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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)
[
reply
]
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)
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reply
]
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)
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reply
]
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)
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reply
]
(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 ).
- The energy Ep in the second equation needs to be defined.
Xxanthippe
(
talk
) 23:16, 22 December 2009 (UTC).
[
reply
]
Should the section on
zero rest mass
from the
Spinor field
article be moved here?
70.247.169.197
(
talk
) 17:42, 21 August 2010 (UTC)
[
reply
]
I came across
Polar form of the Dirac equation
on
new page patrol
, and it looked to me like that article is just a proof related to Dirac fields, which themselves are currently only covered as a section in this article about Fermionic fields in general, and thus it seems appropriate to merge its content here. I don't really understand any of the math though, so I'll leave it to other editors to figure out how to actually go about doing that.
signed,
Rosguill
talk
05:21, 15 December 2018 (UTC)
[
reply
]
As someone with a bit more background, I agree the aforementioned page should be a subsection of this pages Dirac field section
Cmcraes
(
talk
) 20:03, 28 March 2019 (UTC)
[
reply
]