Can weak interaction be defined as a force related to distance between objects?

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Weak interaction can be related to distance between objects, but its complexity arises from its role in particle creation and decay. Unlike gravitational and electromagnetic forces, which have more straightforward distance dependencies, weak interaction involves Z-bosons for neutrino interactions. Neutrinos do not interact via gluons but are influenced by weak interaction and gravity. The nuclear force is suggested to stem from unbalanced quark interactions. Overall, while weak interaction can be framed in terms of distance, it requires a more intricate mathematical approach.
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Gravitational force between masses is given by the law of universal gravitation. Electrodynamics force between electric charges is the Lorentz force. Nuclear force between nucleons falls off exponentially with rising the distance. The force between quarks grows in proportion to the distance. Can weak interaction be expressed in term of a force as a function of the distance between objects?
 
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Yes, it can, to some extent, but the weak interaction also explains particles creation and decay, so the mathematical apparatus is a bit more complex. Classical gravitation and e-m implicitly assume that the number of particles of any particular kind is constant.

Try to compute attraction force of neutrinos through Z-boson :).
 
Do you imply that neutrinos are attracted not through gluons only but through Z-bosons also?
 
Neutrinos certainly do not interact through gluons but certainly through Z bosons.
 
Neutrinos aren't affected by the strong interaction (gluons), only by the weak interaction and gravity.
 
It seems to me that nuclear force is caused by an uncompensated quark interaction
 
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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