Related papers: Generalized possibilistic Theories: the multiparti…
In the paper the basic concepts of extended probability theory are introduced. The basic idea: the concept of an event as a subset of \Omega is replaced with the concept of an event as a partition. The partition is any set of disjoint…
It has been shown that quantum paradoxes have followed from one special assumption, i.e., from attributing basic physical meaning to Hamiltonian eigenfunctions and representing all physical states by vectors of the Hilbert space spanned on…
We revisit the standard axioms of domain theory with emphasis on their relation to the concept of partiality, explain how this idea arises naturally in probability theory and quantum mechanics, and then search for a mathematical setting…
In this paper I give overviews of the polysymplectic approach to covariant Hamiltonian field theory and the simplest geometric quantization of classical particle theories. I then give a synopsis of a recently proposed toy model for applying…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that…
Many-party correlations between measurement outcomes in general probabilistic theories are given by conditional probability distributions obeying the non-signalling condition. We show that any such distribution can be obtained from…
We introduce a new "positive formalism" for encoding quantum theories in the general boundary formulation, somewhat analogous to the mixed state formalism of the standard formulation. This makes the probability interpretation more natural…
The notion of context (complex of physical conditions) is basic in this paper. We show that the main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space,…
This paper contributes to a burgeoning area of investigation, the ambiguity inherent in mathematics and the implications for physics of this ambiguity. To display the mathematical form of equations of quantum theory used to describe…
In this paper we develop a duality theory for all finite-dimensional near-vector spaces and introduce a notion of inner product tailored to the broad and natural class of strongly regular near-vector spaces. This generalized construction…
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…
Genuine multipartite entanglement underlies correlation experiments corroborating quantum mechanics and it is an expedient empowering many quantum technologies. One of many counterintuitive facets of genuine multipartite entanglement is its…
We explore the interplay between random and deterministic phenomena using a representation of uncertainty based on the measure-theoretic concept of outer measure. The meaning of the analogues of different probabilistic concepts is…
The principle of tomographic locality states that the operational state of a multipartite system can be fully characterized by the statistics obtained from measurements that are local to the individual subsystems. This property holds in…
General relativity is a deterministic theory with non-fixed causal structure. Quantum theory is a probabilistic theory with fixed causal structure. In this paper we build a framework for probabilistic theories with non-fixed causal…
A realistic measurement-free theory for the quantum physics of multiple qubits is proposed. This theory is based on a symbolic representation of a fractal state-space geometry which is invariant under the action of deterministic and locally…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
In this paper we will analyse the inner product for a general tensor field theory. We will first analyse a generalized inner product for scalar field theories. Then we will use it to construct a inner product for tensor field theories. We…
One of the crucial differences between mathematical models of classical and quantum mechanics is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an…