Set Of Symmetries Research Articles

Building 1D lattice models with $G$-graded fusion category

We construct a family of one-dimensional (1D) quantum lattice models based on GG-graded unitary fusion category \mathcal{C}_G𝒞G. This family realize an interpolation between the anyon-chain models and edge models of 2D symmetry-protected topological states, and can be thought of as edge models of 2D symmetry-enriched topological states. The models display a set of unconventional global symmetries that are characterized by the input category \mathcal{C}_G𝒞G. While spontaneous symmetry breaking is also possible, our numerical evidence shows that the category symmetry constrains the models to the extent that the low-energy physics has a large likelihood to be gapless.

The Geometry of the Centre Symmetry Set of a Planar Curve

The Geometry of the Centre Symmetry Set of a Planar Curve

On a Symmetry-Based Structural Deterministic Fractal Fractional Order Mathematical Model to Investigate Conjunctivitis Adenovirus Disease

In the last few years, the conjunctivitis adenovirus disease has been investigated by using the concept of mathematical models. Hence, researchers have presented some mathematical models of the mentioned disease by using classical and fractional order derivatives. A complementary method involves analyzing the system of fractal fractional order equations by considering the set of symmetries of its solutions. By characterizing structures that relate to the fundamental dynamics of biological systems, symmetries offer a potent notion for the creation of mechanistic models. This study investigates a novel mathematical model for conjunctivitis adenovirus disease. Conjunctivitis is an infection in the eye that is caused by adenovirus, also known as pink eye disease. Adenovirus is a common virus that affects the eye’s mucosa. Infectious conjunctivitis is most common eye disease on the planet, impacting individuals across all age groups and demographics. We have formulated a model to investigate the transmission of the aforesaid disease and the impact of vaccination on its dynamics. Also, using mathematical analysis, the percentage of a population which needs vaccination to prevent the spreading of the mentioned disease can be investigated. Fractal fractional derivatives have been widely used in the last few years to study different infectious disease models. Hence, being inspired by the importance of fractal fractional theory to investigate the mentioned human eye-related disease, we derived some adequate results for the above model, including equilibrium points, reproductive number, and sensitivity analysis. Furthermore, by utilizing fixed point theory and numerical techniques, adequate requirements were established for the existence theory, Ulam–Hyers stability, and approximate solutions. We used nonlinear functional analysis and fixed point theory for the qualitative theory. We have graphically simulated the outcomes for several fractal fractional order levels using the numerical method.

Green electricity product menu design for retailers without knowing consumer environmental awareness

Adverse selection problem due to asymmetry of consumer environmental awareness (CEA) could reduce electricity retailer's profit and obstructs renewable energy (RE) consumption. This study analyzes mechanism design problem of retailer constricted by RE consumption quota to incentive consumers display true CEA in competitive retail market. Based on principal-agent theory, we develop an extended principal-agent model with the addition of an RE consumption quota constraint to design a green electricity product menu which includes the green level, the price and electric quantity. Influence of information symmetry and quota setting on product attributes, retailer's profit, consumer utility, RE consumption is analyzed, and results show that: (1) Compare to symmetric information, under asymmetric information, green level of product provided to consumers with CEA (denoted as C1) distorts upward, information rent is greater than zero when quota is large, while green level of product provided to consumers without CEA (denoted as C2) distorts downward, with no information rent. (2) Under asymmetric information, unit environmental premium (UEP) of green electricity positively relates to proportion of C1, CEA level, and incremental WTP, and reaches the maximum value at a certain quota. (3) Under asymmetric information, retailer's profit and RE consumption positively relates to proportion of C1, and CEA level. (4) Under asymmetric information, quota difference could contribute to improve retail service quality under competitive retail market, and RE consumption elevation.

