All Questions
Tagged with quantum-field-theory symmetry
433
questions
101
votes
1
answer
10k
views
Classical and quantum anomalies
I have read about anomalies in different contexts and ways. I would like to read an explanation that unified all these statements or points of view:
Anomalies are due to the fact that quantum field ...
- 6,889
54
votes
2
answers
2k
views
Symmetries of the Standard Model: exact, anomalous, spontaneously broken
There are a number of possible symmetries in fundamental physics, such as:
Lorentz invariance (or actually, Poincaré invariance, which can itself be broken down into translation invariance and ...
- 810
46
votes
3
answers
9k
views
What role does "spontaneous symmetry breaking" play in the "Higgs Mechanism"?
In talking about Higgs mechanism, the first part is always some introduction to the concept of spontaneous symmetry breaking (SSB), some people saying that Higgs mechanism is the results of SSB of ...
- 6,095
37
votes
1
answer
4k
views
Emergent symmetries
As we know, spontaneous symmetry breaking(SSB) is a very important concept in physics. Loosely speaking, zero temprature SSB says that the Hamiltonian of a quantum system has some symmetry, but the ...
29
votes
5
answers
5k
views
Rigorous approaches to quantum field theory
I have been reading Quantum Mechanics: A Modern Development by L. Ballentine. I like the way everything is deduced starting from symmetry principles.
I was wondering if anyone familiar with the book ...
29
votes
3
answers
4k
views
What is the role of the vacuum expectation value in symmetry breaking and the generation of mass?
Consider a theory of one complex scalar field with the following Lagrangian.
$$
\mathcal{L}=\partial _\mu \phi ^*\partial ^\mu \phi +\mu ^2\phi ^*\phi -\frac{\lambda}{2}(\phi ^*\phi )^2.
$$
The ...
- 8,540
29
votes
1
answer
2k
views
Why do we assume local conformal transformations are symmetries in 2D CFT?
The global conformal group in 2D is $SL(2,\mathbb{C})$. It consists of the fractional linear transforms that map the Riemann sphere into itself bijectively and is finite dimensional.
However, when ...
- 2,667
29
votes
1
answer
475
views
Can a theory gain symmetries through quantum corrections?
It is well known that not all symmetries are preserved when quantising a theory, as evinced by renormalising composite operators or by other means, which show that quantum corrections may alter a ...
- 721
28
votes
2
answers
11k
views
Dirac spinors under Parity transformation or what do the Weyl spinors in a Dirac spinor really stand for?
My problem is understanding the transformation behaviour of a Dirac spinor (in the Weyl basis) under parity transformations. The standard textbook answer is
$$\Psi^P = \gamma_0 \Psi = \begin{...
- 10.1k
27
votes
2
answers
21k
views
How to count and 'see' the symmetry factor of Feynman diagrams?
Could somebody explain how one can derive the symmetry factor both by counting possible contractions and by looking at the symmetry of a diagram. Consider for example this diagram
in $\phi^4$-theory ...
- 1,274
27
votes
2
answers
6k
views
Why does the classical Noether charge become the quantum symmetry generator?
It is often said that the classical charge $Q$ becomes the quantum generator $X$ after quantization. Indeed this is certainly the case for simple examples of energy and momentum. But why should this ...
- 7,936
26
votes
2
answers
10k
views
Connection between conserved charge and the generator of a symmetry
I'm trying to understand the connection between Noether charges and symmetry generators a little better. In Schwartz QFT book, chapter 28.2, he states that the Noether charge $Q$ generates the ...
- 10.1k
26
votes
2
answers
3k
views
Why am I wrong about how to view gauge theory?
Edit: I know there have been some similar questions but I don't think any had quite articulated my particular confusion.
If gauge symmetries are really just redundancies in our description accounting ...
- 562
24
votes
3
answers
7k
views
Problem understanding the symmetry factor in a Feynman diagram
I am trying to understand a $1/2$ in the symmetry factor of the "cactus" diagram that appears in the bottom of page 92 In Peskin's book. This is the diagram in question (notice that we are ...
- 6,067
22
votes
4
answers
6k
views
QM and Renormalization (layman)
I was reading Michio Kaku's Beyond Einstein. In it, I think, he explains that when physicsts treat a particle as a geometric point they end up with infinity when calculating the strength of the ...
- 2,808