Related papers: Quantum mechanics in an evolving Hilbert space

We show that the impact of the fundamental length in quantum mechanics can be studied within the formalism of Berry's geometrical phase with the line broadening as a resulting physical effect.

Standard quantum mechanics unquestionably violates the separability principle that classical physics (be it point-like analytic, statistical, or field-theoretic) accustomed us to consider as valid. In this paper, quantum nonseparability is…

In the earlier works on quantum geometrodynamics in extended phase space it has been argued that a wave function of the Universe should satisfy a Schrodinger equation. Its form, as well as a measure in Schrodinger scalar product, depends on…

If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime.…

We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…

Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…

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…

We reveal strong and weak inequalities relating two fundamental macroscopic quantum geometric quantities, the quantum distance and Berry phase, for closed paths in the Hilbert space of wavefunctions. We recount the role of quantum geometry…

In the absence of a satisfactory interpretation of quantum theory, physical law lacks physical basis. This paper reviews the orthodox, or Dirac-von Neumann interpretation, and makes explicit that Hilbert space describes propositions about…

We present a technique to coarse-grain quantum states in a finite-dimensional Hilbert space. Our method is distinguished from other approaches by not relying on structures such as a preferred factorization of Hilbert space or a preferred…

The complete quantum metric of a parametrized quantum system has a real part (usually known as the Provost-Vallee metric) and a symplectic imaginary part (known as the Berry curvature). In this paper, we first investigate the relation…

We illustrate an isomorphic representation of the observable algebra for quantum mechanics in terms of the functions on the projective Hilbert space, and its Hilbert space analog, with a noncommutative product in terms of explicit…

We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in…

Group field theory is a background-independent approach to quantum gravity whose starting point is the definition of a quantum field theory on an auxiliary group manifold (not interpreted as spacetime, but rather as the finite-dimensional…

The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…

Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical…

Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this…

Physics explains the laws of motion that govern the time evolution of observable properties and the dynamical response of systems to various interactions. However, quantum theory separates the observable part of physics from the…

We present an overview of the role of generating functions in quantum mechanical contexts, mainly in the modern theory of polarization and in the study of quantum phase transitions. Generating functions enable the derivation of moments and…

The equivalence between the Schr\"odinger and Heisenberg representations is a cornerstone of quantum mechanics. However, this relationship remains unclear in the non-Hermitian regime, particularly when the Hamiltonian is time-dependent. In…