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The paper investigates the static, non-commutative solutions of wormholes (WHs) that exhibit spherical symmetry. The study is conducted in the setting of modified Gauss–Bonnet gravity. Our investigation employs two methods: to construct a shape function using a viable f(G) gravity model and to infer the f(G) model through a specific shape function. We then carefully analyze the energy constraints for both methods. Our findings reveal the following results. For each value of r, the first technique provides a physically viable solution of WH related to the ordinary matter. The second approach has a feasible solution only when the values of r are high. This study analyzes the complex procedure of the development of cosmic structures to demonstrate a connection between hypothetical and observed data. [ABSTRACT FROM AUTHOR]

The generalized uncertainty principle provides a promising phenomenological approach to reconciling the fundamentals of general relativity with quantum mechanics. As a result, noncommutativity, measurement uncertainty, and the fundamental theory of quantum mechanics are subject to finite gravitational fields. The generalized uncertainty principle (RGUP) on curved spacetime allows for the imposition of quantum-induced elements on general relativity (GR) in four dimensions. In the relativistic regimes, the determination of a test particle’s spacetime coordinates, 〈xμ〉, becomes uncertain. There exists a specific range of coordinates where the accessibility to 〈(xμ)2〉 is notably limited. Consequently, the spacetime coordinates lack both smoothness and continuity. The quantum-mechanical calculations of the spacetime coordinates are directly linked to their measurement through the expectation value 〈xμ〉. This expectation value is dependent on 〈(xμ)2〉, which is itself limited by a minimum measurable length Δxmin2. A crucial finding presented in this script is the existence of a lower bound for the Hamiltonian, which implies the stability of the quantum nature of spacetime. The direct correlation between Δxmin and −〈g〉μν is a significant discovery, suggesting a proportional relationship. The conjecture is made that the primary metric g carries all essential information regarding spacetime curvature and serves a role akin to the Jacobian determinant in general relativity. Moreover, the linear relationship between Δxmin and the Planck length ℓp is established with a proportionality factor of −〈g〉μνβ2, where β2 denotes the RGUP parameter. The discretization of spacetime coordinates results in the discontinuity of the test particle’s wavefunction ψ(x,t), leading to an unrealistic Δp. It is also noted that the lower limit of 〈(pμ)2〉 is directly proportional to the fundamental tensor. [ABSTRACT FROM AUTHOR]

A new mechanism based on space-time noncommutativity has shown to produce anisotropy and an axial-like interaction, yielding leptonic asymmetry for fermionic particles propagating in a noncommutative curved FRW universe. As a byproduct, an analytical expression of this asymmetry for ultra-relativistic particles, such as neutrinos, is derived explicitly. Constraints and bounds from the cosmological parameters are also discussed. [ABSTRACT FROM AUTHOR]

We solve for quantum geometrically realised pre-spectral triples or ‘Dirac operators’ on the noncommutative torus C θ [ T 2 ] and on the algebra M 2 (C) of 2 × 2 matrices with their standard quantum metrics and associated quantum Riemannian geometry. For C θ [ T 2 ] , we obtain a standard even spectral triple but now uniquely determined by full geometric realisability. For M 2 (C) , we are forced to a particular flat quantum Levi-Civita connection and again obtain a natural fully geometrically realised even spectral triple. In both cases there is an odd spectral triple for a different choice of a sign parameter. We also consider an alternate quantum metric on M 2 (C) with curved quantum Levi-Civita connection and find a natural 2-parameter family of Dirac operators which are almost spectral triples, where fails to be antihermitian. In all cases, we split the construction into a local tensorial level related to the quantum Riemannian geometry, where we classify the results more broadly, and the further requirements relating to the pre-Hilbert space structure. We also illustrate the Lichnerowicz formula for which applies in the case of a full geometric realisation. [ABSTRACT FROM AUTHOR]

Lie–Poisson gauge formalism provides a semiclassical description of noncommutative U(1) gauge theory with Lie algebra type noncommutativity. Using the Dirac approach to constrained Hamiltonian systems, we focus on a class of Lie–Poisson gauge models, which exhibit an admissible Lagrangian description. The underlying noncommutativity is supposed to be purely spatial. Analyzing the constraints, we demonstrate that these models have as many physical degrees of freedom as there are present in the Maxwell theory. [ABSTRACT FROM AUTHOR]

We study a Hermitian matrix model with a kinetic term given by T r (H Φ 2) , where H is a positive definite Hermitian matrix, similar as in the Kontsevich Matrix model, but with its potential Φ 3 replaced by Φ 4 . We show that its partition function solves an integrable Schrödinger-type equation for a non-interacting N-body Harmonic oscillator system. [ABSTRACT FROM AUTHOR]

Within the quantum field theory approach and using the technique of Bogoliubov transformations, the von Neumann boson-antiboson pair creation quantum entanglement entropy is studied in the context of the noncommutative Bianchi I universe. The investigations have shown that the behavior of entanglement entropy is strongly influenced by the choice of the noncommutativity θ parameter, k ⊥ -frequency modes and the structure of the curved spacetime. Moreover, the relationship between thermodynamics, Bose–Einstein condensation and quantum entanglement is also discussed. [ABSTRACT FROM AUTHOR]

