Related papers: Quantum periods: A census of \phi^4-transcendental…
The classical and quantum models of the Friedmann universe originally filled with a scalar field and radiation have been studied. The radiation has been used to specify a reference frame that makes it possible to remove ambiguities in…
The quantum mechanics is proved to admit no hidden-variable in 1960s, which means the quantum systems are contextual. Revealing the mathematical structure of quantum mechanics is a significant task. We develop the approach of partial…
We show that a class of background independent models of quantum spacetime have local excitations that can be mapped to the first generation fermions of the standard model of particle physics. These states propagate coherently as they can…
After distinguishing the role of classical and quantum inhomogeneities in cosmological backgrounds, we constrain the initial states of the relic gravitons as soon as the different wavelengths of the spectrum cross the comoving Hubble…
We analyze the origin of the quasiclassical realm from the no-boundary proposal for the universe's quantum state in a class of minisuperspace models. The models assume homogeneous, isotropic, closed spacetime geometries, a single scalar…
We summarize different approaches to the theory of quantum graphs and provide several ways to construct concrete examples. First, we classify all undirected quantum graphs on the quantum space $M_2$. Secondly, we apply the theory of…
A large class of quantum phase transitions for quantum lattice systems are characterized by local order parameters. It is shown that local order parameters may be systematically constructed from tensor network representations of quantum…
The (large-scale) structures we observe in the Universe are classical, but within the inflationary scenario they do originate from quantum fluctuations. This leads to the question: ''How did this quantum-to-classical transition occur?''. A…
We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field…
We investigate recurrence phenomena in coupled two degrees of freedom systems. It is shown that an initial well localized wave packet displays recurrences even in the presence of coupling in these systems. We discuss the interdependence of…
We offer a perspective on some recent results obtained in the context of the group field theory approach to quantum gravity, on top of reviewing them briefly. These concern a natural mechanism for the emergence of non-commutative field…
Quantum and classical mechanics are derived using four natural physical principles: (1) the laws of nature are invariant under time evolution, (2) the laws of nature are invariant under tensor composition, (3) the laws of nature are…
In perturbative quantum field theory one encounters certain, very specific geometries over the integers. These perturbative quantum geometries determine the number contents of the amplitude considered. In the article `Modular forms in…
We present quantum graphs with remarkably regular spectral characteristics. We call them {\it regular quantum graphs}. Although regular quantum graphs are strongly chaotic in the classical limit, their quantum spectra are explicitly…
We review certain emergent notions on the nature of spacetime from noncommutative geometry and their radical implications. These ideas of spacetime are suggested from developments in fuzzy physics, string theory, and deformation…
We invert the period map defined by the second structure connection of quantum cohomology of $\mathbb{P}^2$. For small quantum cohomology the inverse is given explicitly in terms of the Eisenstein series $E_4$ and $E_6$, while for big…
This paper proposes a general framework for nonperturbatively defining continuum quantum field theories. Unlike most such frameworks, the one offered here is finitary: continuum theories are defined by reducing large but finite quantum…
The neutral massless scalar quantum field $\Phi$ in four-dimensional space-time is considered, which is subject to a simple bilinear self-interaction. Is is well-known from renormalization theory that adding a term of the form…
For the O(N) field theory with lambda Phi^4 self-coupling, we construct the two-particle-irreducible (2PI), closed-time-path (CTP) effective action in a general curved spacetime. From this we derive a set of coupled equations for the mean…
In this survey article we give basic introduction to the theory of quantum families of maps. We begin with a general look at non-commutative (or "quantum") topology. Then we formulate all our results in this language. Existence of quantum…