Nearly critical superfluid: effective field theory and holography

We study a nearly critical superfluid system from two complementary approaches. Within the first approach, we formulate a Schwinger-Keldysh effective field theory (EFT) for the system when it is located slightly above the critical temperature. The dynamical variables in the EFT construction are two scalars: a neutral scalar associated with the conserved U(1) charge, and a complex scalar describing the order parameter. The set of symmetries, particularly the dynamical Kubo-Martin-Schwinger (KMS) symmetry and chemical shift symmetry, strictly constrains the form of EFT action. Within the second approach, using the holographic Schwinger-Keldysh technique, we derive the effective action for a “microscopic” holographic superfluid, confirming the EFT construction. A systematic inclusion of non-Gaussianity is one highlight of present study.

Towards natural and realistic E7 GUTs in F-theory

We consider phenomenological aspects of a natural class of Standard Model-like supersymmetric F-theory vacua realized through flux breaking of rigid E7 gauge factors. Three generations of Standard Model matter are realized in many of these vacua. We further find that many other Standard Model-like features are naturally compatible with these constructions. For example, dimension-4 and 5 terms associated with proton decay are ubiquitously suppressed. Many of these features are due to the group theoretical structure of E7 and associated F-theory geometry. In particular, a set of approximate global symmetries descends from the E7 group, leading to exponential suppression of undesired couplings.

Exactly solvable Hamiltonian fragments obtained from a direct sum of Lie algebras.

Exactly solvable Hamiltonians are useful in the study of quantum many-body systems using quantum computers. In the variational quantum eigensolver, a decomposition of the target Hamiltonian into exactly solvable fragments can be used for the evaluation of the energies via repeated quantum measurements. In this work, we apply more general classes of exactly solvable qubit Hamiltonians than previously considered to address the Hamiltonian measurement problem. The most general exactly solvable Hamiltonians we use are defined by the condition that within each simultaneous eigenspace of a set of Pauli symmetries, the Hamiltonian acts effectively as an element of a direct sum of so(N) Lie algebras and can, therefore, be measured using a combination of unitaries in the associated Lie group, Clifford unitaries, and mid-circuit measurements. The application of such Hamiltonians to decomposing molecular electronic Hamiltonians via graph partitioning techniques shows a reduction in the total number of measurements required to estimate the expectation value compared to previously used exactly solvable qubit Hamiltonians.

Counting \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 8 black holes as algebraic varieties

We calculate the helicity trace index B14 for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 8 pure D-brane black holes using various techniques of computational algebraic geometry and find perfect agreement with the existing results in the literature. For these black holes, microstate counting is equivalent to finding the number of supersymmetric vacua of a multi-variable supersymmetric quantum mechanics which in turn is equivalent to solving a set of multi-variable polynomial equations modulo gauge symmetries. We explore four different techniques to solve a set of polynomial equations, namely Newton Polytopes, Homotopy continuation, Monodromy and Hilbert series. The first three methods rely on a mixture of symbolic and high precision numerics whereas the Hilbert series is symbolic and admit a gauge invariant analysis. Furthermore, exploiting various exchange symmetries, we show that quartic and higher order terms are absent in the potential, which if present would have spoiled the counting. Incorporating recent developments in algebraic geometry focusing on computational algorithms, we have extended the scope of one of the authors previous works [1, 2] and presented a new perspective for the black hole microstate counting problem. This further establishes the pure D-brane system as a consistent model, bringing us a step closer to \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 2 black hole microstate counting.

