Virtual Particles: Exploring Energy Mass & Conservation

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Virtual particles, such as sea quarks, contribute to the mass of baryons like nucleons by existing momentarily in accordance with the Heisenberg uncertainty principle, which allows for transient fluctuations in energy. These quark-antiquark pairs pop in and out of existence, potentially leaving behind residual effects that align with the conservation of energy. The discussion highlights that sea quarks are part of the wave function rather than mere virtual pairs, indicating a more complex interaction in mass contribution. Radiative corrections from virtual particles further complicate this relationship, suggesting that the mechanisms of energy contribution are not straightforward. Understanding these interactions is crucial for reconciling them with the first law of thermodynamics.
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How exactly do virtual particles add to energy mass while still complying with the conservation of energy? For instance, sea quarks, (virtual quark, antiquark pairs) are suppose to contribute to the mass of a brayon. Do they exist for a fleeting moment below the Heisenberg limit by popping in and out of existence before they are detected (ΔEΔt<ħ/2) leaving behind some kind of residual energy or gravitational potential and if so, how does this work within the the first law of thermodynamics (or has it always been the case and what energy they provide has always been taken into account)?
 
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Sea quarks, in their usual implementation, are not virtual pairs.
They are a 5 quark (4q and 1 antiq) part of the wave function.
|p>=a\psi_3+b\psi_5, with a^2+b^2=1.
Radiative corrections due to virtual pairs are something else.
 
Thanks for the reply clem. So how exactly do the sea quarks contribute to the mass of a nucleon and how do virtual particles provide radiative corrections (I imagine the answer isn't that simple but any info/links would be appreciated).
 
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Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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