All Questions
Tagged with renormalization symmetry-breaking
24
questions
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52
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Conformal invariance and mass terms in QFT
We know that a physically sensible QFT must be renormalizable. If I understand correctly, when this happens, the theory has "asymptotic freedom" and is conformally invariant past some high ...
- 407
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0
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39
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Loop Calculations of A Spontaneous Broken gauge theory with fermions
Let me first rephrase the background. Consider adding a massless fermion to the spontaneously broken $U(1)$ gauge theory through a chiral interaction:
$$
\mathcal{L}=\bar{\psi}_{L}i \gamma_{\mu}D^{\mu}...
- 81
1
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36
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Does the changes of flow regimes of the renormalization group flow diagram imply always that a symmetry has been broken?
Usually we can use RG flow diagrams to understand that a phase transition has happened. Because they are intimately related to a broken symmetry, does that imply that it always implies that a symmetry ...
- 11
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Relation between RG flow and space of vacua
When studying supersymmetric QFT's, it is very common to compute the moduli space of the theory by solving all F-term equation (derivatives of the superpotential). More precisely, one should also ...
- 1,044
1
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1
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86
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Quantum correction to the relation of mass and vacuum expectation value
On Peskin & Schroeder's QFT, page 387, the book gives a general analysis about renormalization and symmetry.
For the example of $\sigma$ mass in the linear sigma model, the classical relation is
$$...
- 1,421
2
votes
1
answer
339
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Peskin and Schroeder, Linear sigma model, renormalized perturbation theory
On Peskin & Schroeder's QFT pages 353-355, the book uses the Linear sigma model to illustrate the renormalization and symmetry.
We can write the Lagrangian of Linear sigma model with
$$
\begin{...
- 1,421
8
votes
3
answers
448
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Relation between Spontaneous Symmetry Breaking and Renormalization Group
I have two different pictures in my head of how a phase transition occurs, but I am not sure of the relation between these two pictures.
SSB: Our theory has a global symmetry and when the parameters ...
- 642
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52
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Doesn't vector bosons enter in the formula for the calculation of beta function coefficients?
It is a well established result that, for a popular set of conventions, the lowest order $\beta$ function coefficient is calculated as
$$
b=-\frac{11}{3}C_2(G)+\frac{4}{3}\kappa S_2(F)+\frac{1}{6}\eta ...
- 1,742
4
votes
1
answer
246
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Explicit breaking of conformal symmetry
I think of a relativistic conformal field theory as basically any theory which does not have a length scale. Say all particles are massless and all couplings are dimensionless. (I could really talk ...
- 1,586
10
votes
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answer
367
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Renormalization of mass: does it change sign from high temperature to low temperature?
Consider a Landau Ginzburg theory for ferromagnets with Hamiltonian
$$H=\int d^{D} x \frac{1}{2}(\nabla\phi(x))^{2} + \frac{1}{2} \mu^{2} \phi^{2}(x) + \frac{\lambda}{4!}\phi^{4}(x)$$
I can compute ...
- 53
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answers
264
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Renormalization of linear sigma model fixing the Vacuum Expectation Value (VEV)
In the linear sigma model
$$ \mathcal L = (\partial_{\mu} \phi^i)^2 + \frac 12 \mu_0 (\phi^i)^2 + \frac{\lambda_0}{4} ((\phi^i)^2)^2 ,$$
the symmetry is broken around the vacuum expectation value (VEV)...
- 186
2
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answers
77
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Why can't we interpret the W, Z bosons as massive vector bosons not arising from a gauge theory? [duplicate]
The standard story goes as follows: gauge bosons cannot have a mass term because it would break gauge invariance in the lagrangian. This is clear, but why can't we just have massive vector bosons ...
- 187
6
votes
2
answers
1k
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Higgs mechanism and phase transition
Generally speaking, phase transitions divide into two types: First order and second order. To me, Higgs field's SSB sounds like a second-order one though I don't know the dependency of Higgs field's ...
- 1,268
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109
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Bare mass versus the mass form spontaneous symmetry breaking
Consider renormalization in $\phi^4$ theory $$\mathscr{L}=(\partial\phi)^2-\frac{1}{2}m^2\phi^2+\frac{\lambda}{4}\phi^4$$ where $m$ and $\lambda$ are respectively the unobservable bare mass and bare ...
- 26.8k
1
vote
1
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Why is the relation $M_W=M_Z\cos\theta_W$ true only at tree-level?
In Glashow-Weinberg-Salam electroweak theory, the relation $$M_W=M_Z\cos\theta_W\tag{1}$$ is said to be remain true only at the tree-level; it receives corrections from the loop diagrams. See here. ...
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