Global propagation of massive quantum fields in the plane gravitational waves and electromagnetic backgrounds

The behavior of massive quantum fields in the general plane wave spacetime and external, non-plane, electromagnetic waves is studied. The asymptotic conditions, the ``in" (``out") states and the cross sections are analysed. It is observed that, despite of the singularities encountered, the global form of these states can be obtained: at the singular points the Dirac delta-like behavior emerges and there is a discrete change of phase of the wave function after passing through each singular point. The relations between these phase corrections and local charts are discussed. Some examples of waves of infinite range (including the circularly polarized ones) are presented for which the explicit form of solutions can be obtained. All these results concern both the scalar as well as spin one-half fields; in latter case the change of the spin polarization after the general sandwich wave has passed is studied.

An introduction to the superunified theory of quantum fields & fundamental interactions (Discoveries in pure mathematics)

This is intended to describe the physical Universe as self-excited and self-organized mathematical continuum. There does exist the universal pure (not applied) mathematical machine perceived by the intelligent observers in a capacity of certain material world. In this short article we are able to indicate only some key points of the theory which suggests practically infinite amount of combinatorics.

Quantum Fields as Category Algebras

In the present paper, we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution structures. By utilizing category algebras and states on categories instead of simply considering categories, we can directly integrate relativity as a category theoretic structure and quantumness as a noncommutative probabilistic structure. Conceptual relationships with conventional approaches to quantum fields, including Algebraic Quantum Field Theory (AQFT) and Topological Quantum Field Theory (TQFT), are also be discussed.

Thermodynamics of Reduced State of the Field

Recent years have seen the flourishing of research devoted to quantum effects on mesoscopic and macroscopic scales. In this context, in Entropy 2019, 21, 705, a formalism aiming at describing macroscopic quantum fields, dubbed Reduced State of the Field (RSF), was envisaged. While, in the original work, a proper notion of entropy for macroscopic fields, together with their dynamical equations, was derived, here, we expand thermodynamic analysis of the RSF, discussing the notion of heat, solving dynamical equations in various regimes of interest, and showing the thermodynamic implications of these solutions.