Related papers: Are Hilbert Spaces Unphysical? Hardly, My Dear!

The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…

The quantum world is described by a unit vector in the Hilbert space and the Hamiltonian. Do these abstract basis-independent objects give a complete description of the physical world, or should we include observables like positions and…

It is shown that a Hilbert space can be constructed for a quantum system starting from a framework in which histories are fundamental. The Decoherence Functional provides the inner product on this "History Hilbert space". It is also shown…

We discuss the dynamical quantum systems which turn out to be bi-unitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space. We give a necessary and sufficient condition so that the…

The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…

It is shown that quantum mechanics is noncontextual if quantum properties are represented by subspaces of the quantum Hilbert space (as proposed by von Neumann) rather than by hidden variables. In particular, a measurement using an…

Field theories place one or more degrees of freedom at every point in space. Hilbert spaces describing quantum field theories, or their finite-dimensional discretizations on lattices, therefore have large amounts of structure: they are…

Hilbert-Space Fundamentalism (HSF) states that the only fundamental structures are the quantum state vector and the Hamiltonian, and from them everything else emerge uniquely, including the 3D-space, a preferred basis, and a preferred…

We derive the Hilbert space formalism of quantum mechanics from epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. An…

Many-body Hilbert space is a functional vector space with the natural structure of an algebra, in which vector multiplication is ordinary multiplication of wave functions. This algebra is finite-dimensional, with exactly $N!^{d-1}$…

Why does quantum theory need the complex numbers? With a view toward answering this question, this paper argues that the usual Hilbert-space formalism is a special case of the general method of Markovian embeddings. This paper then…

As established by Sol\`er, Quantum Theories may be formulated in real, complex or quaternionic Hilbert spaces only. St\"uckelberg provided physical reasons for ruling out real Hilbert spaces relying on Heisenberg principle. Focusing on this…

In recent work (Nii et al., arXiv:1603.06291; Iinuma et al., Phys. Rev. A 93, 032104 (2016)(arXiv:1510.03958)) we have studied the relation between experimental outcomes and the physical properties represented by Hilbert space operators of…

We discuss some general properties of quantum gravity in De Sitter space. It has been argued that the Hilbert space is of finite dimension. This suggests a macroscopic argument that General Relativity cannot be quantized -- unless it is…

W consider the problem of testing if a given matrix in the Hilbert space formulation of quantum mechanics or a function in the phase space formulation of quantum theory represent a quantum state. We propose several practical criteria to…

In this paper we study the Hilbert space structure underlying the Koopman-von Neumann (KvN) operatorial formulation of classical mechanics. KvN limited themselves to study the Hilbert space of zero-forms that are the square integrable…

It is shown that when properly analyzed using principles consistent with the use of a Hilbert space to describe microscopic properties, quantum mechanics is a local theory: one system cannot influence another system with which it does not…

Determining the physical Hilbert space is often considered the most difficult but crucial part of completing the quantization of a constrained system. In such a situation it can be more economical to use effective constraint methods, which…

In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…

Despite its long history, a canonical formulation of quantum ergodicity that applies to general classes of quantum dynamics, including driven systems, has not been fully established. Here we introduce and study a notion of quantum…