354 results match your criteria Algebras And Representation Theory[Journal]


On Multimatrix Models Motivated by Random Noncommutative Geometry II: A Yang-Mills-Higgs Matrix Model.

Ann Henri Poincare 2022 23;23(6):1979-2023. Epub 2022 Apr 23.

Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warsaw, Poland.

We continue the study of fuzzy geometries inside Connes' spectral formalism and their relation to multimatrix models. In this companion paper to Pérez-Sánchez (Ann Henri Poincaré 22:3095-3148, 2021, arXiv:2007.10914), we propose a gauge theory setting based on noncommutative geometry, which-just as the traditional formulation in terms of almost-commutative manifolds-has the ability to also accommodate a Higgs field. Read More

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Quantum Relativity of Subsystems.

Phys Rev Lett 2022 Apr;128(17):170401

Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA.

One of the most basic notions in physics is the partitioning of a system into subsystems and the study of correlations among its parts. In this Letter, we explore this notion in the context of quantum reference frame (QRF) covariance, in which this partitioning is subject to a symmetry constraint. We demonstrate that different reference frame perspectives induce different sets of subsystem observable algebras, which leads to a gauge-invariant, frame-dependent notion of subsystems and entanglement. Read More

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On the role of continuous symmetries in the solution of the three-dimensional Euler fluid equations and related models.

Philos Trans A Math Phys Eng Sci 2022 Jun 9;380(2226):20210050. Epub 2022 May 9.

School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland.

We review and apply the continuous symmetry approach to find the solution of the three-dimensional Euler fluid equations in several instances of interest, via the construction of constants of motion and infinitesimal symmetries, without recourse to Noether's theorem. We show that the vorticity field is a symmetry of the flow, so if the flow admits another symmetry then a Lie algebra of new symmetries can be constructed. For steady Euler flows this leads directly to the distinction of (non-)Beltrami flows: an example is given where the topology of the spatial manifold determines whether extra symmetries can be constructed. Read More

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The universal algebra of the electromagnetic field III. Static charges and emergence of gauge fields.

Lett Math Phys 2022 21;112(2):27. Epub 2022 Mar 21.

Dipartimento di Matematica, Universitá di Roma "Tor Vergata", Via della Ricerca Scientifica 1, 00133 Roma, Italy.

A universal C*-algebra of gauge invariant operators is presented, describing the electromagnetic field as well as operations creating pairs of static electric charges having opposite signs. Making use of Gauss' law, it is shown that the string-localized operators, which necessarily connect the charges, induce outer automorphisms of the algebra of the electromagnetic field. Thus they carry additional degrees of freedom which cannot be created by the field. Read More

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SU(2/1) superchiral self-duality: a new quantum, algebraic and geometric paradigm to describe the electroweak interactions.

J High Energy Phys 2021 Apr 1;2021(4). Epub 2021 Apr 1.

School of Natural Sciences (Mathematics and Physics), University of Tasmania, Private Bag 37, Hobart, Tasmania 7001, Australia.

We propose an extension of the Yang-Mills paradigm from Lie algebras to internal chiral superalgebras. We replace the Lie algebra-valued connection one-form , by a superalgebra-valued polyform mixing exterior-forms of all degrees and satisfying the chiral self-duality condition , where denotes the superalgebra grading operator. This superconnection contains Yang-Mills vectors valued in the even Lie subalgebra, together with scalars and self-dual tensors valued in the odd module, all coupling only to the charge parity CP-positive Fermions. Read More

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A signature invariant geometric algebra framework for spacetime physics and its applications in relativistic dynamics of a massive particle and gyroscopic precession.

Authors:
Bofeng Wu

Sci Rep 2022 Mar 7;12(1):3981. Epub 2022 Mar 7.

Department of Physics, College of Sciences, Northeastern University, Shenyang, 110819, China.

