dorsal/arxiv
View SchemaKinematics and hydrodynamics of spinning particles
| Authors | Erasmo Recami, Giovanni Salesi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9607025 |
| URL | https://arxiv.org/abs/quant-ph/9607025 |
| DOI | 10.1103/PhysRevA.57.98 |
| Journal | Phys.Rev.A57:98-105,1998 |
Abstract
In the first part (Sections 1 and 2) of this paper --starting from the Pauli current, in the ordinary tensorial language-- we obtain the decomposition of the non-relativistic field velocity into two orthogonal parts: (i) the "classical part, that is, the 3-velocity w = p/m OF the center-of-mass (CM), and (ii) the so-called "quantum" part, that is, the 3-velocity V of the motion IN the CM frame (namely, the internal "spin motion" or zitterbewegung). By inserting such a complete, composite expression of the velocity into the kinetic energy term of the non-relativistic classical (i.e., newtonian) lagrangian, we straightforwardly get the appearance of the so-called "quantum potential" associated, as it is known, with the Madelung fluid. This result carries further evidence that the quantum behaviour of micro-systems can be adirect consequence of the fundamental existence of spin. In the second part (Sections 3 and 4), we fix our attention on the total 3-velocity v = w + V, it being now necessary to pass to relativistic (classical) physics; and we show that the proper time entering the definition of the four-velocity v^mu for spinning particles has to be the proper time tau of the CM frame. Inserting the correct Lorentz factor into the definition of v^mu leads to completely new kinematical properties for v_mu v^mu. The important constraint p_mu v^mu = m, identically true for scalar particles, but just assumed a priori in all previous spinning particle theories, is herein derived in a self-consistent way.
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"abstract": "In the first part (Sections 1 and 2) of this paper --starting from the Pauli\ncurrent, in the ordinary tensorial language-- we obtain the decomposition of\nthe non-relativistic field velocity into two orthogonal parts: (i) the\n\"classical part, that is, the 3-velocity w = p/m OF the center-of-mass (CM),\nand (ii) the so-called \"quantum\" part, that is, the 3-velocity V of the motion\nIN the CM frame (namely, the internal \"spin motion\" or zitterbewegung). By\ninserting such a complete, composite expression of the velocity into the\nkinetic energy term of the non-relativistic classical (i.e., newtonian)\nlagrangian, we straightforwardly get the appearance of the so-called \"quantum\npotential\" associated, as it is known, with the Madelung fluid. This result\ncarries further evidence that the quantum behaviour of micro-systems can be\nadirect consequence of the fundamental existence of spin. In the second part\n(Sections 3 and 4), we fix our attention on the total 3-velocity v = w + V, it\nbeing now necessary to pass to relativistic (classical) physics; and we show\nthat the proper time entering the definition of the four-velocity v^mu for\nspinning particles has to be the proper time tau of the CM frame. Inserting the\ncorrect Lorentz factor into the definition of v^mu leads to completely new\nkinematical properties for v_mu v^mu. The important constraint p_mu v^mu = m,\nidentically true for scalar particles, but just assumed a priori in all\nprevious spinning particle theories, is herein derived in a self-consistent\nway.",
"arxiv_id": "quant-ph/9607025",
"authors": [
"Erasmo Recami",
"Giovanni Salesi"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.57.98",
"journal_ref": "Phys.Rev.A57:98-105,1998",
"title": "Kinematics and hydrodynamics of spinning particles",
"url": "https://arxiv.org/abs/quant-ph/9607025"
},
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