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What do we mean when we say on shell particles? 
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#1
May2409, 03:16 PM

P: 32

Hello!
What do we mean when we say a particle in on shell? What is off shell? I gather it is related to energy and momentum conservation to say if a process is possible, but I've no idea what it actually is. Is it something to do with writing E^2 = p^2 + m^2? Cheers, Samantha 


#2
May2409, 03:34 PM

P: 527

By onshell one means "satisfying the equations of motion". For relativistic particles this indeed includes the property that the particle satisfies the energymass relation: E^2 = p^2 + m^2.
But it's a broader concept than that. For instance, Noether's theorem links conserved quantities to symmetries of the system. But this theorem only holds onshell. 


#3
May2409, 04:08 PM

P: 1,160

If one makes calculations with help of Fourier representation, they are expressed via Fourier variables denoted historically also as p (also four variables used in the Fourier integrals). As soon as these variables are independent of each other, they are not bound by any relationship, so the combination E(p) takes nonphysical values (E(p) is just meaningless). They say "off shell" or virtual particles. So any actual calculation includes on and offshell "particles". Bob. 


#4
May2409, 04:37 PM

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Thanks
P: 26,157

What do we mean when we say on shell particles?
(try using the X^{2} tag just above the Reply box ) On shell means real (physical), and is E^{2} = p^{2} + m^{2}. Off shell means not real (not physical), and is only used in the maths. Off shell occurs only in the middle of calculations, never at the beginning or end. Energy and momentum conservation applies to both on shell and off shell equations (but E^{2} = p^{2} + m^{2}, which applies to each particle individually, does not apply off shell). Unless you're doing Feynman diagrams and the Dyson expansion (a math technique in Quantum Field heory), you won't come across off shell. 


#5
May2509, 02:41 AM

P: 32

Thank you all very much for your help. :) However, how could I tell if a process is possible for onshell particles? So... picking a simple process a photon annihilating to give an electron and positron. How can I determine if this is possible for onshell particles?
Cheers, Samantha 


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