Related papers: Quantum Reference Frames and Correlation Geometry
In this essay, we explore the geometric structures involved in the Wolfram model of fundamental physics. Furthermore, we propose some directions of research aiming to get the bosons and fermions out of this framework.
The possible extensions of GR for description of fermions on a curved space, for supergravity and for loop quantum gravity require a richer set of 16 independent variables. These variables can be assembled in a coframe field, i.e., a local…
Starting from a Unified Field Theory (UFT) proposed previously by the author, the possible fermionic representations arising from the same spacetime are considered from the algebraic and geometrical viewpoint. We specifically demonstrate in…
This work has the purpose of applying the concept of Geometric Calculus (Clifford Algebras) to the Fibre Bundle description of Quantum Mechanics. Thus, it is intended to generalize that formulation to curved spacetimes [the base space of…
Modern theories of fundamental interactions describe strong, electromagnetic and weak interactions as quantum field theories with certain kinds of embedded internal symmetries called `gauge symmetries'. This article introduces quantum field…
The theory of causal fermion systems is a recent approach to fundamental physics. Giving quantum mechanics, general relativity and quantum field theory as limiting cases, it is a candidate for a unified physical theory. The dynamics is…
In the absence of external relata, internal quantum reference frames (QRFs) appear widely in the literature on quantum gravity, gauge theories and quantum foundations. Here, we extend the perspective-neutral approach to QRF covariance to…
An analysis is given of the local phase space of gravity coupled to matter to second order in perturbation theory. Working in local regions with boundaries at finite distance, we identify matter, Coulomb, and additional boundary modes. The…
Several years ago the so-called quantum geometrodynamics in extended phase space was proposed. The main role in this version of quantum geometrodynamics is given to a wave function that carries information about geometry of the Universe as…
Correlated many-fermion systems emerge in a broad range of phenomena in warm dense matter, plasmonics, and ultracold atoms. Quantum hydrodynamics (QHD) complements common first-principles methods for many-fermion systems and enables…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
Reference frames are used to parameterize measurements of physical effects, but since their practical realization uses material objects, they may affect observations performed in a combined quantum state of the measured system together with…
In the present article, Chern-Simons gauge theory and its relationship with gravity are revisited from a geometrical viewpoint. In this setting, our goals are twofold: In one hand, to show how to represent the family of variational problems…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
The motivations for the construction of an 8-component representation of fermion fields based on a two dimensional representation of time reversal transformation and CPT invariance are discussed. Some of the elementary properties of the…
This thesis is broadly split into two parts. In the first part, simple state sum models for minimally coupled fermion and scalar fields are constructed on a $1$-manifold. The models are independent of the triangulation and give the same…
In loop quantum gravity we now have a clear picture of the quantum geometry of space, thanks in part to the theory of spin networks. The concept of `spin foam' is intended to serve as a similar picture for the quantum geometry of spacetime.…
Quantum mechanics for a four-state-system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical…
In this work, we have studied classical and quantum systems in interaction by means of geometric reduction procedure. The main target is the description in these terms of fundamental interactions. We have shown that, to describe in a…
A sketch is given of a circle of ideas relating quantum field theories with representation theory. The main mathematical ingredients are spinor geometry and the gauge group equivariant K-theory of the space of connections.