Related papers: Functional Formalism for Algebraic Classical and Q…
We develop a general framework for the quantization of bosonic and fermionic field theories on affine bundles over arbitrary globally hyperbolic spacetimes. All concepts and results are formulated using the language of category theory,…
Perturbative QFT is developed in terms of off-shell fields (that is, functionals on the configuration space not restricted by any field equation), and by quantizing the (underlying) free theory by an $\hbar$-dependent deformation of the…
Quantum fields are generally taken to be operator-valued distributions, linear functionals of test functions into an algebra of operators; here the effective dynamics of an interacting quantum field is taken to be nonlinearly modified by…
We establish the existence of local, covariant time ordered products of local Wick polynomials for a free scalar field in curved spacetime. Our time ordered products satisfy all of the hypotheses of our previous uniqueness theorem, so our…
In the abelian case (the subject of several beautiful books) fixing some combinatorial structure (so called theta structure of level k) one obtains a special basis in the space of sections of canonical polarization powers over the…
We propose a new formalism for quantum field theory which is neither based on functional integrals, nor on Feynman graphs, but on marked trees. This formalism is constructive, i.e. it computes correlation functions through convergent rather…
We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the…
A covariant description of quantum matter fields in the early universe underpins models for the origin of species, e.g. baryogenesis and dark matter production. In nearly all cases the relevant cosmological observables are computed in a…
The quantization rules recently proposed by M. Navarro (and independently I.V. Kanatchikov) for a finite-dimensional formulation of quantum field theory are applied to the Klein-Gordon and the Dirac fields to obtain the quantum equations of…
Thinking back the long history of physics, we see that the calculation used by physicists was nothing but the ordinary calculus. Another word, physicists have never wrote theories beyond the basic axioms of the calculus. This is not to…
Motivated by some well-known results in the phase space description of quantum optics and quantum information theory, we aim to describe the formalism of quantum field theory by explicitly considering the holomorphic representation for a…
The formalism of generalized Wigner transformations developped in a previous paper, is applied to kinetic equations of the Lindblad type for quantum harmonic oscillator models. It is first applied to an oscillator coupled to an equilibrium…
This paper presents a research program aimed at establishing relational foundations for relativistic quantum physics. Although the formalism is still under development, we believe it has matured enough to be shared with the broader…
We develop a semiclassical framework for studying quantum particles constrained to curved surfaces using the momentous quantum mechanics formalism, which extends classical phase-space to include quantum fluctuation variables (moments). In a…
In modern physics, one of the greatest divides is that between space-time and quantum fields, as the fiber bundle of the Standard Model indicates. However on the operational grounds the fields and spacetime are not very different. To…
A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as…
This work explores the intersection of quantum mechanics and curved spacetime by employing the Wigner formalism to investigate quantum systems in the vicinity of black holes. Specifically, we study the quantum dynamics of a probe particle…
The space of continuous states of perturbative interacting quantum field theories in globally hyperbolic curved spacetimes is determined. Following Brunetti and Fredenhagen, we first define an abstract algebra of observables which contains…
Algebraic quantum field theory is a general mathematical framework for relativistic quantum physics, based on the theory of operator algebras. It comprises all observable and operational aspects of a theory. In its framework the entire…
We introduce a novel class of coherent states, termed $\mathcal{W}^{(\bar{\alpha},\bar{\nu})}(z)$-coherent states, constructed using a deformed boson algebra based on the generalized factorial $[n]_{\alpha,\beta,\nu}!$. This algebra extends…