nLab non-relativistic particle

Idea

The mechanics/dynamics of a single particle propagating at low enough speed that the non-relativistic mechanics applies.

Definition

For the time being see at 1d WZW model.

Related concepts

• relativistic particle

• rigid body dynamics

References

General

(…)

Spin-statistics theorem

Discussion/proof of the spin-statistics theorem for non-relativistic particles via the topology/homotopy theory of their configuration spaces of points (cf. also braid group statistics):

• Michael G. G. Laidlaw, Cécile Morette DeWitt, Feynman Functional Integrals for Systems of Indistinguishable Particles, Phys. Rev. D 3 6 (1971) 1375-1378 [doi:10.1103/PhysRevD.3.1375]

• A. P. Balachandran, A. Daughton, Z. C. Gu, Giuseppe Marmo, Rafael D. Sorkin Spin statistics theorems without relativity or field theory, Int. J. Mod. Phys. A 8 (1993) 2993-3044 [doi:10.1142/S0217751X93001223]

• Michael V. Berry, Jonathan M. Robbins, Indistinguishability for quantum particles: spin, statistics and the geometric phase, Proceedings of the Royal Society A 453 1963 (1997) 1771-1790 [doi:10.1098/rspa.1997.0096]

  (cf. also the Atiyah-Sutcliffe conjecture)

• Michael V. Berry, Jonathan M. Robbins: Quantum indistinguishability: alternative constructions of the transported basis, J. Phys. A: Math. Gen. 33 (2000) L207 [doi:10.1088/0305-4470/33/24/101, pdf]

• Murray Peshkin: Spin and Statistics in Nonrelativistic Quantum Mechanics: The Zero Spin Case, Phys. Rev.A 67 (2003) 042102 [doi:10.1103/PhysRevA.67.042102, arXiv:quant-ph/0207017]

• Charis Anastopoulos, International Journal of Modern Physics A 19 05 (2004) 655-676 [doi:10.1142/S0217751X04017860, arXiv:quant-ph/0110169]

  (via geometric quantization)

• Nikolaos A. Papadopoulos, Mario Paschke, Andrés F. Reyes-Lega, F. Florian Scheck, The spin-statistics relation in nonrelativistic quantum mechanics and projective modules, Annales Mathematiques Blaise Pascal 11 (2004) 205-220 [doi:10.5802/ambp.193, arXiv:quant-ph/0608125, numdam:AMBP_2004__11_2_205_0/]

• J. M. Harrison, Jonathan M. Robbins, Quantum indistinguishability from general representations of $SU(2n)$, J. Math. Phys. 45 (2004) 1332–1358 [doi:10.1063/1.1666979, arXiv:math-ph/0302037]

• Bernd Kuckert, Spin and statistics in nonrelativistic quantum mechanics, I, Physics Letters A 322 1–2 (2004) 1–2 47-53 [doi:10.1016/j.physleta.2003.12.051, arXiv:quant-ph/0208151]

• Bernd Kuckert, Jens Mund, Spin & Statistics in Nonrelativistic Quantum Mechanics, II, Ann. Phys. 517 5 (2005) 309-311 [doi:10.1002/andp.200410129, arXiv:quant-ph/0411197]

• Murray Peshkin: Spin-Zero Particles must be Bosons: A New Proof within Nonrelativistic Quantum Mechanics, Found Phys 36 (2006) 19–29 [doi:10.1007/s10701-005-9011-2]

• Nikolaos A. Papadopoulos Andrés F. Reyes-Lega: On the Geometry of the Berry-Robbins Approach to Spin-Statistics, Found Phys 40 (2010) 829-851 [doi:10.1007/s10701-009-9365-y, arXiv:0910.1659]

• Andrés F. Reyes-Lega, Carlos Benavides, Remarks on the Configuration Space Approach to Spin-Statistics, Found Phys 40 (2010) 1004-1029 [doi:10.1007/s10701-009-9397-3, arXiv:0911.0579]

• Andrés F. Reyes-Lega: On the geometry of quantum indistinguishability, J. Phys. A: Math. Theor. 44 33 (2011) 325308 [doi:10.1088/1751-8113/44/32/325308, arXiv:1112.6300]

• Jonathan Bain: Non-RQFT Derivations of CPT Invariance and the Spin–Statistics Connection, Chapter 4 in: CPT Invariance and the Spin-Statistics Connection, Oxford University Press (2016) [doi:10.1093/acprof:oso/9780198728801.003.0005, ISBN:9780198728801]

• Michael Berry, Jonathan Robbins: Quantum Indistinguishability: Spin-statistics without Relativity or Field Theory?, in: A Half-Century of Physical Asymptotics and Other Diversions – Selected Works by Michael Berry, World Scientific (2017) 108-120 [doi:10.1142/9789813221215_0009, pdf]