Essential self-adjointness ofn-dimensional Dirac operators with a variable mass term
| Autor: | Hubert Kalf, Osanobu Yamada |
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| Rok vydání: | 2001 |
| Předmět: | |
| Zdroj: | Journal of Mathematical Physics. 42:2667-2676 |
| ISSN: | 1089-7658 0022-2488 |
| DOI: | 10.1063/1.1367331 |
| Popis: | We give some results about the essential self-adjointness of the Dirac operator $$ H = \sum\limits_{j = 1}^n {\alpha _j p_j } + m\left( x \right)\alpha _{n + 1} + V\left( x \right)I_N \left( {N = 2^{\left[ {\tfrac{{n + 1}} {2}} \right]} } \right), $$ on \({{\left[ {C_{0}^{\infty }\left( {{{R}^{n}}\backslash 0} \right)} \right]}^{N}} \), where the \({{\alpha }_{j}}\left( {j = 1,2,\cdot \cdot \cdot ,n} \right) \) are Dirac matrices and m(x) and V(x) are real-valued functions. We are mainly interested in a singularity of V(x) and m(x) near the origin which preserves the essential self-adjointness of H. As a result, if m = m(r) is spherically symmetric or, then we can permit a singularity of m and V which is stronger than that of the Coulomb potential. |
| Databáze: | OpenAIRE |
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