Related papers: A numerical approach to harmonic non-commutative s…
In order to extend the spectral action principle to non-compact spaces, we propose a framework for spectral triples where the algebra may be non-unital but the resolvent of the Dirac operator remains compact. We show that an example is…
A universal formula for an action associated with a noncommutative geometry, defined by a spectal triple $(\Ac ,\Hc ,D)$, is proposed. It is based on the spectrum of the Dirac operator and is a geometric invariant. The new symmetry…
Very high energy physics needs a coherent description of the four fundamental forces. Non-commutative geometry is a promising mathematical framework which already allowed to unify the general relativity and the standard model, at the…
We develop a non-perturbative functional framework for computing real-time correlation functions in strongly correlated systems. The framework is based on the spectral representation of correlation functions and dimensional regularisation.…
Non-commutative Euclidean scalar field theory is shown to have an eigenvalue sector which is dominated by a well-defined eigenvalue density, and can be described by a matrix model. This is established using regularizations of R^{2n}_\theta…
We consider aspects of the noncommutative approach to the standard model based on the spectral action principle. We show that as a consequence of the incorporation of the Clifford structures in the formalism, the spectral action contains an…
We study metric properties stemming from the Connes spectral distance on three types of non compact noncommutative spaces which have received attention recently from various viewpoints in the physics literature. These are the noncommutative…
We compute the leading terms of the spectral action for a noncommutative geometry model that has no fermion doubling. The spectral triple describing it, which is chiral and allows for CP-symmetry breaking, has the Dirac operator that is not…
Quantum harmonic analysis extends classical harmonic analysis by integrating quantum mechanical observables, replacing functions with operators and classical convolution structures with their noncommutative counterparts. This paper explores…
In a previous work, we proposed an integrability setup for computing non-planar corrections to correlation functions in $\mathcal{N}=4$ super Yang-Mills theory at any value of the coupling constant. The procedure consists of drawing all…
General positivity constraints linking various powers of observables in energy eigenstates can be used to sharply locate acceptable regions for the energy eigenvalues, provided that efficient recursive methods are available to calculate the…
The harmonic term in the scalar field theory on the Moyal space removes the UV-IR mixing, so that the theory is renormalizable to all orders. In this paper, we review the three principal interpretations of this harmonic term: the…
We construct in a rigorous mathematical way interacting quantum field theories on a p-adic spacetime. The main result is the construction of a measure on a function space which allows a rigorous definition of the partition function. The…
A consistent functional calculus approach to the spectral theorem for strongly commuting normal operators on Hilbert spaces is presented. In contrast to the common approaches using projection-valued measures or multiplication operators,…
For a large class of quantum mechanical models of matter and radiation we develop an analytic perturbation theory for non-degenerate ground states. This theory is applicable, for example, to models of matter with static nuclei and…
Classical spectral theory provides powerful tools for analyzing linear operators, but does not extend naturally to nonlinear or compositional settings. In particular, there is no general way to transport spectral invariants in a functorial…
Starting from a semiclassical approach recently developed for spectral correlation functions of quantum systems whose classical dynamics is chaotic, we focus on the case of broken time-reversal symmetry, the so-called unitary class. We…
A brief description of the elements of noncommutative spectral geometry as an approach to unification is presented. The physical implications of the doubling of the algebra are discussed. Some high energy phenomenological as well as various…
A non-associative Groenewold-Moyal plane is constructed using quaternion-valued function algebras. The symmetrized multi-particle states, the scalar product, the annihilation/creation algebra and d the formulation in terms of a Hopf algebra…
We demonstrate the feasibility of a nonperturbative analysis of quantum field theory in the worldline formalism with the help of an efficient numerical algorithm. In particular, we compute the effective action for a super-renormalizable…