2
votes
1answer
95 views

Mass term in the Lagrangian

I have read that the mass term appearing in the electroweak Lagrangian stops it (the Lagrangian) from becoming gauge invariance. Can someone explain where and why this term is creating the problem?
4
votes
0answers
86 views

Gauge Invariance of Yang Mills Lagrangian

I am trying to show the invariance of the following Yang Mills Lagrangian: $$L= -\frac{1}{4} F^a_{\mu \nu} F_a^{\mu\nu} + J_a^\mu A_\mu^a$$ under the following gauge transformation ($\theta$ being a ...
3
votes
2answers
109 views

When can we add a total time derivative of $f(q, \dot{q}, t)$ to a Lagrangian?

The other day, I was listening to this lecture on the Lagrangian for a charged particle in an electromagnetic field, and at one point in the video, the lecturer mentions that we can add any total time ...
0
votes
0answers
32 views

How could I show that ${\mathcal{L}\left(e\right)}$ is ${SU\left(2\right)_{L}\times U\left(1\right)_{Y}}$ invariant?

How can I show that ${\mathcal{L}\left(e\right)}$ is ${SU\left(2\right)_{L}\times U\left(1\right)_{Y}}$ invariant by checking explicitly that the ${\chi_{L}}$, ${e_{R}}$, ${\vec{W}_{\mu}}$ and ...
3
votes
1answer
289 views

How to introduce the electromagnetic field in Quantum Field Theory?

There are many ways to introduce the electromagnrtic field in Quantum Field Theory(QFT), such as canonical quantization method which introduces the creation and annihilation oprators by treating the ...
4
votes
2answers
414 views

Gauge fixing and equations of motion

Consider an action that is gauge invariant. Do we obtain the same information from the following: Find the equations of motion, and then fix the gauge? Fix the gauge in the action, and then find the ...
4
votes
1answer
545 views

Noether current for the Yang-mills-higgs lagrangian

I am trying to calculate the Noether's current, more specifically, the energy density of the Yang-mills-Higgs Lagrangian. Please refer to the equations in the Harvey lectures on Magnetic Monopoles, ...