- #1
izzi wekwek
- 4
- 0
My question is why there is -1/2 for ω meson?
Why is there a -1/2 in the Lagrangian density for ω mesons?
- Context: Undergrad
- Thread starter izzi wekwek
- Start date
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SUMMARY
The discussion centers on the inclusion of the -1/2 factor in the Lagrangian density for ω mesons. Participants confirm that this factor is necessary for maintaining the correct sign for the kinetic and mass terms when using the east-coast metric, specifically where the metric tensor is defined as ημν = diag(1, -1, -1, -1). The physical degrees of freedom for the ω meson are three spatial vectors, which further necessitates the presence of the -1/2 term to ensure accurate representation of the meson's properties.
PREREQUISITES- Understanding of Lagrangian mechanics
- Familiarity with quantum field theory
- Knowledge of metric tensors, specifically east-coast metric
- Concept of physical degrees of freedom in particle physics
- Study the implications of the east-coast metric in quantum field theory
- Explore the role of Lagrangian density in particle physics
- Investigate the properties of ω mesons and their interactions
- Learn about the derivation of kinetic and mass terms in Lagrangians
Physicists, particularly those specializing in quantum field theory, particle physicists, and students studying the properties of mesons and their mathematical representations.
My question is why there is -1/2 for ω meson?
- #2
my2cts
- 362
- 26
Where did you find these lagrangians?
I would remove the (-)1/2( ...) bit.
Then it can be correct if σ is complex and ω is real valued.
I would remove the (-)1/2( ...) bit.
Then it can be correct if σ is complex and ω is real valued.
- #3
- 24,488
- 15,059
No, you shouldn't remove the ##-1/2## ;-), because it's correct. You obviously work in the east-coast metric, where ##(\eta_{\mu \nu})=\mathrm{diag}(1,-1,-1,-1)##. The physical degrees of freedom of ##\omega^{\mu}## are three space like vectors, and thus to get the right sign for the kinetic and the mass term there must be that additional - sign.
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