Related papers: Relativization is naturally functorial
The kinematical foundations of Schwinger's algebra of selective measurements were discussed in a previous paper (arXiv:1905.12274) and, as a consequence of this, a new picture of quantum mechanics based on groupoids was proposed. In this…
We consider the possibility that the basic space of physics is not spacetime, but configuration space. We illustrate this on the example with a system of gravitationally interacting point particles. It turns out that such system can be…
We construct the algebra of operators acting on the Hilbert spaces of Quantum Mechanics for systems of $N$ identical particles from the field operators acting in the Fock space of Quantum Field Theory by providing the explicit relation…
Orbits of automorphism groups of partially ordered sets are not necessarily congruence classes, i.e. images of an order homomorphism. Based on so-called orbit categories a framework of factorisations and unfoldings is developed that…
We define a unified categorical framework for studying six subproblems arising from the classical Four Subspace Problem. For each subproblem, we construct a functor from its associated category to the category of representations of the…
Started from our work "Fields on the Poincare Group and Quantum Description of Orientable Objects" (EPJC,2009), we consider here a classification of orientable relativistic quantum objects in 3+1 dimensions. In such a classification, one…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
We find a connection between the existence of a factorization of a quantum channel and the existence of low-rank solutions to certain linear matrix equations. Using this, we show that if a quantum channel is factorized by a direct integral…
General relativity can be recast as a theory of connections by performing a canonical transformation on its phase space. In this form, its (kinematical) structure is closely related to that of Yang-Mills theory and topological field…
We study the question of how to decompose Hilbert space into a preferred tensor-product factorization without any pre-existing structure other than a Hamiltonian operator, in particular the case of a bipartite decomposition into "system"…
Quantum superchannels are maps whose input and output are quantum channels. Rather than taking the domain to be the space of all linear maps we motivate and define superchannels on the operator system spanned by quantum channels. Extension…
One of the key ways in which quantum mechanics differs from relativity is that it requires a fixed background reference frame for spacetime. In fact, this appears to be one of the main conceptual obstacles to uniting the two theories.…
Algebraic quantum field theory, or AQFT for short, is a rigorous analysis of the structure of relativistic quantum mechanics. It is formulated in terms of a net of operator algebras indexed by regions of a Lorentzian manifold. In several…
The equivalence principle postulates a frame. This implies globally special and locally general relativity. It is proposed here that spacetime emerges from the gauge potential of translations, whilst the Lorenz symmetry is gauged into the…
The theory of canonical linearized gravity is quantized using the Projection Operator formalism, in which no gauge or coordinate choices are made. The ADM Hamiltonian is used and the canonical variables and constraints are expanded around a…
A "minimal" generalization of Quantum Mechanics is proposed, where the Lagrangian or the action functional is a mapping from the (classical) states of a system to the Lie algebra of a general compact Lie group, and the wave function takes…
Due to the existence of incompatible observables, the propositional calculus of a quantum system does not form a Boolean algebra but an orthomodular lattice. Such lattice can be realised as a lattice of subspaces on a real, complex or…
We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are the multi-time probability distributions estimated from the results of…
Geometric quantization is a natural way to construct quantum models starting from classical data. In this work, we start from a symplectic vector space with an inner product and -- using techniques of geometric quantization -- construct the…
Quantum Relativity is supposed to be a new theory, which locally is a deformation of Special Relativity, and globally it is a background independent theory including the main ideas of General Relativity, with hindsight from Quantum Theory.…