# Tag Info

### How does the absence of quadratic terms in the Lagrangian imply massless quanta?

I will expand a bit on one of the answers to be clearer why a quadratic term usually leads to the 'mass' term. Because the coefficient in front of the $A_\mu A^\mu$ term has dimension $2$ doesn't by ...
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### How does the absence of quadratic terms in the Lagrangian imply massless quanta?

If by mass we mean the coefficient in front of the quadratic terms, then the answer is straightforward... (although one might ask whether such a situation could be also treated as a case of infinite ...
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### How does the absence of quadratic terms in the Lagrangian imply massless quanta?

This is because if you have a term in the Lagrangian that is proportional to $A_{\mu}A^{\mu}$, with some coefficient in front of it, then its coefficient is going to automaticlly be considered the ...
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### Why do we put factors of zero in a Lagrangian that is to be extremized?

I will expand a bit on why this Lagrangian is defined this way. If I want to maximize a function $f(p_1,\dots,p_n)$ over all its parameters I can set the gradient to zero. $$\nabla f(\vec p)=0$$ This ...
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### Can you rewrite the QCD lagrangian in terms of hadron?

By "exactly" you seem to imply "directly", or ab initio. People have built bridges between fundamental QCD on the lattice and σ-models summarizing chiral symmetry breaking for ...
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### How Feynman's path integral lead to least action principle? Math proof needed

You can look up "Laplace approximation" for integrals. In the path integral formalism the word "instanton" is also used.
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### How do I understand the Hodge $⋆$ operator in Yang-Mills Lagrangian?
Intuitively, you can think of the Hodge dual and outer product geometrically as you already do, and this combination as a sort of generalised dot product. $A\wedge B$ has a magnitude that extracts the ...
### How do I understand the Hodge $⋆$ operator in Yang-Mills Lagrangian?
The Hodge dual of a $p$-form (antisymmetric $(0,p)$ tensor) in $d$ dimensions is a $(d-p)$-form whose components are defined by  (\star A)_{\mu_1 \cdots \mu_{d-p}} \equiv \frac{1}{p!} \epsilon_{\...