A signature invariant geometric algebra framework for spacetime physics is formulated. By following the original idea of David Hestenes in the spacetime algebra of signature [Formula: see text], the techniques related to relative vector and spacetime split are built up in the spacetime algebra of signature [Formula: see text]. The even subalgebras of the spacetime algebras of signatures [Formula: see text] share the same operation rules, so that they could be treated as one algebraic formalism, in which spacetime physics is described in a signature invariant form. Read More

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K-Theory for Semigroup C*-Algebras and Partial Crossed Products.

Authors:
Xin Li

Commun Math Phys 2022 22;390(1):1-32. Epub 2021 Aug 22.

School of Mathematics and Statistics, University of Glasgow, University Place, Glasgow, G12 8QQ UK.

Using the Baum-Connes conjecture with coefficients, we develop a K-theory formula for reduced C*-algebras of strongly 0--unitary inverse semigroups, or equivalently, for a class of reduced partial crossed products. This generalizes and gives a new proof of previous K-theory results of Cuntz, Echterhoff and the author. Our K-theory formula applies to a rich class of C*-algebras which are generated by partial isometries. Read More

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Miura operators, degenerate fields and the M2-M5 intersection.

J High Energy Phys 2022 17;2022(1):86. Epub 2022 Jan 17.

Center for Theoretical Physics, University of California, Berkeley, CA USA.

We determine the mathematical structures which govern the Ω deformation of supersymmetric intersections of M2 and M5 branes. We find that the supersymmetric intersections govern many aspects of the theory of W-algebras, including degenerate modules, the Miura transform and Coulomb gas constructions. We give an algebraic interpretation of the Pandharipande-Thomas box counting in ℂ. Read More

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January 2022

Sheffer operation in relational systems.

Soft comput 2022 17;26(1):89-97. Epub 2021 Nov 17.

Faculty of Science, Department of Algebra and Geometry, Palacký University Olomouc, 17. listopadu 12, 771 46 Olomouc, Czech Republic.

The concept of a Sheffer operation known for Boolean algebras and orthomodular lattices is extended to arbitrary directed relational systems with involution. It is proved that to every such relational system, there can be assigned a Sheffer groupoid and also, conversely, every Sheffer groupoid induces a directed relational system with involution. Hence, investigations of these relational systems can be transformed to the treatment of special groupoids which form a variety of algebras. Read More

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November 2021

Causality in Schwinger's Picture of Quantum Mechanics.

Entropy (Basel) 2022 Jan 1;24(1). Epub 2022 Jan 1.

Dipartimento di Matematica ed Applicazioni, Università Federico II, Napoli, 40, 80138 Naples, Italy.

This paper begins the study of the relation between causality and quantum mechanics, taking advantage of the groupoidal description of quantum mechanical systems inspired by Schwinger's picture of quantum mechanics. After identifying causal structures on groupoids with a particular class of subcategories, called causal categories accordingly, it will be shown that causal structures can be recovered from a particular class of non-selfadjoint class of algebras, known as triangular operator algebras, contained in the von Neumann algebra of the groupoid of the quantum system. As a consequence of this, Sorkin's incidence theorem will be proved and some illustrative examples will be discussed. Read More

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January 2022

Along the Lines of Nonadditive Entropies: -Prime Numbers and -Zeta Functions.

Entropy (Basel) 2021 Dec 28;24(1). Epub 2021 Dec 28.

National Institute of Science and Technology of Complex Systems, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, Brazil.

The rich history of prime numbers includes great names such as Euclid, who first analytically studied the prime numbers and proved that there is an infinite number of them, Euler, who introduced the function ζ(s)≡∑n=1∞n-s=∏pprime11-p-s, Gauss, who estimated the rate at which prime numbers increase, and Riemann, who extended ζ(s) to the complex plane and conjectured that all nontrivial zeros are in the R(z)=1/2 axis. The nonadditive entropy Sq=k∑ipilnq(1/pi)(q∈R;S1=SBG≡-k∑ipilnpi, where BG stands for Boltzmann-Gibbs) on which nonextensive statistical mechanics is based, involves the function lnqz≡z1-q-11-q(ln1z=lnz). It is already known that this function paves the way for the emergence of a -generalized algebra, using -numbers defined as ⟨x⟩q≡elnqx, which recover the number for q=1. Read More

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December 2021

Grassmannians and Cluster Structures.

