Gauge Transformations of a Relativistic Field of Quantum Harmonic Oscillators

Generalized Heisenberg relation and Quantum Harmonic Oscillators

We study the consequences of the generalized Heisenberg uncertainty relation which admits a minimal uncertainty in length such as the case in a theory of quantum gravity. In particular, the theory of quantum harmonic oscillators arising from such a generalized uncertainty relation is examined. We demonstrate that all the standard properties of the quantum harmonic oscillators prevail when we em...

The One-dimensional Thermal Properties for the Relativistic Harmonic Oscillators

The relativistic harmonic oscillator is one of the most important quantum system, as it is one of the very few that can be solved exactly. The Dirac relativistic oscillator (DO) interaction is an important potential both for theory and application. It was for the first time studied by Ito et al [1]. They considered a Dirac equation in which the momentum p is replaced by p − imβω r, with r being...

Relativistic Quantum Field Theory

Relativistic Quantum Mechanics without Gauge Invariance

_ _. We argue that th&crossing (CPT) y s mmetry of relativistic quantum mechanics requires that both the Coulombic and the Newtonian force between pairs of particles will reverse when one is replaced by its anti-particle. For consistency, this requires a theory in which both the equivalence principle and gauge invariance are abandoned. Thus whether ant,i-hydrogen " falls " up or down will provi...

The effective action and quantum gauge transformations

The concept of symmetry was and remains a very powerful tool for construction of the quantum field theory. One of its main virtues is that the symmetry restricts a form of the action, which lies in the ground of the theory. Consequences of the classical symmetry play a crucial role for renormalizability of the quantum theory. And in the investigation of this problem the effective action takes a...