Semirelativistic Hamiltonians and the auxiliary field method

Abstract

Approximate analytical closed energy formulas for semirelativistic Hamiltonians of the form $\sigma \sqrt{{\mathbf{p}}^2+m^2}+V(r)$ are obtained within the framework of the auxiliary field method. This method, which is equivalent to the envelope theory, has been recently proposed as a powerful tool to get approximate analytical solutions of the Schrödinger equation. Various shapes for the potential $V(r)$ are investigated: power-law, funnel, square root, and Yukawa. A comparison with the exact results is discussed in detail.

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• Glueball phenomenology and the relativistic flux tube model
• A general comparison theorem
• Light baryon masses in different large-$N_c$ limits
• The auxiliary field method in quantum mechanics
• An upper bound for asymmetrical spinless Salpeter equations
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• Meson spectrum in SU(N) gauge theories with quarks in higher representations: A check of Casimir scaling hypothesis
• Bounds for Hamiltonians with arbitrary kinetic parts
• Accuracy Tests of the Envelope Theory