Talk:Fermionic field

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I removed the text

"Since all observables are built out of an even number of fermion fields, the commutation relation vanishes between any two observables at spacetime points within the light cone. As we know from elementary quantum mechanics two simultaneously commuting observables cannot be measured simultaneously. We have therefore correctly implemented Lorentz invariance for the Fermion field, thereby preserving causality."

It's bad logic and mostly wrong. Melchoir 03:04, 30 October 2005 (UTC)

This article is mostly about the free Dirac field, but fermion fields are far more general than that! QFT 19:46, 29 January 2006 (UTC)

The original text makes sense with some slight modifications. It should read

":Since all reasonable observables (such as energy, charge, particle number, etc.) are built out of an even number of fermion fields, the commutation relation vanishes between any two observables at spacetime points within the light cone. As we know from elementary quantum mechanics two simultaneously commuting observables cannot be measured simultaneously. We have therefore correctly implemented Lorentz invariance for the Fermion field, and preserved causality."

See for example Peskin and Schroeder pg. 56. DiracAttack 08:04, 15 September 2006 (UTC)

[edit] What is this entry about?

This article doesn't really explain what a ferminonic field is. What is the physical reality of this field? It isn't the same as the supposed luminiferous ether (the classicaly imagined medium that light waves were once imagined to propagate through) yet the fermionic field seems to have an analogous role. Could someone flesh this out, without going into detailed mathematics? See also Bosonic field. RK 19:51, 21 May 2006 (UTC)

(David Edwards) As Whitaker pointed out in volume II of his history of the aether, quantum field theory allows a reentry of a relativistic ether; namely, spacetime is the seat of potential observables, i.e. it is a tectured medium.

See my (David Edwards) entry under limitations of quantum logic:

In any case, these quantum logic formalisms must be generalized in order to deal with supergeometry (which is needed to handle Fermi-fields) and non-commutative geometry (which is needed in string theory and quantum gravity theory). Both of these theories use a partial algebra with an "integral" or "trace". The elements of the partial algebra are not observables; instead the "trace" yields "greens functions" which generate scattering amplitudes. One thus obtains a local S-matrix theory (see D. Edwards). Since around 1978 the Flato school ( see F. Bayen ) has been developing an alternative to the quantum logics approach called deformation quantization (see Weyl quantization ).