Placing a Dirac--Schrödinger operator along the orbit of a flow on a compact manifoldM defines an R-equivariant spectral triple over the algebra of smooth functions on M. We study some of the properties of these triples, with special attention to their zeta functions. These zeta functions are defined for Re(s) > 1 by Trace(fpH-8), where fp is the uniformly continuous function on the real line obtained by restricting the continuous or smooth function f on M to the orbit of a point p ∈ M, and H = -∂²/∂x² + x² is the harmonic oscillator. The meromorphic continuation property and pole structure of these zeta functions are related to ergodic time averages in dynamics. In the case of the periodic flow on the circle, one obtains a spectral triple over the smooth irration torus A∞h ⊂ Ah already studied by Lesch and Moscovici. We strengthen a result of these authors, showing that the zeta function Trace(aH-8) extends meromorphically to C for any element a of the C*-algebra Ah. Another variant of our construction yields a spectral cycle for Ah ⊗ A1/h and a spectral triple over a suitable subalgebra with the meromorphic continuation property if h satisfies a Diophantine condition. The class of this cycle defines a fundamental class in the sense that it determines a KK-duality between Ah and A1/h. We employ the local index theorem of Connes and Moscovici in order to elaborate an index theorem of Connes for certain classes of differential operators on the line and compute the intersection form on K-theory induced by the fundamental class. [ABSTRACT FROM AUTHOR]

Despite the obvious progress made by the Feynman, Ravndal, and Kislinger relativistic model in describing the internal motion of a system with confinement of quarks in a nucleon, it turned out to be insufficiently realistic for a number of reasons. In particular, the model does not take into account some cornerstone properties of QCD, namely, gluon exchange between quarks, the influence of the resulting quark sea on valence quarks, and the self-interaction of colored gluons. It is these phenomena that spontaneously break the chiral symmetry of the quark system and form the bulk of the nucleon. To eliminate the above shortcomings of the model, the problem of self-organization of a three-quark dynamical system immersed in a colored quark–antiquark sea is considered within the framework of complex probabilistic processes that satisfy the stochastic differential equation of the Langevin–Kline–Gordon–Fock type. Taking into account the hidden symmetry of the internal motion of a dynamical system, a mathematically closed nonperturbative approach was developed, which makes it possible to construct the mathematical expectation of the wave function and other parameters of the nucleon in the form of multiple integral representations. It is shown that additional subspaces arising in a representation characterized by a noncommutative geometry with topological features participate in the formation of an effective interaction between valence quarks against the background of harmonic interaction between them. [ABSTRACT FROM AUTHOR]

We study a real symmetric Φ 4 -matrix model whose kinetic term is given by Tr (E Φ 2) , where E is a positive diagonal matrix without degenerate eigenvalues. We show that the partition function of this matrix model corresponds to a zero-energy solution of a Schrödinger type equation with Calogero–Moser Hamiltonian. A family of differential equations satisfied by the partition function is also obtained from the Virasoro algebra. [ABSTRACT FROM AUTHOR]

We investigate the relations between the (completely bounded) local Coulhon-Varopoulos dimension and the spectral dimension of spectral triples associated to sub-Markovian semigroups (or Dirichlet forms) acting on classical (or noncommutative) L p -spaces associated to finite measure spaces. More precisely, we prove that the completely bounded local Coulhon-Varopoulos dimension d exceeds the spectral dimension, i.e. that the associated Hodge-Dirac operator is d + -summable. We explore different settings to compare these two values: compact Riemannian manifolds, compact Lie groups, sublaplacians, metric measure spaces, noncommutative tori and quantum groups. Specifically, we prove that, while very often equal in smooth compact settings, these dimensions can diverge. Finally, we show that the existence of a symmetric sub-Markovian semigroup on a von Neumann algebra with finite completely bounded local Coulhon-Varopoulos dimension implies that the von Neumann algebra is necessarily injective. [ABSTRACT FROM AUTHOR]

We study the Laplacian operator Δ ∂ ‾ associated to a Kähler structure (Ω (• , •) , κ) for the Heckenberger–Kolb differential calculus of the quantum quadrics O q (Q N) , which is to say, the irreducible quantum flag manifolds of types B n and D n. We show that the eigenvalues of Δ ∂ ‾ on zero forms tend to infinity and have finite multiplicity. [ABSTRACT FROM AUTHOR]

We introduce ringed spaces, referred to as para-manifolds, whose non-commutative nilpotent coordinates naturally describe parafermions at the classical level in a similar way as Grassmann variables describe usual fermions. Given a supermanifold X , we construct a family of para-manifolds X (p) for positive integers p , such that X (1) recovers the supermanifold itself. A differential analysis on para-manifolds is developed, which can be readily applied to model physical problems. Two classes of para-manifolds, respectively corresponding to X being affine superspaces and projective superspaces, are treated in detail as examples. Green's theory of parafermions is reformulated in terms of para-manifolds. [ABSTRACT FROM AUTHOR]

We study aspects of noncommutative Riemannian geometry of the path algebra arising from the Kronecker quiver with N arrows. To start with, the framework of derivation based differential calculi is recalled together with a discussion on metrics and bimodule connections compatible with the ⁎-structure of the algebra. As an illustration, these concepts are applied to the noncommutative torus where examples of torsion free and metric (Levi-Civita) connections are given. In the main part of the paper, noncommutative geometric aspects of (generalized) Kronecker algebras are considered. The structure of derivations and differential calculi is explored, and torsion free bimodule connections are studied together with their compatibility with hermitian forms, playing the role of metrics on the module of differential forms. Moreover, for several different choices of Lie algebras of derivations, non-trivial Levi-Civita connections are constructed. [ABSTRACT FROM AUTHOR]

We consider operator systems associated to spectral truncations of tori. We show that their state spaces, when equipped with the Connes distance function, converge in the Gromov–Hausdorff sense to the space of all Borel probability measures on the torus equipped with the Monge–Kantorovich distance. A crucial role will be played by the relationship between Schur and Fourier multipliers. Along the way, we introduce the spectral Fejér kernel and show that it is a good kernel. This allows to make the estimates sufficient to prove the desired convergence of state spaces. We conclude with some structure analysis of the pertinent operator systems, including the C*-envelope and the propagation number, and with an observation about the dual operator system. [ABSTRACT FROM AUTHOR]