Authors:
Karin Baur

Bull Iran Math Soc 2021 22;47(Suppl 1):5-33. Epub 2021 Apr 22.

University of Graz (on leave) and University of Leeds CIMPA School, 4/2019, Isfahan, Iran.

Cluster structures have been established on numerous algebraic varieties. These lectures focus on the Grassmannian variety and explain the cluster structures on it. The tools include dimer models on surfaces, associated algebras, and the study of associated module categories. Read More

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Classification of singular differential invariants in ()-dimensional space and integrability.

Sci Prog 2021 Oct;104(4):368504211054258

DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa.

Singularity is one of the important features in invariant structures in several physical phenomena reflected often in the associated invariant differential equations. The classification problem for singular differential invariants in (1+3)-dimensional space associated with Lie algebras of dimension 4 is investigated. The formulation of singular invariants for a Lie algebra of dimension possessed by the underlying system of three second-order ordinary differential equations is studied in detail and the corresponding canonical forms for these systems are deduced. Read More

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October 2021

Structural losses, structural realism and the stability of Lie algebras.

Authors:
Jorge Manero

Stud Hist Philos Sci 2022 02 23;91:28-40. Epub 2021 Nov 23.

Czech Academy of Sciences, Institute of Philosophy, Jilská 1, 11000, Prague, Czech Republic. Electronic address:

One of the key assumptions associated with structural realism is the claim that successful scientific theories approximately preserve their structurally based content as they are progressively developed and that this content alone can explain their relevant predictions. The precise way in which these theories are preserved is not trivial but, according to this realist thesis, any kind of structural loss should not occur among theoretical transitions. Although group theory has been proven effective in accounting for preserved structures in the context of physics, structural realists are confronted with the fact that even group-theoretic structures are not immune to these structural discontinuities. Read More

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February 2022

A symmetry-inclusive algebraic approach to genome rearrangement.

J Bioinform Comput Biol 2021 12 19;19(6):2140015. Epub 2021 Nov 19.

Discipline of Mathematics, University of Tasmania, Private Bag 37, Sandy Bay, Tasmania 7001, Australia.

Of the many modern approaches to calculating evolutionary distance via models of genome rearrangement, most are tied to a particular set of genomic modeling assumptions and to a restricted class of allowed rearrangements. The "position paradigm", in which genomes are represented as permutations signifying the position (and orientation) of each region, enables a refined model-based approach, where one can select biologically plausible rearrangements and assign to them relative probabilities/costs. Here, one must further incorporate any underlying structural symmetry of the genomes into the calculations and ensure that this symmetry is reflected in the model. Read More

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December 2021

On Boolean posets of numerical events.

Adv Comput Intell 2021 7;1(4). Epub 2021 Jun 7.

Faculty of Mathematics and Geoinformation, Institute of Discrete Mathematics and Geometry, TU Wien, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria.

With many physical processes in which quantum mechanical phenomena can occur, it is essential to take into account a decision mechanism based on measurement data. This can be achieved by means of so-called numerical events, which are specified as follows: Let be a set of states of a physical system and () the probability of the occurrence of an event when the system is in state . A function is called a numerical event or alternatively, an -probability. Read More

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An exceptional G(2) extension of the Standard Model from the correspondence with Cayley-Dickson algebras automorphism groups.

Authors:
Nicolò Masi

Sci Rep 2021 Nov 18;11(1):22528. Epub 2021 Nov 18.

Physics Department, INFN & Bologna University, Via Irnerio 46, 40136, Bologna, Italy.

