Talk:On shell and off shell

message: On the topic of off mass shell, I'm not convinced energy violation is an issue.
For instance, in Feynman diagrams, energy and momentum conservation are explicitly included in the calculation.
Virtual particles just don't have the usual correspondence between the two.
74.131.48.12 07:51, 29 August 2007 (UTC)

message: I was about to add the following line:
In literature, one may also encounter p^\mu p_\mu \equiv p^2 = - m^2, where the extra minus sign is due to sign convention in the metric.
although I'm not sure it is appropriate, relevant and sufficiently general. --CompuChip (talk) 10:26, 2 October 2009 (UTC)
replies: text: If E = m c^2 then the particle is at rest and so  - |\vec{p} \,|^2 c^2 = 0 is true.  —Preceding unsigned comment added by 94.15.20.39 (talk) 23:19, 4 January 2011 (UTC)

text: I think it's encountered often enough that it's worth mentioning. I'll go ahead and add it as well as some examples. --Anagogist (talk) 12:15, 7 May 2014 (UTC)
thread_title:  Minus sign 

message: I'd like to see consideration mentioned for a case where the opposing flows can be (if not always) destructive in nature, and cancelling as the creation of an 'off mass shell' vector, even if temporary (We see this all the time in water wave propagation, acoustic sound (dead zones) and photon wave destructive interference) .  This would be equivalent to the same process as creating an eigenstate from complex vectors only from our fram the translational frame of reference is our coordinate system to complex.  In other words, the process appears one sided mathematically.  So far, I don't know if this is mathematically founded or not (matrix translation), at this time it appears (to me) the reverse of this is unfounded mathematically; however, if that's the case then it opens a whole new consideration for mathematics in quantum mechanics.  I think it's simpler to think of conjugates as dimensional rotations, even though I can't get away from 'classical' understanding of the concept of conjugates as a one way street mathematically. (Perhaps in matrices, the coordinate reference can be any frame including a 'classical' complex frame and I forgot or didn't realize this. I even see this in the Pauli exclusion principle where from another frame, the collapse is from on shell, to off shell. Providing, of course, I'm understanding this 'shell' concept properly in that 'virtual' means imaginary complex abstract or am I misunderstanding that by squaring everything the process is intended to use 'virtual' as special case of local realism, which I believe is under question right now due to entanglement.)http://arxiv.org/pdf/1303.0614v2.pdf  
In our current frame, a complex sum of squares results in eigenvalues which are real.  If we reverse the process we create either 4 complex vectors, or if we reverse the concept mathematically we create the same as complex to real, a single vector, then real sums of squares might create a single complex vector (though not mathematically based on my understanding).  Perhaps my understanding of Linear Algebra is weak, and I need to realize that the math has a polar independence from any 'real' frame of coordinates. I'll admit to that, I'm weak in this; however I still find the case of quantum decoherence existing in 'real' conjugates moving the process from 'on shell' to 'off shell', and visa versa. (Since I consider myself a scientist, naturally I consider opposing viewpoints and would love to hear such an argument in support or contrast).Cyberchip (talk) 12:23, 5 January 2015 (UTC)
thread_title: Re: "negative and positive on-shell E then simply represent opposing flows of positive energy"

message: For a mathematician , this kind of thing is at the fringe of sense, yet it's stimulating and I think re QFT it is much of the point. Can we put a delimiting fence about it, however large and loose? 198.129.67.88 (talk) 22:45, 29 March 2016 (UTC)
thread_title:  Wow