Geometric foundations for classical U(1)-gauge theory on noncommutative manifoldsWe systematically extend the elementary differential and Riemannian geometry of classical U(1)-gauge theory to the noncommutative setting by combining recent advances in noncommutative…Branimir Ćaćić·Jan 4, 2023SaveLearn
Necessity of Tensorial Connections for Spinorial SystemsWe consider spinorial fields in polar form to deduce their respective tensorial connection in various physical situations: we show that in some cases the tensorial connection is a useful tool,…Luca Fabbri·Jan 4, 2023SaveLearn
TQFT, Homological Algebra and elements of K.Saito's Theory of Primitive Form: an attempt of mathematical text written by mathematical physicistThe text is devoted to explanation of the concept of Topological Quantum Field Theory (TQFT), its application to homological algebra and to the relation with the theory of good section from K.Saito's…Andrey Losev·Jan 3, 2023SaveLearn
More insights into symmetries in multisymplectic field theoriesThis work provides a general overview for the treatment of symmetries in classical field theories and (pre)multisymplectic geometry. The geometric characteristics of the relation between how…Arnoldo Guerra, Narciso Román-Roy·Jan 3, 2023SaveLearn
Special Vinberg cones, invariant admissible cubics and special real manifoldsBy Vinberg theory any homogeneous convex cone V may be realized as the cone of positive Hermitian matrices in a T-algebra of generalised matrices. The level hypersurfaces $ Vq…Dmitri V. Alekseevsky, Alessio Marrani, Andrea Spiro·Jan 3, 2023SaveLearn
BKP-Affine Coordinates and Emergent Geometry of Generalized Br\'ezin-Gross-Witten Tau-FunctionsFollowing Zhou's framework, we consider the emergent geometry of the generalized Br\'ezin-Gross-Witten models whose partition functions are known to be a family of tau-functions of the BKP hierarchy.…Zhiyuan Wang, Chenglang Yang, Qingsheng Zhang·Jan 3, 2023SaveLearn
Higher order first integrals of autonomous dynamical systems in terms of geometric symmetriesIn general, a system of differential equations is integrable if there exist `sufficiently many' first integrals (FIs) so that its solution can be found by means of quadratures. Therefore, the…Antonios Mitsopoulos, Michael Tsamparlis·Jan 2, 2023SaveLearn
Integrable and superintegrable 3d Newtonian potentials using quadratic first integrals: A reviewThe determination of the first integrals (FIs) of a dynamical system and the subsequent assessment of their integrability or superintegrability in a systematic way is still an open subject. One…Antonios Mitsopoulos, Michael Tsamparlis·Jan 2, 2023SaveLearn
A Linear Stochastic Model of Turbulent Cascades and Fractional FieldsTurbulent cascades characterize the transfer of energy injected by a random force at large scales towards the small scales. In hydrodynamic turbulence, when the Reynolds number is large, the velocity…Gabriel B. Apolinário, Geoffrey Beck, Laurent Chevillard et al.·Jan 2, 2023SaveLearn
Hopf monoids in perturbative algebraic quantum field theoryWe develop an algebraic formalism for perturbative quantum field theory (pQFT) which is based on Joyal's combinatorial species. We show that certain basic structures of pQFT are correctly viewed as…William Norledge·Jan 2, 2023SaveLearn
Wigner equations for phonons transport and quantum heat fluxStarting from the quantum Liouville equation for the density operator and applying the Weyl quantization, Wigner equations for the longitudinal and transversal optical and acoustic phonons are…Vito Dario Camiola, Giorgia Vitanza, Vittorio Romano·Jan 1, 2023SaveLearn
Large deviations for the ground state of weakly interacting Bose gasesWe consider the ground state of a Bose gas of N particles on the three-dimensional unit torus in the mean-field regime that is known to exhibit Bose-Einstein condensation. Bounded one-particle…Simone Rademacher·Jan 1, 2023SaveLearn
