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### Why do we believe local gauge invariance (that tells us photons are exactly massless)? [duplicate]

There are experimental upper limits on the photon's mass, but they are finite. I heard that the reason we know that photons have exactly zero rest mass (and thus travel exactly at the universal ...
27 views

### What problems arise when mass is introduced as a parameter in Quantum Field Theory instead of through the Higgs Mechanism? [duplicate]

https://www.youtube.com/watch?v=Ni-Lf1y51Dc I always wondered why mass is not considered as a fundamental feature of particles, but instead it is explained through the Higgs mechanism. I am aware of ...
2k views

### What are the alternatives to the Higgs mechanism?

Can someone summarize, with references if possible, all of the alternatives to the simplest model (that requires only a single scalar Higgs field with the Mexican Hat potential) of spontaneous ...
842 views

### Gauge invariance is just a redundancy. Why is massive abelian gauge field renormalizable but massive non-abelian gauge field nonrenormalizable?

For example, Kaku's QFT pp. 214-215: Massive vector theory with non-Abelian group is non-renormalizable. Massive vector Abelian theory is renormalizable. I heard about the following arguments,...
672 views

### Is Higgs mechanism necessary in QCD?

As we known, we introduce Higgs mechanism into Standard model to explain mass of Gauge boson, lepton and neutrino(maybe?). Higgs mechanism is necessary for electroweak theory because gauge symmetry ...
237 views

### Condensed Matter or High Energy examples in which higher-loop $n\ge 2$ correction can have important physical consequence?

In QFT for high energy or condensed matter, tree level diagram means classical result or mean field. Loop diagram means quantum correction or (thermal or quantum) fluctuation above mean field. In most ...
564 views

### What's the key point to argue that pure gravity can't be renormalizable from two-loop?

Gravity is not power-counting renormalizable in dimensions greater than two. It is known by Gerard 't Hooft, M.J.G. Veltman that pure gravity in four-dimensions is finite to the first loop order ...
333 views

### Massive Gauge Bosons without Higgs fields

In a possible theory like our Standard model but without a Higgs i.e.: $$\mathcal{L}=i\bar{\Psi}_f\gamma_\mu D^\mu\Psi_f-\text{Tr}[G^b_{\mu\nu}G^{b\,\mu\nu}]$$ where $b,f$ run over the typical ...
247 views

### What is the problem with a Lagrangian that isn't gauge invariant?

In every textbook I've read the only argument why gauge bosons can't have mass is "because a mass term would break gauge invariance". Even fermions can't have mass because it would break the $SU(2)_L$ ...