Search results

1. Mass dimension of coupling constant -- always an integer?

Well I was thinking whether it'd be pseudoscalar (that shouldn't be any big problem -- if we really want a parity violating theory). I just thought about gauge transformations, and yup, you were right -- the term wouldn't transform as a (pseudo)scalar but as a spinor. Adding scalar and spinor...
2. Mass dimension of coupling constant -- always an integer?

Thinking beyond SM, what are the physical consequences if the Lagrangian contains an interaction term with an odd number (i.e. only one) of fermions?
3. Mass dimension of coupling constant -- always an integer?

Just a simple question -- can the dimension of coupling constant be a rational number or should it always be an integer? The question arose when I was trying to construct a Lagrangian with an interaction term involving two spin-1 particles and a fermion. The dimensions add up to 7/2, which...
4. Feynman rules - where do the imaginary numbers come from?

I'm trying to learn how to derive Feynman rules (what else to do during xmas, lol). The book I'm using is QFT 2nd ed by Mandl&Shaw. On p 428 they're trying to show how to derive a Feynman rule for W W^\dagger Z^2 interaction term g^2 \cos^2\theta_W\left[W_\alpha W_\beta^\dagger Z^\alpha Z^\beta...
5. Relative velocity of beams

doh... natural units... thx
6. Relative velocity of beams

How come relative velocity of the beams can be expressed by v_{12} = \left| \vec{v}_1 - \vec{v}_2 \right| = \left|\frac{\vec{p}_1}{E_1} - \frac{\vec{p}_2}{E_2}\right| where \vec{p}_{1,2} and E_{1,2} is the momenta and energies of incoming particles, respectively? Similar equation is in Peskin &...
7. Plane wave expansion of massive vector boson

So... I think I'll go with two sets of ladder operators as usual in complex scalar field/fermions. It seems that the thesis uses them implicitly -- in Wick contraction the other operator is neglected because of the normal ordering requirement. About path integral.. thanks but I'll skip it for...
8. Plane wave expansion of massive vector boson

I'm trying to derive Feynman rules for massive vector boson and its antiparticle. It all boils down to plane wave expansion of the bosons which atm is a little bit confusing. Should I account for two different set of ladder operators (as in the case of complex KG or spinors, cf Peskin&Schröder...
9. Dual tensors in Lagrangian

Yeah, I forgot to mention I'm interested in U(1) theory. Thanks for the link, will read it.
10. Dual tensors in Lagrangian

Thanks, Bill_K, I didn't know that before. A quick proof for the eager: \begin{align*}\widetilde{F}^{\mu\nu}\widetilde{F}_{\mu\nu} &= \frac{1}{4}\epsilon^{\mu\nu\rho\sigma}\epsilon_{\mu\nu\alpha\beta}F_{ \rho \sigma}F^{\alpha\beta} = \frac{1}{2}\delta_{\alpha...
11. Dual tensors in Lagrangian

Why is it the case that dual field tensors, e.g. \widetilde{F}^{\mu\nu}=\frac{1}{2}\epsilon^{\mu\nu\rho\sigma}F_{\rho \sigma}, aren't being included in the Lagrangian? For example, one doesn't encounter terms like -\frac{1}{4}\widetilde{F}^{\mu\nu}\widetilde{F}_{\mu\nu} in QED or...
12. Mega quick question: must the Lagrangian (density) be real valued?

It basically says that the Lagrangian must not be hermitian since it's not observable. But I still have mixed feelings about it. After googling "hermicity of the Lagrangian" this popped up stating that the Lagrangian of the theory invariant under CPT symmetry must be hermitian (don't know...
13. Mega quick question: must the Lagrangian (density) be real valued?

Mega quick question: must the Lagrangian (density) be hermitian? In other words, must \mathcal{L}=\mathcal{L}^\dagger always be valid?