Related papers: Origin of the quantum operator formalism and its c…
We use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. Building upon previous work, we construct an object of *Hilb having quantum fields as…
The investigation of quantum-classical correspondence may lead to gain a deeper understanding of the classical limit of quantum theory. We develop a quantum formalism on the basis of a linear-invariant theorem, which gives an exact…
The quantum theory of a harmonic oscillator with a time dependent frequency arises in several important physical problems, especially in the study of quantum field theory in an external background. While the mathematics of this system is…
We discuss the action principle and resulting Hamiltonian equations of motion for a class of integer-valued cellular automata introduced recently [1]. Employing sampling theory, these deterministic finite-difference equations are mapped…
The minimal-length paradigm is a cornerstone of quantum gravity phenomenology. Recently, it has been demonstrated that minimal-length quantum mechanics can alternatively be described as an undeformed theory set on a nontrivial momentum…
Heisenberg motion equations in Quantum mechanics can be put into the Hamilton form. The difference between the commutator and its principal part, the Poisson bracket, can be accounted for exactly. Canonical transformations in Quantum…
The Koopman operator allows for handling nonlinear systems through a (globally) linear representation. In general, the operator is infinite-dimensional - necessitating finite approximations - for which there is no overarching framework.…
We present a derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. Combined to Gleason's theorem, this approach naturally leads to the usual…
Time-dependent response theories are foundational to the development of algorithms that determine quantum properties of electronic excited states of molecules and periodic systems. They are employed in wave-function, density-functional, and…
Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian…
The non-relativistic quantum theory has been interpreted causally by de Broglie, David Bohm, and others, where a quantum entity is viewed as a particle with a definite position and momentum. This interpretation opposes the Copenhagen…
The existence of a hermitian time operator is proposed in the framework of non-relativistic quantum mechanics.The Heisenberg equation of motion is shown to yield constant rate of flow of time.It is shown to yield results consistent with…
We present a theory of quantized radiation fields described in terms of q-deformed harmonic oscillators. The creation and annihilation operators satisfy deformed commutation relations and the Fock space of states is constructed in this…
A model of particle interacting with quantum field is considered. The model includes as particular cases the polaron model and non-relativistic quantum electrodynamics. We show that the field operators obey q-commutation relations with q…
We reconstruct the transformations of quantum theory using a physically motivated postulate. This postulate states that transformations should be locally applicable, and recovers the linear isometries from pure quantum theory, as well as…
We describe rigorous quantum measurement theory in the Heisenberg picture by applying operator deformation techniques previously used in noncommutative quantum field theory. This enables the conventional observables (represented by…
Although the Hamiltonian in quantum physics has to be a linear operator, it is possible to make quantum systems behave as if their Hamiltonians contained antilinear (i.e., semilinear or conjugate-linear) terms. For any given quantum system,…
We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content…
We summarize a new realist interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content essentially intact.…
After the development of a self-consistent quantum formalism nearly a century ago, there ensued a quest to understand the often counterintuitive predictions of the theory. These endeavors invariably begin with the assumption of the "truth"…