In this article I propose a new criterion to extend the Standard Model of particle physics from a straightforward algebraic conjecture: the symmetries of physical microscopic forces originate from the automorphism groups of main Cayley-Dickson algebras, from complex numbers to octonions and sedenions. This correspondence leads to a natural enlargement of the Standard Model color sector, from a SU(3) gauge group to an exceptional Higgs-broken G(2) group, following the octonionic automorphism relation guideline. In this picture, an additional ensemble of massive G(2)-gluons emerges, which is separated from the particle dynamics of the Standard Model. Read More

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November 2021

Complete Gradient Estimates of Quantum Markov Semigroups.

Commun Math Phys 2021 30;387(2):761-791. Epub 2021 Aug 30.

Institute of Science and Technology Austria (IST Austria), Am Campus 1, 3400 Klosterneuburg, Austria.

In this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which implies semi-convexity of the entropy with respect to the recently introduced noncommutative 2-Wasserstein distance. We show that this complete gradient estimate is stable under tensor products and free products and establish its validity for a number of examples. As an application we prove a complete modified logarithmic Sobolev inequality with optimal constant for Poisson-type semigroups on free group factors. Read More

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Scaling Limits of Lattice Quantum Fields by Wavelets.

Commun Math Phys 2021 14;387(1):299-360. Epub 2021 Aug 14.

Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy.

We present a rigorous renormalization group scheme for lattice quantum field theories in terms of operator algebras. The renormalization group is considered as an inductive system of scaling maps between lattice field algebras. We construct scaling maps for scalar lattice fields using Daubechies' wavelets, and show that the inductive limit of free lattice ground states exists and the limit state extends to the familiar massive continuum free field, with the continuum action of spacetime translations. Read More

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The large limit of orbifold vertex operator algebras.

Lett Math Phys 2021 31;111(4):104. Epub 2021 Jul 31.

Department of Mathematics, University of Arizona, Tucson, AZ 85721-0089 USA.

We investigate the large limit of permutation orbifolds of vertex operator algebras. To this end, we introduce the notion of nested oligomorphic permutation orbifolds and discuss under which conditions their fixed point VOAs converge. We show that if this limit exists, then it has the structure of a vertex algebra. Read More

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Causal Algebras on Chain Event Graphs with Informed Missingness for System Failure.

Entropy (Basel) 2021 Oct 6;23(10). Epub 2021 Oct 6.

Statistics Department, University of Warwick, Coventry CV4 7AL, UK.

Graph-based causal inference has recently been successfully applied to explore system reliability and to predict failures in order to improve systems. One popular causal analysis following Pearl and Spirtes et al. to study causal relationships embedded in a system is to use a Bayesian network (BN). Read More

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October 2021

Reasoning about conscious experience with axiomatic and graphical mathematics.

Conscious Cogn 2021 10 6;95:103168. Epub 2021 Oct 6.

Department of Computer Science, University of Oxford, United Kingdom; Cambridge Quantum Computing Ltd., United Kingdom.

We cast aspects of consciousness in axiomatic mathematical terms, using the graphical calculus of general process theories (a.k.a symmetric monoidal categories and Frobenius algebras therein). Read More

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October 2021

Third Way to Interacting p-Form Theories.

Phys Rev Lett 2021 Aug;127(9):091603

Max-Planck-Insitut für Gravitationsphysik, Albert-Einstein-Institut Am Mühlenberg 1, D-14476 Potsdam, Germany.

We construct a class of interacting (d-2)-form theories in d dimensions that are "third-way" consistent. This refers to the fact that the interaction terms in the p-form field equations of motion neither come from the variation of an action nor are they off-shell conserved on their own. Nevertheless, the full equation is still on-shell consistent. Read More

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An algebraic approach to physical fields.

Stud Hist Philos Sci 2021 10 28;89:188-201. Epub 2021 Aug 28.

Department of Mathematics, University of Innsbruck, Austria. Electronic address:

According to the algebraic approach to spacetime, a thoroughgoing dynamicism, physical fields exist without an underlying manifold. This view is usually implemented by postulating an algebraic structure (e.g. Read More

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October 2021

The Quantum Nature of Color Perception: Uncertainty Relations for Chromatic Opposition.

