Canonical Coherent States for the Relativistic Harmonic Oscillator

Abstract

In this paper we construct manifestly covariant relativistic coherent states on the entire complex plane which reproduce others previously introduced on a given $SL(2,R)$ representation, once a change of variables $z\in C\to z_D\in$ unit disk is performed. We also introduce higher-order, relativistic creation and annihilation operators, $\C,\Cc$, with canonical commutation relation $[\C,\Cc]=1$ rather than the covariant one $[\Z,\Zc]\approx$ Energy and naturally associated with the $SL(2,R)$ group. The canonical (relativistic) coherent states are then defined as eigenstates of $\C$. Finally, we construct a canonical, minimal representation in configuration space by mean of eigenstates of a canonical position operator.

arXiv comment11 LaTeX pages, final version, shortened and corrected, to appear in J. Math. Phys

References in corpus (3)

• Thermal noise and oscillations of photon distribution for squeezed and correlated light
• A (1+3) Relativistic Harmonic Oscillator Simulated by an Anti-de Sitter Background
• Finite-Difference Equations in Relativistic Quantum Mechanics

Cited by in corpus (4)

• Robertson Intelligent States
• Quantum Mechanics of Klein-Gordon Fields II: Relativistic Coherent States
• Coherent State for a Relativistic Spinless Particle
• Erratum to: Canonical coherent states for the relativistic harmonic oscillator