AutoEFT: Automated operator construction for effective field theories

The program AutoEFT is described. It allows one to generate Effective Field Theories (EFTs) from a given set of fields and symmetries. Allowed fields include scalars, spinors, gauge bosons, and gravitons. The symmetries can be local or global Lie groups based on U(1) and SU(N). The mass dimension of the EFT is limited only by the available computing resources. The operators are stored in a compact, human and machine-readable format. Aside from the program itself, we provide input files for EFTs based on the Standard Model and a number of its extensions. These include additional particles and symmetries, EFTs with minimal flavor violation, and gravitons. Program summaryProgram title:AutoEFTCPC Library link to program files:https://doi.org/10.17632/z8xm2hpbsp.1Developer's repository link:https://gitlab.com/auto_eft/autoeftLicensing provisions: MIT licenseProgramming language:PythonNature of problem: The bottom-up construction of an Effective Field Theory (EFT) which describes physics below a certain energy scale Λ requires obtaining a set of operators, composed of fields with mass m≪Λ, that are invariant under certain symmetries. One is primarily interested in complete sets of independent operators, called operator bases. Their construction for a given mass dimension of the operators is nontrivial due to algebraic and kinematic relations that may render different operators redundant. Except for the lowest mass dimensions, the number of operators is so large that the task of constructing an explicit EFT operator basis requires a high degree of automation on a computer. In addition, an automated approach will allow one to immediately take into account newly postulated or discovered light particles beyond the Standard Model.Solution method: Based on the group theoretical techniques and concepts established in Refs. [1–9] and in particular Refs. [10,11], we developed the program AutoEFT, capable of constructing a non-redundant on-shell operator basis for general EFTs and arbitrary mass dimension. Provided a suitable model file, the respective operator basis is generated explicitly, including contractions of the symmetry group indices, in a fully automated fashion. Due to the generality of the algorithm, it can be applied to a variety of low-energy scenarios. The underlying low-energy theory is encoded in a model file which defines the symmetries and the field content. The fairly simple format enables the user to compose their own model files and to construct the respective operator basis with minimal effort.Additional comments including restrictions and unusual features: In its current form, AutoEFT is restricted to theories including particles with spin 0, 1/2, 1, and 2, where the latter two are considered massless. In addition, AutoEFT only constructs operators that mediate proper interactions, meaning that any operator must be composed of at least three fields. The internal symmetries must be given as factors of U(1) and SU(N) groups. In principle, operator bases can be generated for any mass dimension, which is, however, limited by the available computing resources.

Optimal system and conservation laws for the generalized Fisher equation in cylindrical coordinates

The reaction diffusion equation arises in physical situations in problems from population growth, genetics and physical sciences. In many practical situations, the physical domain of the problem is adequately described in cylindrical Coordinates. Therefore, we consider the Fisher equation in cylindrical coordinates. We consider the generalised Fisher equation in cylindrical coordinates from Lie theory stand point. An invariance method is performed and the optimal set of nonequivalent symmetries is obtained. Finally, the conservation laws are constructed using ’multiplier method’. We determine multipliers as functions of the dependent and independent variables only. The conservation laws are computed and presented in terms of conserved vector corresponding to each multiplier.

Painlevé analysis, Prelle–Singer approach, symmetries and integrability of damped Hénon–Heiles system

We consider a modified damped version of Hénon–Heiles system and investigate its integrability. By extending the Painlevé analysis of ordinary differential equations we find that the modified Hénon–Heiles system possesses the Painlevé property for three distinct parametric restrictions. For each of the identified cases, we construct two independent integrals of motion using the well known Prelle–Singer method. We then derive a set of nontrivial non-point symmetries for each of the identified integrable cases of the modified Hénon–Heiles system. We infer that the modified Hénon–Heiles system is integrable for three distinct parametric restrictions. Exact solutions are given explicitly for two integrable cases.

The Predicament of Ethnic Federal System

The paper inquiries into ethnic federalism in lights of ethnic conflict and federal constitutional viability. It raises the basic question why some ethnic federations are successful in regulating ethnic relations while others are not. The history of federations has ample evidences that ethnic conflict, encompassing ethnic tensions and direct violence conflicts, causes and be caused by the failure of ethnic federalism. How a given ethnic federal system designed to adjust ethnic relations could self-contradictory induce far-reaching communal ethnic conflicts and ethnic based anti-regime activities is an interesting question. Answering that, the paper has given due consideration to the practices of defunct, fragile and mature ethnic federations and to the relevant conceptual and theoretical-back standings. The differences in the viabilities of these federations have shown the complicacy of ethnic federalism in meeting with the convulsive interplay between ethnic conflicts and federal system stability. In that regard, the paper finds seven factors: the democratic representativeness of federal structures, political parties, inclusive and overarching identities crossing ethnic lines, ethnic demographic shares, number of ethnic federal units and their ethnic composition, ethnic federal unit symmetry and geo-political setting. The concussion goes that ethnic federal design is not always an antidote for ethnic based claims and counter-claims. It rather could exacerbate the condition of ethnic politics, if it lacks those political, institutional and social ingredients inferred from the indicated factors.

