Related papers: Properties of field functionals and characterizati…
Given an action of a Lie group on a smooth manifold, we discuss the induced action on the Hochschild cohomology of smooth functions, and notions of invariance on this space. Depending on whether one considers invariance of cochains or…
We study conformal properties of local terms such as contact terms and semi-local terms in correlation functions of a conformal field theory. Not all of them are universal observables but they do appear in physically important correlation…
A density functional theory is developed for fermions in one dimension, interacting via a delta-function. Such systems provide a natural testing ground for questions of principle, as the local density approximation should work well for…
We define positive and strictly positive definite functions on a domain and study these functions on a list of regular domains. The list includes the unit ball, conic surface, hyperbolic surface, solid hyperboloid, and simplex. Each of…
The scalar functional determinants on sectors of the two-dimensional disc and spherical cap are determined for arbitrary angles (rational factors of $\pi$). The wholesphere and hemisphere expressions are also given, in low dimensions, for…
Variational (Rayleigh-Ritz) methods are applied to local quantum field theory. For scalar theories the wave functional is parametrized in the form of a superposition of Gaussians and the expectation value of the Hamiltonian is expressed in…
Multifractal analysis refers to the study of the local properties of measures and functions, and consists of two parts: the fine multifractal theory and the coarse multifractal theory. The fine and the coarse theory are linked by a web of…
Physical systems with symmetries are described by functions containing kinematical and dynamical parts. We consider the case when kinematical symmetries are described by a noncompact semisimple real Lie group $G$. Then separation of…
Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcomes; dually, states can be modelled as functions from the algebra of observables to outcomes. The…
Motivated by DeWitt's viewpoint of covariant field theory, we define a general notion of non-local classical observable that applies to many physical lagrangian systems (with bosonic and fermionic variables), by using methods that are now…
We introduce the notion of rationality for hyperholomorphic functions (functions in the kernel of the Cauchy-Fueter operator). Following the case of one complex variable, we give three equivalent definitions: the first in terms of…
We delve into the in-in formalism and derive general expressions for the computation of n-point functions for a self-interacting scalar field by means of a probability density functional (PDF). Even though in typical situations these…
Mostly self-contained script on functorial topological quantum field theories. These notes give a slow introduction to the basic notions of category theory which serve a closer investigation of cobordisms and (commutative) Frobenius…
Conventional functional/path integrals used in physics are most often defined and understood, either explicitly or implicitly, as the infinite-dimensional analog of Fourier transform. In this paper, the infinite-dimensional analog of Mellin…
The richly developed theory of complex manifolds plays important roles in our understanding of holomorphic functions in several complex variables. It is natural to consider manifolds that will play similar roles in the theory of holomorphic…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
The conditions for observation of the particle coordinates, required by logic of the Special Relativity and filtering the quantum field effects, are described. A general relation between the corresponding density of probability and the wave…
Two classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other, are extended to…
In this article, we show some density properties of smooth and compactly supported functions in fractional Musielak-Sobolev spaces essentially extending the results of Fiscella, Servadei, and Valdinoci obtained in the fractional Sobolev…
Covariant stochastic partial (pseudo-)differential equations are studied in any dimension. In particular a large class of covariant interacting local quantum fields obeying the Morchio-Strocchi system of axioms for indefinite quantum field…