active systems where creation and annihilation of particles play a role.

A field theoretic approach to the energy–momentum–tensor for theories coupled with gravity

We provide a field-theoretic algorithm of obtaining energy–momentum–tensor (EMT) for gravitationally coupled scalar field theories. The method is equally applicable to both minimal and non-minimal coupling. The algorithm illuminates the connection between the EMT, obtained by functional variation of the metric, and local balance of energy and momentum.

Field theory of hyperfluid

A hyperfluid model is constructed on the basis of its action entirely free from external constraints, regarding the hyperfluid as a self-consistent classical field. Intrinsic hypermomentum is no longer a supplemental variable given by external constraints, but arises purely from the diffeomorphism covariance of dynamical field. The field-theoretic approach allows natural classification of a hyperfluid on the basis of its symmetry group and corresponding homogeneous space; scalar, spinor, vector, and tensor fluids are introduced as simple examples. Apart from phenomenological constraints, the theory predicts the hypermomentum exchange of fluid via field-theoretic interactions of various classes; fluid–fluid interactions, minimal and non-minimal -gauge couplings, and coupling with metric-affine gravity are all successfully formulated within the classical regime.

Structure and properties of polydisperse polyelectrolyte brushes studied by self-consistent field theory.

Two complementary self-consistent field theoretical approaches are used to analyze the equilibrium structure of binary and ternary brushes of polyions with different degrees of polymerization. Stratification in binary brushes is predicted: the shorter chains are entirely embedded in the proximal sublayer depleted of end-points of longer chains while the peripheral sublayer contains exclusively terminal segments of longer chains. The boundary between sublayers is enriched with counterions that neutralize the residual charge of the proximal sublayer. These analytical predictions for binary brushes are confirmed and extended to ternary brushes using the numerical Scheutjens-Fleer approach.

Unravelling ambivalence: A field-theoretical approach to moralised markets

Moralised markets are often referred to as ethical consumption markets. They are supposed to relieve a source of major distress in capitalist societies: the conflict between morality and economy. But under what conditions do these markets grow, and when do they stagnate? Deviating from the dominant focus on external constraints, this article emphasises the intrinsic ambivalence of moralised markets. Being caught between moral and economic exigencies becomes an obstacle for market growth. The article addresses ‘unravelling ambivalence’ on two levels. First, a field-theoretical framework is used to unravel the concept of ambivalence. Inspired by Pierre Bourdieu, the article proposes introducing ambivalence as an analytical category in economic sociology. Second, a historic study based on correspondence analysis depicts the development of the German organic milk market. What distinguishes growth from stagnation is the degree of ambivalence within this market. Only if opposition is mitigated and ambivalence unravels into a more pluralistic field structure does the transition from niche to mass market become viable.

Comparison of Field-Theoretic Approaches in Predicting Polymer Nanocomposite Phase Behavior

Because of the considerable parameter space, efficient theoretical and simulation methods are required to predict the morphology and guide experiments in polymer nanocomposites (PNCs). Unfortunately, theoretical and simulation methods are restricted in their ability to accurately map to experiments based on necessary approximations and numerical limitations. In this study, we provide direct comparisons of two recently developed coarse-grained approaches for modeling polymer nanocomposites (PNCs): polymer nanocomposite field theory (PNC-FT) and dynamic mean-field theory (DMFT). These methods are uniquely suited to efficiently capture mesoscale phase behavior of PNCs in comparison to other theoretical and simulation frameworks. We demonstrate the ability of both methods to capture macrophase separation and describe the thermodynamics of PNCs. We systematically test how the nanoparticle morphology in PNCs is affected by a uniform probability distribution of grafting sites, common in field-based methods, vers...

LHC searches for dark sector showers

This paper proposes a new search program for dark sector parton showers at the Large Hadron Collider (LHC). These signatures arise in theories characterized by strong dynamics in a hidden sector, such as Hidden Valley models. A dark parton shower can be composed of both invisible dark matter particles as well as dark sector states that decay to Standard Model particles via a portal. The focus here is on the specific case of ‘semi-visible jets,’ jet-like collider objects where the visible states in the shower are Standard Model hadrons. We present a Simplified Model-like parametrization for the LHC observables and propose targeted search strategies for regions of parameter space that are not covered by existing analyses. Following the ‘mono-X’ literature, the portal is modeled using either an effective field theoretic contact operator approach or with one of two ultraviolet completions; sensitivity projections are provided for all three cases. We additionally highlight that the LHC has a unique advantage over direct detection experiments in the search for this class of dark matter theories.

Quantum field theoretical description of neutrino oscillations and reactor antineutrino anomaly

We suggest a possible explanation of the reactor antineutrino anomaly derived from a covariant quantum field-theoretical approach to neutrino oscillations. Some disadvantages of the currently prevailing interpretation of the anomaly, based upon the sterile neutrino hypothesis are pointed out.