Infinite $\mathrm{T\bar T}$-like symmetries of compactified LST

We show that the three-dimensional asymptotically linear dilaton background that arises in the near-horizon decoupling region of NS5-branes compactified on T^4T4 admits boundary conditions that lead to an infinite set of symmetries. The associated conserved charges, which implement field-dependent coordinate transformations, are found to be identical to the corresponding generators in a symmetric product orbifold of T\bar TTT‾ - deformed CFTs. Their algebra is a non-linear modification of the Virasoro × Virasoro algebra, which precisely coincides with the algebra of the “unrescaled” symmetry generators in T\bar TTT‾-deformed CFTs. This further strengthens a previously proposed link between the single-trace T\bar TTT‾ deformation and compactified little string theory.

Schrödinger Symmetry in Gravitational Mini-Superspaces

We prove that the simplest gravitational symmetry-reduced models describing cosmology and black hole mechanics are invariant under the Schrödinger group. We consider the flat FRW cosmology filled with a massless scalar field and the Schwarzschild black hole mechanics and construct their conserved charges using the Eisenhart–Duval (ED) lift method in order to show that they form a Schrödinger algebra. Our method illustrates how the ED lift and the more standard approach analyzing the geometry of the field space are complementary in revealing different sets of symmetries of these systems. We further identify an infinite-dimensional symmetry for those two models, generated by conserved charges organized in two copies of a Witt algebra. These extended charge algebras provide a new algebraic characterization of these homogeneous gravitational sectors. They guide the path to their quantization and open the road to non-linear extensions of quantum cosmology and quantum black hole models in terms of hydrodynamic equations in field space.

Re-evaluating the structure of consciousness through the symintentry hypothesis

The Projective Consciousness Model and its extension to the phenomenal selfhood model are the generic invariant structures of consciousness through five symmetries. They include the following: situated 3D spatiality; temporal integration through encompassing the three “nows” that constitute the Now; multimodal synchronic integration; relational phenomenal intentionality; and consciousness entails a pre-reflective awareness of the uniqueness of the phenomenal self. These symmetries stem from the evolution and emergence of the phenomenal self through modeling, and that is realized through the phenomenal modeling of the intentionality relationship. We propose that this set of symmetries is based on and can be explicated in terms of a more fundamental symmetry, symmetry-based modeling. The proposal stems from (a) Kant's transcendental structuralism, which asserts that “Objects” conform to models prescribed through the inherent structure of the phenomenal mind, and (b) Cassirer's proposition that a mathematical group underpins this structure. To validate our proposal, we stipulate this group defining symmetry-based modeling and its emergence and adaptation into structuring the Now. We find that Cassirer's group requires a more powerful dual quaternion operator to be able to support intentionality and the five symmetries. We propose that the efficacy of this operator stems from unifying symmetry-based modeling and intentionality as “symintentry.” Symintentry, we argue, is not just a new form of symmetry but is the archetypical form of symmetry. Symintentry provides fresh insights into the nature of symmetry, intentionality, and consciousness.

Symmetry analysis, optimal system, and invariant solutions for a (2+1)-dimensional two-phase mass flow model

The paper investigates a two-phase mass flow model governed by gravity, involving solid particles and a viscous fluid. By utilizing the Lie symmetries admitted by the system, similarity solutions for the (2+1)-dimensional two-phase mass flow model are obtained. A comprehensive set of local point symmetries is established, and a well-suited collection of two-dimensional subalgebras is constructed from the maximal Lie invariance algebra. The optimal system’s vector fields are then utilized to directly reduce the governing model to a system of ordinary differential equations. Through analytical solutions, we successfully solve the resulting systems and further analyze their physical behaviors numerically.

