The symmetry tag has no wiki summary.
6
votes
3answers
261 views
Is hydrogen the same everywhere?
Silly thought. Feel free to shoot it down
Does a hydrogen atom undergo any kind of change subject to it's environment?
If one were to study a hydrogen atom on the surface of Mercury, another above ...
0
votes
0answers
104 views
Time reversal symmetry and reversal of vectors
Firstly: I have been told that under time reversal transformations, i.e. $t\rightarrow -t$, vector fields must change sign. Why is this? I haven't found this in the literature, any references?
...
1
vote
1answer
101 views
transformations with commutators and anticommutators that generate displacements
is well known that composition of point reflections generate pure displacements. This implies that the commutator of two point reflections will be a pure displacement. Are there similar elemental ...
1
vote
1answer
120 views
Searching the point group of symmetry
I am engaged in the field of quantum-chemical calculations using programs written by myself. I have found out that I have a problem in finding the point group symmetry of the molecule.
The first idea ...
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 ...
1
vote
1answer
100 views
Does turbulence violate Galilean relativity?
Fluid flows become turbulent beyond a certain velocity. The velocity is almost always with respect to a fixed boundary. However, an observer in a frame of reference travelling with the fluid will also ...
1
vote
1answer
237 views
Why are all observable gauge theories not vector-like?
Why are all observable gauge theories not vector-like?
Will this imply that the electron and/or fermions do not have mass?
How is this issue resolved?
Background:
The Standard Model is a ...
4
votes
1answer
105 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 ...
6
votes
1answer
105 views
Request for Reference: BRST formalism/transformations
Could anyone please suggest a very basic paper/reference/literature on BRST symmetry/formalism that requires rudimentary knowledge of Dirac's method for dealing with constrained systems and generation ...
0
votes
2answers
208 views
Scalar potential, vector potential, and spinor potnetial
In Particle Physics, I've seen Scalar potentials which look like this $$ V = a \Phi^2 + b \Phi^4$$
$\Phi$ is scalar (a number).
What about vector potentials, and spinor potentials? How are they ...
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, ...
2
votes
1answer
100 views
Lorentz invariance and the vacuum expectation value of fields with spin > 0
I had a question about Moduli space, which I was reading about here, but then I read this sentence:
"Lorentz invariance forces the vacuum expectation values of any higher
spin fields to ...
2
votes
1answer
159 views
What is the Lie algebra of the Galilean group and what is the structure of it?
I read Freeman Dyson's article Missed Opportunities, in which he talked about the mathematical attractiveness of the Lorenz group compared to the Galilean group. I am reading Florian Scheck's book on ...
7
votes
3answers
89 views
Rotationally invariant body and principal axis
Suppose a rigid body is invariant under a rotation around an axis $\mathsf{A}$ by a given angle $0 \leq \alpha_0 < 2\pi$ (and also every multiple of $\alpha_0$).
Is it true that in this case the ...
8
votes
1answer
1k views
Spontaneous Time Reversal Symmetry Breaking?
It is known that you can break P spontaneously--- look at any chiral molecule for an example. Spontaneous T breaking is harder for me to visualize. Is there a well known condensed matter system which ...
3
votes
1answer
177 views
Lepton Number Conservation
What is the global symmetry of the electroweak Lagrangian that gives rise to lepton number conservation?
As I understand it, electric charge is some linear combination of the conserved quantities ...
0
votes
1answer
245 views
Understanding units and the units of the derivative operator
Suppose that $f$ is a function from unit $A$ to $B$, then what is the unit of $f'(x)$?. We can do $f'(x)\Delta x$ to get an estimate of $f(x + \Delta x)$. Since the latter has unit $B$, so has the ...
1
vote
1answer
222 views
Why do humans have bilateral symmetry? [closed]
About the eyes I know that it requires for gauging distance as in Modern 3D cameras have two sensors. And two ears for sound source localization using differences in levels and timing (But not yet two ...
1
vote
1answer
246 views
Wigner-Eckart projection theorem
I'm following the proof of Wigner-Eckart projection theorem which states that:
$$\langle \bf{A} \rangle ~=~ \frac{\langle \bf{A} \cdot \bf{J} \rangle}{\langle {\bf{J}}^2 \rangle} \langle \bf{J} ...
3
votes
6answers
545 views
Time Reversal Invariance in Quantum Mechanics
I thought of a thought experiment that had me questioning how time reversal works in quantum mechanics and the implications. The idea is this ... you are going forward in time when you decide to ...
5
votes
1answer
166 views
Goldstone's theorem and massless modes for $\phi^4$ theory
Consider a scalar field doublet $(\phi_1, \phi_2)$ with a Mexican hat potential
$$V~=~\lambda (\phi_1^2+\phi_2^2-a^2)^2.$$
When $a=0$ this is a quartic potential and the symmetry is not ...
4
votes
1answer
203 views
U(1) Charged Fields
I don't quite understand what is actually meant by a field charged under a $U(1)$ symmetry.
Does it mean that when a transformation is applied the field transforms with an additional phase? More ...
2
votes
0answers
216 views
Influence of Joe Rosen work, is it marginal, or significantly accepted?
I have prepared a paper that relies on work of Joe Rosen on symmetry (e.g. "Symmetry Rules: How Science and Nature Are Founded on Symmetry"). I am wondering about his influence. For example, when I ...
17
votes
5answers
811 views
Is the converse of Noether's first theorem true: Every conservation law has a symmetry?
Noether's (first) theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law.
Is the converse true: Any conservation law of a physical ...
5
votes
2answers
186 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
297 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 ...
4
votes
1answer
153 views
What is replica symmetry breaking, and what is a good resource for learning it?
