Exploring the QCD Lagrangian: Why is it Abbreviated?

In summary, the QCD Lagrangian is often quoted as just the first part, which includes the gluon field and quark fields, without the last term involving theta and the gluon field tensor. This is because observations have shown that theta is equal to zero to experimental precision, and including this term would introduce CP violation that is not observed. This is known as the strong CP problem, and one solution is the Peccei-Quinn mechanism.
  • #1
Kara386
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The QCD Lagrangian is
##\mathcal{L}=-\frac{1}{4}G^{a}_{\mu\nu}G^{a\mu\nu}+\sum\limits_{j=1}^n \left[\bar{q}_j\gamma^{\mu}iD_{\mu}q_j - (m_jq^{\dagger}_{Lj}q_{Rj}+h.c.)\right]+\frac{\theta g^2}{32\pi^2}G^{a}_{\mu\nu}\widetilde{G}^{a\mu\nu}##
Why is it so often quoted as just
##\mathcal{L}=-\frac{1}{4}G^{a}_{\mu\nu}G^{a\mu\nu}+\sum\limits_{j=1}^n \left[\bar{q}_j\gamma^{\mu}iD_{\mu}q_j - (m_jq^{\dagger}_{Lj}q_{Rj}+h.c.)\right]##?
I've seen both and I'm assuming the longer one is more complete somehow, but in those cases where the short version is being used, there's not even a mention of the missing term.
 
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  • #2
Observationally, ##\theta = 0## to experimental precision. The presence of the last term would introduce CP violation that is not observed. Why this is the case is known as the strong CP problem. One possible solution is the Peccei-Quinn mechanicsm.
 
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FAQ: Exploring the QCD Lagrangian: Why is it Abbreviated?

What is QCD Lagrangian and why is it abbreviated?

QCD Lagrangian stands for Quantum Chromodynamics Lagrangian, which is a mathematical formula used to describe the interactions between quarks and gluons in the theory of strong nuclear force. It is abbreviated as QCD because it is derived from the Quantum Field Theory of Quantum Electrodynamics (QED), and it is easier to refer to it by its acronym.

How is the QCD Lagrangian important in particle physics?

The QCD Lagrangian is an essential tool in particle physics as it helps us understand the behavior of quarks and gluons, which are the fundamental particles that make up protons and neutrons. It is also the basis for studying the strong interaction, which is one of the four fundamental forces in nature.

What does the QCD Lagrangian equation look like?

The QCD Lagrangian equation is a complex mathematical equation that describes the interactions between quarks and gluons. It includes terms for the kinetic energy of quarks and gluons, their potential energy, and the interaction between them through the strong force.

How does the QCD Lagrangian help us understand the behavior of quarks and gluons?

The QCD Lagrangian equation allows us to calculate the properties and behavior of quarks and gluons, such as their mass, spin, and charge. It also helps us understand the strong force and how it binds quarks together to form protons and neutrons.

Are there any limitations to the QCD Lagrangian?

Like any other scientific theory, the QCD Lagrangian also has its limitations. It only applies to high-energy interactions and does not take into account the effects of gravity. Also, solving the equations of the QCD Lagrangian is challenging, and most solutions are approximations.

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