Massive Particle Notation: Exploring the p_\mu of m^2<0

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Is the particle stable? Does it decay? What are its interactions with other particles? How does it fit into the Standard Model? These are the questions that will determine whether or not such a particle is physically viable.In summary, the conversation discusses the concept of imaginary mass particles and their implications in the field of quantum physics. The idea of imaginary mass arises from the mathematical framework of field theory, but its physical existence is still a topic of debate and further study. While it is possible to construct a consistent mathematical model for these particles, their physical viability is determined by their behavior and interactions with other particles. Further research and study is required to fully understand the implications of imaginary mass particles in the Standard Model of physics.
  • #1
noamriemer
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Hi! I can't understand something in field theory and need your assistance:

I wish to understand why a particle of mass m^2<0 can't exist.
For a massive particle, in its reference frame, one would write:
[itex]p_\mu=(m,0,0,0)[/itex]. I understand that.
But for m=0, why is:
[itex]p_\mu=(p,0,0,p)[/itex]
And for [itex]m^2<0[/itex]
Why is:
[itex]p_\mu=(0,0,0,m)[/itex]
?
Thank you...!
 
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  • #2
That would imply that the mass is imaginary ... what would that mean?
 
  • #3
Simon Bridge said:
That would imply that the mass is imaginary ... what would that mean?

I don't know... an adjoint term maybe?
 
  • #4
One of the things it may mean is that it is traveling faster than the speed of light - or that it is highly unstable... once you realize that m must be imaginary if m2 < 0 you'll have something to google for:
Wiki: http://en.wikipedia.org/wiki/Tachyonic_field
Here: https://www.physicsforums.com/showthread.php?t=107988
Arxiv: http://arxiv.org/pdf/physics/0604003.pdf (no date?!)
In contrast: http://www.quora.com/Quantum-Field-Theory/Can-real-particles-such-as-neutrinos-have-imaginary-mass

Some measurements of neutrinos mass have suggested that m2 < 0 is a possibility - however, experimental uncertainty tells us more about the measurement process than it does about the thing being measured. I'm guessing this is where you are coming from.

The second-to-last link above probably has the most accessible answer to your question.

When you think of things like this it is a good idea to try think through the consequences... try putting the imaginary mass into the momentum 4-vector for a simple problem and find an equation of motion or otherwise see what that does to the calculations ;) play around.
 
  • #5
Thank you so much for a wonderful reply!
 
  • #6
No worries. Have fun :)

I realized I didn't actually answer the whole question! You were talking about notation:
... a massless particle will be moving with momentum p and energy pc (think: photons) so the 4-vector is scatalogical for motion in the z direction if P0 = E/c ;)

The last one is because the imaginary mass gives it a space-like 4-momentum.
Find the inner product of that vector with itself and you'll get a negative mass-squared out.
If you try a naive construction with E=(-m)c2 you won't get negative mass-squared out.
http://en.wikipedia.org/wiki/Minkowski_space#Causal_structure
 
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  • #7
I will take advantage of your kindness and ask another thing:

For m^2<0:
[itex]W^\mu=\frac {1} {2} \varepsilon^{\alpha\beta\gamma\delta}M_{\beta\alpha} p[/itex]
out of it we will get both L's and K's, meaning the algebra is not close in su2. so, there is no finite way to write the states you can get. That is not physically, and therefore, there exist no such particle.
But if we look at a wider range, and include both K's and L's, the algebra does form a complete "basis". Why is this not enough for such particle to exist?

I hope my intentions are possible to understand... :)
Thanks!
 
  • #8
Well what you've shown is that you have a consistent mathematics (I didn't check - don't take my word for it) to allow imaginary-mass particles. You'll see the idea discussed in the literature ... so where did you get the idea that these "cannot exist" as a consequence of the math?

Your next step is to propose an imaginary math particle and work out the consequences.
 

FAQ: Massive Particle Notation: Exploring the p_\mu of m^2<0

What is Massive Particle Notation?

Massive Particle Notation is a system used by scientists to represent the properties of particles with a mass, specifically those with a squared mass less than zero.

What is the significance of the p_\mu in Massive Particle Notation?

The p_\mu represents the momentum of the particle in the three-dimensional space, with \mu being the direction (x, y, or z). It is an important factor in understanding the behavior and interactions of the particle.

What does m^2<0 mean in Massive Particle Notation?

This notation indicates that the squared mass of the particle is less than zero, which means that the particle is an imaginary or tachyonic particle. These particles have a complex mass and travel faster than the speed of light.

How is Massive Particle Notation used in particle physics research?

Massive Particle Notation is used to study the properties and interactions of particles with a mass, including their decay processes, production, and scattering. It is an important tool in understanding the fundamental particles and forces in the universe.

Can Massive Particle Notation be applied to all particles?

No, Massive Particle Notation is only applicable to particles with a non-zero mass. Particles with zero mass, such as photons, do not have a squared mass and therefore cannot be represented using this notation.

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