Particle realization of Bondi-Metzner-Sachs symmetry in 2 + 1 space-time

We construct a Lorentz invariant massive particle model in (2+1) space-time with an enlarged set of symmetries which includes Bondi-Metzner-Sachs (BMS) translations (supertranslations), using the non-linear realization framework. The Hamiltonian formalism for the resulting Lagrangian is constructed, and the infinite phase-space constraints and the set of gauge transformations are analysed. We also compute the massless limit of the theory in phase-space. After eliminating the gauge degrees of freedom, the physical reduced space is left only with the degrees of freedom of a standard Poincaré particle but with a residual set of symmetries that we prove to be BMS. A similar result for the massless limit, including in this case superrotations, is pointed out.

A unifying framework for BRST and BRST-related symmetries

We propose a general framework to study BRST-related transformations. We investigate different forms of BRST and BRST-related symmetries, realized within a prototypical first-class system, including ordinary BRST, anti-BRST, dual-BRST, anti-dual-BRST and additional sets of new BRST-related symmetries. We identify a precise discrete group of symmetries of the ghost sector, responsible for connecting the various forms of BRST-related transformations. Their distinct roles in different Hamiltonian and Lagrangian approaches are clarified. As a unifying framework, we use a gauge invariant prototypical first-class system encompassing an extensive class of physical models.

Groups of Symmetries of the Two Classes of Synthetases in the Four-Dimensional Hypercubes of the Extended Code Type II.

Aminoacyl-tRNA synthetases (aaRSs) originated from an ancestral bidirectional gene (mirror symmetry), and through the evolution of the genetic code, the twenty aaRSs exhibit a symmetrical distribution in a 6-dimensional hypercube of the Standard Genetic Code. In this work, we assume a primeval RNY code and the Extended Genetic RNA code type II, which includes codons of the types YNY, YNR, and RNR. Each of the four subsets of codons can be represented in a 4-dimensional hypercube. Altogether, these 4 subcodes constitute the 6-dimensional representation of the SGC. We identify the aaRSs symmetry groups in each of these hypercubes. We show that each of the four hypercubes contains the following sets of symmetries for the two known Classes of synthetases: RNY: dihedral group of order 4; YNY: binary group; YNR: amplified octahedral group; and RNR: binary group. We demonstrate that for each hypercube, the group of symmetries in Class 1 is the same as the group of symmetries in Class 2. The biological implications of these findings are discussed.

Symmetry properties and asymmetry evaluation of Bayesian Confirmation Measures

Bayesian Confirmation Measures (BCMs) are used to assess the degree to which an evidence (or premise) E supports or contradicts an hypothesis (or conclusion) H, making use of prior probability Pr(H), posterior probability Pr(H|E) and of probability of evidence Pr(E). In the literature many BCMs have been defined with the consequent need for their comparison. For this purpose, various criteria have been proposed and some of these refer to symmetry properties. We relate the set of possible symmetries of BCMs, via an isomorphism, to the dihedral group of symmetries of the square. In this way it is possible to identify 10 subsets of symmetries that can coexist, for each subset we suggest a representative BCM, defining at this aim two new BCMs. The structure of the subgroups of the dihedral group allows also to provide an algorithm that simplifies the verification of the symmetry properties. Addressing the debate on which symmetry properties should be considered as desirable and which should not, we define asymmetry measures for BCMs. In fact, different BCMs that do not satisfy a specific symmetry property may exhibit different levels of asymmetry, this way resulting more (less) desirable. The evidence for the practical use of the approach is given through the numerical evaluation of the asymmetry degrees of some BCMs, showing this way how it is possible to discover some of their characteristics, similarities and differences.