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JOURNALS // Teoreticheskaya i Matematicheskaya Fizika // Archive

TMF, 1970 Volume 2, Number 3, Pages 377–382 (Mi tmf4044)

This article is cited in 5 papers

On the spectrum of the Dirac operator

S. N. Roze


Abstract: It is proved that the Dirac operator
$$ H \varphi=-i\sum_{j=1}^3\alpha_j\biggl(\frac\partial{\partial x_j}+iA_j(x)\biggr)\varphi+\alpha_4\varphi-q(x)\varphi $$
does not possess a discrete spectrum lying on the continuous spectrum under the condition lim
$$ \lim_{|x|\to\infty}|x|\biggl(\sum_{j=1}^3|A_j(x)|+|q(x)|\biggr)=0. $$


Received: 20.11.1969


 English version:
Theoretical and Mathematical Physics, 1970, 2:3, 275–279


© Steklov Math. Inst. of RAS, 2024