Tagged Questions
2
votes
1answer
62 views
Invariance, covariance and symmetry
Though often heard, often read, often felt being overused, I wonder what are the precise definitions of invariance and covariance. Could you please give me an example from quantum field theory? ...
2
votes
0answers
39 views
CP-symmetry and Ward identities and finite temperature
I have a few questions about Ward-identities which I summarize here. For each I am very greateful for answers and references to literature.
Wikipedia states about Ward-identities:
The ...
11
votes
1answer
426 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 ...
13
votes
1answer
211 views
Spontaneous breaking of Lorentz invariance in gauge theories
I was browsing through the hep-th arXiv and came across this article:
Spontaneous Lorentz Violation in Gauge Theories. A. P. Balachandran, S. Vaidya. arXiv:1302.3406 [hep-th]. (Submitted on 14 ...
4
votes
0answers
58 views
Dimensional transmutation in Gross-Neveu vs others
Firstly I don't know how generic is dimensional transmutation and if it has any general model independent definition.
Is dimensional transmutation in Gross-Neveau somehow fundamentally different ...
6
votes
1answer
128 views
Are group representations possible when the solution space is not a vector space?
As far as I understand, the motivation for using representation theory in high energy physics is as follows. Assume that a theory has some (internal or external) symmetry group which acts on a vector ...
15
votes
4answers
489 views
Elegant 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 ...
3
votes
1answer
189 views
Local and Global Symmetries
Could somebody point me in the direction of a mathematically rigorous definition local symmetries and global symmetries for a given (classical) field theory?
Heuristically I know that global ...
0
votes
2answers
184 views
Harmonic oscillator and Lorentz symmetry
There is a analog between harmonic oscillator $x=\frac{1}{\sqrt{2\omega}}(a+a^\dagger)$ and quantum field $\phi=\int dp^3\frac{1}{(2\pi)^3}\frac{1}{\sqrt{2\omega_p}}(a_p e^{ipx}+a^\dagger e^{-ipx})$, ...
2
votes
1answer
121 views
Relationship between local and global scaling (Weyl) symmetry
Theorem 5.1 on page 80 of this paper says that
Assuming that the matter fields satisfy their equations of motion, the matter field action is locally Weyl invariant if and only if the corresponding ...
4
votes
1answer
127 views
Why Must Conserved Currents of Lorentz Symmetry Satisfy the Lorentz Algebra
I've seen it written many times that the commutation relation
$[M^{I-},M^{J-}]=0$
is required for Lorentz invariance in the light cone gauge quantisation of the bosonic string. This follows ...
3
votes
2answers
300 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 ...
1
vote
0answers
102 views
Why does renormalization need an unbroken symmetry?
Common wisdom is that for a QFT to be renormalizable it must be invariant under a symmetry transformation. Why does renormalization need an unbroken symmetry? Which is the first publication that ...
3
votes
1answer
157 views
What happens to the Lagrangian of the Dirac theory under charge conjugation?
Consider a charge conjugation operator which acts on the Dirac field($\psi$) as
$$\psi_{C} \equiv \mathcal{C}\psi\mathcal{C}^{-1} = C\gamma_{0}^{T}\psi^{*}$$
Just as we can operate the parity operator ...
3
votes
1answer
253 views
Conservation Laws and Symmetries
Usually, in Quantum Mechanics, an observable is an operator on the space of the possible quantum states (labelled as $|\psi\rangle$). If this quantity is conserved, in the meaning that the associated ...
3
votes
3answers
261 views
What is the difference between manifest Lorentz invariance and canonical Lorentz invariance?
I often read that the Lorentz symmetry is manifest in the path integral formulation but is not in the canonical quantization - what does this really mean?
4
votes
3answers
373 views
Must all symmetries have consequences?
Must all symmetries have consequences?
We know that transnational invariance, for example, leads to momentum conservation, etc, cf. Noether's Theorem.
Is it possible for a theory or a model to have ...
12
votes
1answer
591 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 point-views:
Anomalies are due to the fact that quantum field ...
