Related papers: Entropic Dynamics: Reconstructing Quantum Field Th…
Quantum geometrodynamics with intrinsic time development is presented. Paradigm shift from full space-time covariance to spatial diffeomorphism invariance yields a non-vanishing Hamiltonian, a resolution of the `problem of time', and…
We develop a rigorous framework for quantifying quantum coherence in finite-dimensional systems by applying the Schur-Horn majorization theorem to relate eigenvalue distributions and diagonal entries of density matrices. Building on this…
Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of…
The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative…
The complex unit appearing in the equations of quantum mechanics is generalised to a quaternionic structure on spacetime, leading to the consideration of complex quantum mechanical particles whose dynamical behaviour is governed by…
In this thesis we consider the problem of dynamics in canonical loop quantum gravity, primarily in the context of deparametrized models, in which a scalar field is taken as a physical time variable for the dynamics of the gravitational…
Different versions of consistent canonical realizations of hypersurface deformations of spherically symmetric space-times have been derived in models of loop quantum gravity, modifying the classical dynamics and sometimes also the structure…
In a quantum gravity theory, it is expected that the classical notion of spacetime disappears, leading to a quantum structure with new properties. A possible way to take into account these quantum effects is through a noncommutativity of…
The dynamical aspects of a spin-1/2 particle in Hermitian coquaternionic quantum theory is investigated. It is shown that the time evolution exhibits three different characteristics, depending on the values of the parameters of the…
The study of mathematical connections between operator-theoretic formulations of classical dynamics and quantum mechanics began at least as early as the 1930s in work of Koopman and von Neumann and was developed in later decades by many…
We derive an action for scalar quantum field theory with cubic interaction in the context of relative locality. Beginning with the generating functional for standard $\varphi^3$--theory and the corresponding Feynman rules we modify them to…
Building on recent advances in quantum algorithms which measure and reuse qubits and in efficient classical simulation leveraging projective measurements, we extend these frameworks to real-time dynamics of quantum many-body systems…
This paper presents a "historical" formalism for dynamical systems, in its Hamiltonian version (Lagrangian version was presented in a previous paper). It is universal, in the sense that it applies equally well to time dynamics and to field…
The emergence of irreversibility in physical processes, despite the fundamentally reversible nature of quantum mechanics, remains an open question in physics. This thesis explores the intricate relationship between quantum mechanics and…
The study of many-body quantum dynamics in strongly-correlated systems is extremely challenging. To date few numerical methods exist which are capable of simulating the non-equilibrium dynamics of two-dimensional quantum systems, in part…
We develop a multi affine geometric framework to unify classical and quantum mechanical laws through the lens of information geometry. By combining the principle of stationary action with maximum entropy production, we show that divergences…
Inspired by various quantum gravity approaches, we explore quantum field theory where spacetime exhibits scaling properties and dimensional reduction with changing energy scales, effectively behaving as a multifractal manifold. Working…
The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features--such as Poincare invariance and the existence of a preferred vacuum state--that are very special to Minkowski spacetime. In order to…
Polymomentum canonical theories, which are manifestly covariant multi-parameter generalizations of the Hamiltonian formalism to field theory, are considered as a possible basis of quantization. We arrive at a multi-parameter hypercomplex…
We use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. Building upon previous work, we construct an object of *Hilb having quantum fields as…