J Imaging 2021 Feb 22;7(2). Epub 2021 Feb 22.

Institute of Mathematics, Université de Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, F-33400 Talence, France.

In this paper, we provide an overview on the foundation and first results of a very recent quantum theory of color perception, together with novel results about uncertainty relations for chromatic opposition. The major inspiration for this model is the 1974 remarkable work by H.L. Read More

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February 2021

Vibrational Hamiltonian of tetrachloro-, tetrafluoro-, and mono- silanes using U(2) Lie algebras.

Spectrochim Acta A Mol Biomol Spectrosc 2022 Jan 19;264:120289. Epub 2021 Aug 19.

Department of Physics, GITAM (Deemed to be University), Hyderabad, India. Electronic address:

In this paper, we have applied the symmetry adapted one-dimensional framework of the U(2) Lie algebras to estimate the vibrational frequencies of tetrachloro-, tetrafluoro-, and mono- silanes in the gas phase having the spectroscopic interest of terrestrial volcanic plumes and other planetary atmospheres. A vibrational Hamiltonian that preserves the T point group symmetry of each of these silane molecules is devised using ten interacting Morse oscillator bound state spectra. The calculated vibron numbers and locality parameters indicate that the vibrational motion is highly anharmonic in SiH (nearest to local mode), moderately anharmonic in SiF (mixed mode) and the least anharmonic in SiCl (near to local mode). Read More

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January 2022

Is the classical limit "singular"?

Stud Hist Philos Sci 2021 08 9;88:263-279. Epub 2021 Jul 9.

Department of Philosophy, University of Washington, USA. Electronic address:

We argue against claims that the classical ℏ → 0 limit is "singular" in a way that frustrates an eliminative reduction of classical to quantum physics. We show one precise sense in which quantum mechanics and scaling behavior can be used to recover classical mechanics exactly, without making prior reference to the classical theory. To do so, we use the tools of strict deformation quantization, which provides a rigorous way to capture the ℏ → 0 limit. Read More

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Tensor-tensor algebra for optimal representation and compression of multiway data.

Proc Natl Acad Sci U S A 2021 07;118(28)

Department of Mathematics, Emory University, Atlanta, GA 30322

With the advent of machine learning and its overarching pervasiveness it is imperative to devise ways to represent large datasets efficiently while distilling intrinsic features necessary for subsequent analysis. The primary workhorse used in data dimensionality reduction and feature extraction has been the matrix singular value decomposition (SVD), which presupposes that data have been arranged in matrix format. A primary goal in this study is to show that high-dimensional datasets are more compressible when treated as tensors (i. Read More

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Growth and form, Lie algebras and special functions.

Authors:
Raghu Raghavan

Math Biosci Eng 2021 04;18(4):3598-3645

Therataxis, LLC, 4203 Somerset Place, MD 21210 Baltimore, USA.

The formation of a biological organism, or an organ within it, can often be regarded as the unfolding of successive equilibria of a mechanical system. In a mathematical model, these changes of equilibria may be considered to be responses of mechanically constrained systems to a change of a reference configuration and of a reference metric, which are in turn driven by genes and their expression. This paper brings together three major threads of research. Read More

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A Full Nesterov-Todd Step Infeasible Interior-point Method for Symmetric Optimization in the Wider Neighborhood of the Central Path.

Stat Optim Inf Comput 2021 ;9(2):250-267

National Center for Health Statistics, 3311 Toledo Rd, Hyattsville, MD, 20782, USA.

In this paper, an improved Interior-Point Method (IPM) for solving symmetric optimization problems is presented. Symmetric optimization (SO) problems are linear optimization problems over symmetric cones. In particular, the method can be efficiently applied to an important instance of SO, a Controlled Tabular Adjustment (CTA) problem which is a method used for Statistical Disclosure Limitation (SDL) of tabular data. Read More

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January 2021