Planar equilibrium measure problem in the quadratic fields with a point chargeWe consider a two-dimensional equilibrium measure problem under the presence of quadratic potentials with a point charge and derive the explicit shape of the associated droplets. This particularly…Sung-Soo Byun·Jan 1, 2023SaveLearn
Generalized conformal maps as classical symmetries of Yang-Mills fieldsWe show that a class of previously defined maps, called self-dual and causal morphisms, form classical symmetries of Yang-Mills fields in four complex dimensions. These maps generalize conformal…Edward B. Baker·Dec 31, 2022SaveLearn
Autocorrelations of characteristic polynomials for the Alternative Circular Unitary EnsembleWe find closed formulas for arbitrarily high mixed moments of characteristic polynomials of the Alternative Circular Unitary Ensemble (ACUE), as well as closed formulas for the averages of ratios of…Brad Rodgers, Harshith Sai Vallabhaneni·Dec 31, 2022SaveLearn
Symmetries, conservation and dissipation in time-dependent contact systemsIn contact Hamiltonian systems, the so-called dissipated quantities are akin to conserved quantities in classical Hamiltonian systems. In this paper, we prove a Noether's theorem for non-autonomous…Jordi Gaset, Asier López-Gordón, Xavier Rivas·Dec 30, 2022SaveLearn
On the covariant Hamilton-Jacobi formulation of Maxwell's equations via the polysymplectic reductionThe covariant Hamilton-Jacobi formulation of Maxwell's equations is derived from the first-order (Palatini-like) Lagrangian using the analysis of constraints within the De~Donder-Weyl covariant…Monika E. Pietrzyk, Cécile Barbachoux, Igor V. Kanatchikov et al.·Dec 30, 2022SaveLearn
Split Casimir operator for simple Lie algebras in the cube of ad-representation and Vogel parametersWe constructed characteristic identities for the 3-split (polarized) Casimir operators of simple Lie algebras in the adjoint representations ad and deduced a certain class of…A. P. Isaev, S. O. Krivonos, A. A. Provorov·Dec 30, 2022SaveLearn
A Weyl geometric approach to the gradient-flow equations in information geometryThe gradient-flow equations with respect to the potential functions in information geometry are reconsidered from the perspective of the Weyl integrable geometry. The pre-geodesic equations…Tatsuaki Wada·Dec 30, 2022SaveLearn
Flat connection on four-dimensional lattice, related matrix difference equations and their solutionsIn the paper [H.Boos, A.Hutsalyuk and Kh.Nirov, J.Phys.A:Math.Theor. 51 (2018) 445202] the reduced density matrix of the sl(3)-invariant fundamental exchange model was calculated for the operator…H. Boos, A. P. Isaev·Dec 30, 2022SaveLearn
Matrix-valued Cauchy bi-orthogonal polynomials and a novel noncommutative integrable latticeMatrix-valued Cauchy bi-orthogonal polynomials were proposed in this paper, together with its quasideterminant expression. It is shown that the coefficients in four-term recurrence relation for…Shi-Hao Li, Ying Shi, Guo-Fu Yu et al.·Dec 30, 2022SaveLearn
Solution of the Jacobi inversion problem on non-hyperelliptic curvesIn this paper we propose a method of solving the Jacobi inversion problem in terms of multiply periodic functions, also called Kleinian functions. This result is based on the recently…Julia Bernatska, Dmitry Leykin·Dec 30, 2022SaveLearn
The Two Point Function of the SK Model without External Field at High TemperatureWe show that the two point correlation matrix M= ( σi σj)1≤ i,j≤ N of the Sherrington-Kirkpatrick model with zero external field satisfies \[…Christian Brennecke, Adrien Schertzer, Changji Xu et al.·Dec 29, 2022SaveLearn
On propagation of information in quantum many-body systemsWe prove bounds on the minimal time for quantum messaging, propagation/creation of correlations, and control of states for general lattice quantum many-body systems. The proofs are based on a maximal…Israel Michael Sigal, Jingxuan Zhang·Dec 29, 2022SaveLearn
Segal's contractions, AdS and conformal groupsSymmetries and their applications always played an important role in I.E. Segal's work. I shall exemplify this, starting with his correct proof (at the Lie group level) of what physicists call the…Daniel Sternheimer·Dec 29, 2022SaveLearn