# The mass gap problem for the Yang-Mills Field. (arXiv:math-ph/0407004v3 UPDATED)

@inproceedings{Sevostyanov2004TheMG, title={The mass gap problem for the Yang-Mills Field. (arXiv:math-ph/0407004v3 UPDATED)}, author={Alexey Sevostyanov}, year={2004} }

We consider the reduced Hamiltonian of the Yang-Mills field on $\mathbb{R}^4$ equipped with a Lorentzian metric. We show that the secondary quantized principal term $H_0$ of the Taylor expansion of this Hamiltonian at the lowest energy point has a mass gap if and only if zero is not a point of the spectrum of the auxiliary self-adjoint operator ${\rm curl}=*d$ defined on the space of one-forms $\omega$ on $\mathbb{R}^3$ satisfying the condition ${\rm div}~ \omega=*d*\omega=0$, where $*$ is the…

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