3
votes
2answers
404 views
What is the ontological status of Faddeev Popov ghosts?
We all know Faddeev-Popov ghosts are needed in manifestly Lorentz covariant nonabelian quantum gauge theories. We also all know they decouple from the rest of matter asymptotically, although they ...
4
votes
1answer
104 views
What kinds of inconsistencies would one get if one starts with Lorentz noninvariant Lagrangian of QFT?
What kinds of inconsistencies would one get if one starts with Lorentz noninvariant Lagrangian of QFT? The question is motivated by this preprint arXiv:1203.0609 by Murayama and Watanabe.
Also, what ...
2
votes
1answer
209 views
Spontaneous symmetry breaking and 't Hooft and Polyakov monopoles
What is spontaneous symmetry breaking from a classical point of view. Could you give some examples, using classical systems.I am studying about the 't Hooft and Polyakov magnetic monopoles solutions, ...
5
votes
1answer
166 views
Goldstone's theorem and massless modes for $\phi^4$ theory
Consider a scalar field doublet $(\phi_1, \phi_2)$ with a Mexican hat potential
$$V~=~\lambda (\phi_1^2+\phi_2^2-a^2)^2.$$
When $a=0$ this is a quartic potential and the symmetry is not ...
5
votes
2answers
185 views
If the S-matrix has symmetry group G, must the fields be representations of G?
If the fields in QFT are representations of the Poincare group (or generally speaking the symmetry group of interest), then I think it's a straight forward consequence that the matrix elements and ...
6
votes
4answers
295 views
What is meant by the phrase “the mass is protected by a symmetry”?
In a particle physics context I've heard this phrase used. I guess it means that the mass of a particle is less than you'd naively expect from $E=mc^2$ after computing the momentum uncertainty ...
10
votes
1answer
233 views
Time reversal symmetry and T^2 = -1
I'm a mathematician interested in abstract QFT. I'm trying to undersand why, under certain (all?) circumstances, we must have $T^2 = -1$ rather than $T^2 = +1$, where $T$ is the time reversal ...
6
votes
1answer
358 views
Time reversal symmetry and T^2 = -1
I'm a mathematician interested in abstract QFT. I'm trying to undersand why, under certain (all?) circumstances, we must have $T^2 = -1$ rather than $T^2 = +1$, where $T$ is the time reversal ...
10
votes
4answers
726 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 ...
4
votes
0answers
313 views
Gauge redundancies and global symmetries
It is often said that local (gauge) transformation is only redundancy of description of spin one massless particles, to make the number degrees of freedom from three to two. It is often said that ...
3
votes
2answers
551 views
The Energy-Momentum Tensor and the Ward Identity
I have a question regarding a homework problem for my quantum field theory assignment.
For the purposes of the question, we can just assume the Lagrangian is that of a real scalar field:
...
16
votes
2answers
88 views
Can symmetry generators be used for quantization?
Take the Poincaré group for example. The conservation of rest-mass $m_0$ is generated by the invariance with respect to $p^2 = -\partial_\mu\partial^\mu$. Now if one simply claims
The state where ...
8
votes
2answers
877 views
Poincare group vs Galilean group
One can define the Poincare group as the group of isometries of the Minkowski space. Is its Lie algebra given either by the equations 2.4.12 to 2.4.14 (..as also given in this page - ...
5
votes
2answers
646 views
What does “soft” in “soft symmetry breaking” mean?
For example it is stated that if supersymmetry breaking is soft then stability of gauge hierarchy can be still maintained.
14
votes
3answers
794 views
Why does dilation invariance often imply proper conformal invariance?
Why does a quantum field theory invariant under dilations almost always also have to be invariant under proper conformal transformations? To show your favorite dilatation invariant theory is also ...
6
votes
3answers
383 views
What sort of experiment would directly test time reversal invariance?
I guess the title says it all: how could/would you experimentally test whether our universe is truly time reversal invariant, without relying on the CPT theorem? What experiments have been proposed to ...
