Related papers: A novel class of functionals for perturbative alge…
We introduce $\phi^4$ interacting real scalar Quantum Field Theory (QFT) on causal sets. We consider both the canonical framework of causal set free QFT, involving a Hilbert space and operators and so on, and the double path integral…
Upper and lower quantum functionals, introduced by Christandl, Vrana and Zuiddam (STOC 2018, J. Amer. Math. Soc. 2023), are families of monotone functions of tensors indexed by a weighting on the set of subsets of the tensor legs. Inspired…
We give an explicit formula, as a formal differential operator, for quantum microformal morphisms of (super)manifolds that we introduced earlier. Such quantum microformal morphisms are essentially oscillatory integral operators or Fourier…
The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since…
We demonstrate that in a class of disordered quantum systems the dynamical partition function is not an analytical function in a time window after certain quantum quenches. We related this behavior to rare and large regions with atypical…
We introduce a class of diffeological spaces, called elastic, on which the left Kan extension of the tangent functor of smooth manifolds defines an abstract tangent functor in the sense of Rosicky. On elastic spaces there is a natural…
We define a smooth functional calculus for a non-commuting tuple of (unbounded) operators $A_j$ on a Banach space with real spectra and resolvents with temperate growth, by means of an iterated Cauchy formula. The construction is also…
The purpose of this paper is to study some obstruction classes induced by a construction of a homotopy-theoretic version of projective TQFT (projective HTQFT for short). A projective HTQFT is given by a symmetric monoidal projective functor…
We define a novel class of time changed Pearson diffusions, termed stretched non local Pearson diffusions, where the stochastic time change model has the Kilbas Saigo function as its Laplace transform. Moreover, we introduce a stretched…
The paper aims at investigating perturbative quantum field theory (pQFT) in the approach of Epstein and Glaser (EG) and, in particular, its formulation in the language of graphs and Hopf algebras (HAs). Various HAs are encountered, each one…
We present versions of several classical results on harmonic functions and Poisson boundaries in the setting of locally compact quantum groups. In particular, the Choquet--Deny theorem holds for compact quantum groups; also, the result of…
In the present paper, we intent to enlarge the axiomatic framework of non-commutative quantum field theories (QFT). We consider QFT on non-commutative spacetimes in terms of the tempered ultrahyperfunctions of Sebasti\~ao e Silva…
We showcase the advantages of orbital-free density-potential functional theory (DPFT), a more flexible variant of Hohenberg-Kohn density functional theory. DPFT resolves the usual trouble with the gradient-expanded kinetic energy functional…
Sawin recently gave an axiomatic characterization of multiple Dirichlet series over the function field $\mathbb{F}_{q}(T)$ and proved their existence by exhibiting the coefficients as trace functions of specific perverse sheaves. However,…
The Lee-Yang theorem for the zeroes of the partition function is not strictly applicable to quantum systems because the zeroes are defined in units of the fugacity $e^{h\Delta\tau}$, and the Euclidean-time lattice spacing $\Delta\tau$ can…
The aim of this paper is to extend the domain of definition of $(dd^c\centerdot)^q\wedge T$ on some classes of plurisubharmonic (psh) functions, which are not necessary bounded, where $T$ is a positive closed current of bidimension $(q,q)$…
Let $k$ be a field with separable closure $\bar{k}\supset k$, and let $X$ be a qcqs $k$-scheme. We use the theory of profinite Galois categories developed by Barwick-Glasman-Haine to provide a quick conceptual proof that the sequences…
We suggest a version of renormalizable Quantum Field Theory which does not contain non-perturbative effects. This is otained by the proper use of the boundary conditions in the functional integral of the generating functional of Green…
We discuss the scaling of the effective action for the interacting scalar quantum field theory on generic spacetimes with Lorentzian signature and in a generic state (including vacuum and thermal states, if they exist). This is done…
We introduce analytic functionals which act on the crossing equation for CFTs in arbitrary spacetime dimension. The functionals fully probe the constraints of crossing symmetry on the first sheet, and are in particular sensitive to the OPE,…