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- Thread starter ARAVIND113122
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Bill_K

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sorry,but I did not understand.What do you mean by 'virtual'?

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Drakkith

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Virtual particles are a mathematical way to describe the interaction of forces. They aren't real particles.sorry,but I did not understand.What do you mean by 'virtual'?

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If they are a mathematical interpretation of interaction of forces,then how can they have mass?

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Drakkith

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TheIf they are a mathematical interpretation of interaction of forces,then how can they have mass?

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Bill_K

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So I don't think it is appropriate to say that the mass of the virtual W is "not defined" or that "it can be anything". It is just not related through p^2 = m^2. p^2 can be anything, but its mass is fixed and can be read off from the Lagrangian, or by checking the singularities of the propagator.

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Since, [itex]p^2[/itex] is what determines both the inertial properties of a particle and the available energy for decays, it seems a little odd to insist that the pole mass of the field is really the particle's mass.

So I don't think it is appropriate to say that the mass of the virtual W is "not defined" or that "it can be anything". It is just not related through p^2 = m^2. p^2 can be anything, but its mass is fixed and can be read off from the Lagrangian, or by checking the singularities of the propagator.

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Well, in the standard quantum field theory which governs particle physics as we know it, the mass of the quantum field is defined right there in the lagrangian, and can be obtained from the prefactor of the term square in the field operator.Since, [itex]p^2[/itex] is what determines both the inertial properties of a particle and the available energy for decays, it seems a little odd to insist that the pole mass of the field is really the particle's mass.

I try to avoid defining single concepts in several different ways, and prefer the mass to be a constant value to minimize confusion.

I think it would cause unnecessary confusion to work with a mass of the quantum field (m), and a mass for each possible single-particle excitation of the field, depending on its value of p^2 which can have any value for internal states in loop perturbation expansions.

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If you're going to argue based on loops, it seems inconsistent to argue that the Lagrangian mass parameter isWell, in the standard quantum field theory which governs particle physics as we know it, the mass of the quantum field is defined right there in the lagrangian, and can be obtained from the prefactor of the term square in the field operator.

I try to avoid defining single concepts in several different ways, and prefer the mass to be a constant value to minimize confusion.

I think it would cause unnecessary confusion to work with a mass of the quantum field (m), and a mass for each possible single-particle excitation of the field, depending on its value of p^2 which can have any value for internal states in loop perturbation expansions.

This, however, is really neither here nor there, since even

As for the issue of particles in loops, there's nothing overtly wrong with those particles having really weird masses. After all, the only invariants that have any physical meaning are those that can be constructed entirely from external momenta. The difference, then, from the beta decay case that started this discussion is that, in that case, the mass of the W

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Since a quantum field theory should be accompanied by a choice of cut-off scale, I'd use the renormalized mass. At this choice of cut-off scale, the mass of an excitation of a given quantum field would be the same no matter what particle behaviour we are considering (on or off shell). And this mass would also appear in the Yukawa potential for interactions mediated by this field.If you're going to argue based on loops, it seems inconsistent to argue that the Lagrangian mass parameter isthe massof the field, since one-loop corrections require that this parameter actually be either 0 or infinite (in the limite of infinite cutoff scale) in order that the pole mass in the propagator be finite.

I would like to avoid getting into along discussion about terminology. I acknowledge that there are arguments for both viewpoints. To me, simplicity of terminology is important.

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Let's see if I can kind of give you a simple, hand-waving explanation.

A virtual particle with a significantly large amount of mass can be created out of nothing - out of vacuum. The mass or energy is essentially "borrowed" from the vacuum - but you need to "put it back" extremely quickly before the universe notices that it's missing, and the more energy you "borrow", the less time it can be borrowed for. As long as these virtual particles only exist for a fleeting instant, normal ideas about conservation of mass or energy can be ostensibly ignored.

The more mass you create in a virtual particle, the shorter the lifetime of the virtual particle can be before it is destroyed. This can be expressed in the energy-time uncertainty principle.

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