A Toy Model for Quantum Mechanics

Toy Quantum Mechanics Using Hidden Variables

It is used to state that no local theory assuming any kind of evolving-in-time physical field (hidden variables) can reproduce the same predictions as standard quantum mechanics. Bell formulated a corresponding theorem in [1]. An advanced variant of the theorem was proposed in [2]. Feynman, in [3], stated another but analogous idea: not any classical computational device (even when probabilisti...

Quantum interference in thermoelectric molecular junctions: A toy model perspective

A toy model of quantum electrodynamics in (1+1) dimensions

We present a toy model of quantum electrodynamics (QED) in (1 + 1) dimensions. The QED model is much simpler than QED in (3 + 1) dimensions but exhibits many of the same physical phenomena, and serves as a pedagogical introduction to both QED and quantum field theory in general. We show how the QED model can be derived by quantizing a toy model of classical electrodynamics, and we discuss the c...

A toy model of bosonic non-canonical quantum field

A harmonic oscillator is an indefinite-frequency one if the parameter ω is replaced by an operator. An ensemble of N such oscillators may be regarded as a toy model of a bosonic quantum field. All the possible frequencies associated with a given problem are present already in a single oscillator and N can be finite. Due to the operator character of ω the resulting algebra of creationannihilatio...

A gauge model for quantum mechanics on a stratified space

In the Hamiltonian approach on a single spatial plaquette, we construct a quantum (lattice) gauge theory which incorporates the classical singularities. The reduced phase space is a stratified Kähler space, and we make explicit the requisite singular holomorphic quantization procedure on this space. On the quantum level, this procedure yields a costratified Hilbert space, that is, a Hilbert spa...