M. Mezard, G. Parisi and coworkers have written about replica symmetry and its breaking in spin glasses, structural glasses, and hard computational problems.
I am just getting acquainted with this ...
2
votes
1answer
219 views
Constructing the “most general” two-particle spin interaction with $SU(2)$ symmetry
Suppose I want to write down an interaction term for an action for spin 1/2 fermions that is $SU(2)$-symmetric.
I start from the most naive general form of such an action:
$$S_{int} ~=~ \int_{4321} ...
9
votes
2answers
275 views
When “unphysical” solutions are not actually unphysical
When solving problems in physics, one often finds, and ignores, "unphysical" solutions. For example, when solving for the velocity and time taken to fall a distance h (from rest) under earth gravity:
...
3
votes
2answers
351 views
Lorentz invariance of the 3 + 1 decomposition of spacetime
Why is allowed decompose the spacetime metric into a spatial part + temporal part like this for example
$$ds^2 ~=~ (-N^2 + N_aN^a)dt^2 + 2N_adtdx^a + q_{ab}dx^adx^b$$
($N$ is called lapse, $N_a$ is ...
1
vote
1answer
195 views
Conserved quantum observables from symmetries *with density matrix*
I’ve read Ballentine where he derives the conserved observable operators (momentum, energy, ...) from symmetries of space-time.
Can I read up such a derivation in more detail somewhere else or even ...
4
votes
2answers
333 views
Deriving Birkhoff's Theorem
I am trying to derive Birkhoff's theorem in GR as an exercise: a spherically symmetric gravitational field is static in the vacuum area. I managed to prove that $g_{00}$ is independent of t in the ...
2
votes
1answer
372 views
Weinberg's way of deriving Lie algebra related to a Lie group
I was reading the second chapter of the first volume of Weinberg's books on QFT. I am quite confused by the way he derives the Lie algebra of a connected Lie group.
He starts with a connected Lie ...
3
votes
3answers
269 views
The Asymmetry between Real and Imaginary in the three Pauli Spin Matrices
The Pauli spin matrices
$$
\sigma_1 ~=~ (\begin{smallmatrix} 0 & 1 \\ 1 & 0 \end{smallmatrix}),
\qquad\qquad
\sigma_2 ~=~ (\begin{smallmatrix} 0 & -i \\ i & 0 ...
5
votes
2answers
365 views
What's the importance of Noether's theorem in Physics
The Noether's theorem that I want to mention is the following: Noether's theorem.
I know the importance of Noether's contribution to modern algebra. Can anyone write about Noether's theorem in ...
2
votes
2answers
210 views
Correlation Functions, Symmetries and Measurements
Is there a book that goes deep into correlation functions? What I'm interested in a book/article that explains in the detail the relation of the correlation functions with symmetries and how one can ...
7
votes
1answer
75 views
Representation on Hilbert space of the product of two symmetry transformations
We know by Wigner's theorem that the representation of a symmetry transformation on the Hilbert space is either unitary and linear, or anti-unitary and anti-linear.
Let $T$ and $S$ be two symmetry ...
6
votes
2answers
376 views
Why are conformal transformations so prevalent in physics?
What is it about conformal transformations that make them so widely applicable in physics?
These preserve angles, in other words directions (locally), and I can understand that might be useful. Also, ...
2
votes
1answer
130 views
Similar masses and lifetimes of the $\Delta$ baryons
Why do the four spin 3/2 $\Delta$ baryons have nearly identical masses and lifetimes despite their very different $u$ and $d$ quark compositions?
3
votes
0answers
116 views
Symmetries of separable potential
For separable potential, say $x^4+y^4$, its symmetry are degenerate.
Is that a generic case to every separable potential? I will explain my question:
The potential $x^4+y^4$ has $A_1, B_1, A_2, B_2, ...
2
votes
1answer
173 views
How to perform a scale (invariance) transformation?
According to this wikipedia article in the $\phi^4$ section, the equation
$$\frac{1}{c^2}\frac{∂^2}{∂t^2}\phi(x,t)-\sum_i\frac{∂^2}{∂x_i^2}\phi(x,t)+g\ \phi(x,t)^3=0,$$
in 4 dimensions is invariant ...
7
votes
1answer
255 views
Relativistic center of mass
Recently I realized the concept of center of mass makes sense in special relativity. Maybe it's explained in the textbooks, but I missed it. However, there's a puzzle regarding the zero mass case
...
10
votes
1answer
237 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 ...
4
votes
2answers
254 views
Is there a 1-1 correspondence between symmetry and group theory?
The professor in my class of mathematical physics introduces the definition of groups and said that group theory is the mathematics of symmetry.
He gave also some examples of groups such as the set ...
2
votes
2answers
158 views
What are the limitations of the FLRW metric?
I was wondering, given how in any other area of life making an explosion spherically symmetric is more or less impossible is there any reason to expect that the universe is? I appreciate that the FLRW ...
6
votes
1answer
360 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
727 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 ...
7
votes
2answers
322 views
Groups acting on physics - a clarification on electrons and spin
My first question is fairly basic, but I would like to clarify my understanding. The second question is to turn this into something worth answering.
Consider a relativistic electron, described by a ...
2
votes
2answers
205 views
Which symmetry is associated with conservation of flux?
Which symmetry is associated with conservation of flux (e.g., in electromagnetism)?
For example, when working with Gauss's law in electromagnetism, net flux through an arbitrary volume element ...
8
votes
2answers
76 views
More general invariance of the action functional
I will formulate my question in the classical case, where things are simplest.
Usually when one discusses a continuous symmetry of a theory, one means a one-parameter group of diffeomorphisms of the ...
