Gauge potential decomposition, space-time defects, and Planck’s constant. (English) Zbl 0817.53044
Summary: A new geometrization of Planck’s constant is proposed, which also bases on the torsion in the space-time. A quantity is introduced to describe the space-time dislocations that appear due to torsion. It will be pointed out that there is \(U(1)\)-like gauge invariance in this new geometrization. Using the gauge-potential decomposition, the quantity is quantized in units of the Planck length. The quantum number is determined by Hopf indices and Brouwer degrees.
MSC:
53Z05 | Applications of differential geometry to physics |
81T70 | Quantization in field theory; cohomological methods |
References:
[1] | DOI: 10.1007/BF00671851 · Zbl 0692.53032 · doi:10.1007/BF00671851 |
[2] | DOI: 10.1016/0020-7225(90)90130-B · Zbl 0718.73074 · doi:10.1016/0020-7225(90)90130-B |
[3] | DOI: 10.1016/0001-6160(53)90054-6 · doi:10.1016/0001-6160(53)90054-6 |
[4] | DOI: 10.1016/0001-6160(53)90054-6 · doi:10.1016/0001-6160(53)90054-6 |
[5] | DOI: 10.1016/0001-6160(53)90054-6 · doi:10.1016/0001-6160(53)90054-6 |
[6] | DOI: 10.1063/1.529352 · Zbl 0729.53063 · doi:10.1063/1.529352 |
[7] | DOI: 10.1063/1.522521 · doi:10.1063/1.522521 |
[8] | DOI: 10.1016/0370-1573(81)90010-7 · doi:10.1016/0370-1573(81)90010-7 |
[9] | DOI: 10.1016/0370-1573(81)90010-7 · doi:10.1016/0370-1573(81)90010-7 |
[10] | DOI: 10.1016/0020-7225(92)90048-L · doi:10.1016/0020-7225(92)90048-L |
[11] | DOI: 10.1016/0020-7225(92)90048-L · doi:10.1016/0020-7225(92)90048-L |
[12] | DOI: 10.1063/1.530190 · Zbl 0788.53033 · doi:10.1063/1.530190 |
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