Related papers: Quantum Mechanics and Relativity --- Their Unifica…
The locality of thermal quantum states has emerged as a key input for applications to thermalization, response theory, and efficient simulability. Locality is either captured by the decay of correlations or by local indistinguishability,…
In this article, we develop quantum mechanics upon the framework of the quantum mechanical Hamilton-Jacobi theory. We will show, that the Schroedinger point of view and the Hamilton-Jacobi point of view are fully equivalent in their…
The Belinkskii, Khalatnikov and Lifshitz conjecture says that as one approaches space-like singularities in general relativity, 'time derivatives dominate over spatial derivatives' so that the dynamics at any spatial point is well captured…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…
The Nelson stochastic mechanics is derived as a consequence of the basic physical principles such as the principle of relativity of observations and the invariance of the action quantum. The unitary group of quantum mechanics is represented…
It is shown that in presence of certain external fields a well defined self-adjoint time operator exists, satisfying the standard canonical commutation relations with the Hamiltonian. Examples include uniform electric and gravitational…
Although local Hamiltonians exhibit local time dynamics, this locality is not explicit in the Schr\"{o}dinger picture in the sense that the wavefunction amplitudes do not obey a local equation of motion. We show that geometric locality can…
The hyperplane and proper time formalisms are discussed mainly for the spin-half particles in the quantum case. A connection between these covariant Hamiltonian formalisms is established. It is showed that choosing the space-like…
We develop a mathematical framework for quantum time transfer based on commuting families of Hamiltonians and synchronization observables. The synchronization subspace is defined as the kernel of a difference operator between local clocks,…
We study longstanding problem of cosmological clock in the context of Brans-Dicke theory of gravitation. We present the Hamiltonian formulation of the theory for a class of spatially homogenous cosmological models. Then, we show that…
The dynamics of spinning particles in curved space-time is discussed, emphasizing the hamiltonian formulation. Different choices of hamiltonians allow for the description of different gravitating systems. We give full results for the…
We investigate the power of quantum systems for the simulation of Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range…
We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian…
The quantum mechanical motion of a relativistic particle in a non-continuous spacetime is investigated. The spacetime model is a dense, rationale subset of two-dimensional Minkowski spacetime. Solutions of the Dirac equation are calculated…
This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…
All covariant time operators with normalized probability distribution are derived. Symmetry criteria are invoked to arrive at a unique expression for a given Hamiltonian. As an application, a well known result for the arrival time…
The use of a relational time in quantum mechanics is a framework in which one promotes to quantum operators all variables in a system, and later chooses one of the variables to operate like a ``clock''. Conditional probabilities are…
Using a theorem of partial differential equations, we present a general way of deriving the conserved quantities associated with a given classical point mechanical system, denoted by its Hamiltonian. Some simple examples are given to…
The dynamics of a spherically symmetric thin shell with arbitrary rest mass and surface tension interacting with a central black hole is studied. A careful investigation of all classical solutions reveals that the value of the radius of the…
We show that under certain technical assumptions, including the existence of a constant mean curvature (CMC) slice and strict positivity of the scalar field, general relativity conformally coupled to a scalar field can be quantised on a…