The symmetry tag has no wiki summary.
5
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2answers
103 views
What maintains quark spin alignments in baryons?
What maintains quark spin alignments in baryons?
The $uud$ proton and $udd$ neutron are both spin 1/2, implying that two of their spin 1/2 quarks are always parallel and the other is always opposed.
...
4
votes
1answer
99 views
Why is it desirable to have a symmetry to make cosmological constant zero?
It is sometimes stated that absence of a symmetry to make cosmological constant zero is a problem. But observed value of dark energy is very small and non-zero. So why is it desirable to have a ...
2
votes
1answer
126 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
2answers
316 views
How to apply Noether's theorem
Say I have a point transformation:
$$x' ~=~ (1 +\epsilon)x,$$
$$t' ~=~ (1 +\epsilon)^2t,$$
and Lagrangian
$$ L ~=~ \frac{1}{2}m\dot{x}^2 - \frac{\alpha}{x^2}.$$
How do I go out about showing ...
13
votes
6answers
2k views
Can Noether's theorem be understood intuitively?
Noether's theorem is one of those surprisingly clear results of mathematical calculations, for which I am inclined to think that some kind of intuitive understanding should or must be possible. ...
0
votes
1answer
68 views
Poynting vector and Rindler flux under time inversion
This question is about some reply by John Baez on sci.physics.research
the post is this: https://groups.google.com/d/msg/sci.physics.research/F6x5GkFt0ic/fxsfuNl9d8gJ
the article he is talking about ...
4
votes
1answer
130 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
131 views
CPT Violation and Symmetry / Conservation Laws
Ok, so I remember reading that every conservation law has a corresponding symmetry (i.e. conservation of momentum is translational symmetry, conservation of angular momentum is rotational symmetry).
...
3
votes
1answer
124 views
Question on Section 9.1.3 in “Conformal Field Theory” by Philippe Di Francesco et. al
Question on Section 9.1.3 in "Conformal Field Theory" by Philippe Di Francesco et. al.
The basic idea of the Coulomb-gas formalism is to place a background charge in the system, making the $U(1)$ ...
1
vote
1answer
331 views
Schrödinger function: Separable wave function with even potential function of x
I have done the Problem 2.1 in Griffiths' quantum mechanics,
and it seems not making sense to me.
What if the wave function isn't symmetric at all?
Then obviously the proof doesn't work. The ...
1
vote
0answers
80 views
Division algebras $(\mathbb{R,C,H,O})$ and discrete symmetry [closed]
I once saw a statement about the relation between division algebra(which means you can define a division in this algebra, there is a theorem saying we only have 4 kinds of division algebra, real R, ...
6
votes
3answers
263 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 ...
3
votes
2answers
331 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 ...
14
votes
2answers
846 views
Is this Landau's other critical phenomena mistake?
There was an old argument by Landau that while the liquid gas transition can have a critical point, the solid-liquid transition cannot. This argument says that the solid breaks translational symmetry, ...
1
vote
1answer
131 views
Symmetries of spacetime and objects over it
I guess according to mathematical didactic, we first think of spacetime as a set and we reason about elements of its topology and then it's furthermore equipped with a metric. Appearently it is this ...
1
vote
1answer
160 views
Symmetry and overlapping of ground states
In a quantum mechanics, there is the following formula to derive the zero energy $E_0$ of a perturbed Hamiltonian $$H = H_0 + V$$ knowing the zero energy $W_0$ of the free Hamiltonian $H_0$:
$$E_0 = ...
1
vote
0answers
105 views
Why does renormalization need an unbroken symmetry?
Common wisdom is that for a QFT to be renormalizable it must be invariant under a symmetry transformation. Why does renormalization need an unbroken symmetry? Which is the first publication that ...
1
vote
1answer
50 views
Testing covariance of an expression?
This is something I've been unsure of for a while but still don't quite get.
How does one tell whether an expression (e.g. the Dirac equation) is covariant or not? I get it for a single tensor, but ...
12
votes
4answers
2k views
Why are snowflakes symmetrical?
The title says it all. Why are snowflakes symmetrical in shape and not a mush of ice?
Is it a property of water freezing or what? Does anyone care to explain it to me? I'm intrigued by this and ...
3
votes
1answer
166 views
What happens to the Lagrangian of the Dirac theory under charge conjugation?
Consider a charge conjugation operator which acts on the Dirac field($\psi$) as
$$\psi_{C} \equiv \mathcal{C}\psi\mathcal{C}^{-1} = C\gamma_{0}^{T}\psi^{*}$$
Just as we can operate the parity operator ...
0
votes
0answers
48 views
Dilatations in non-relativistic QM and operator tranformation
I was looking at a QM textbook exercise dealing with dilatations, the transformations are $x \rightarrow x' = \lambda x$ transforming $|\psi\rangle$ into $|\psi'\rangle = ...
2
votes
1answer
65 views
How to deal with crossing duality and modular invariance in string field theory?
An answer I gave elsewhere.
Some cases to ponder over.
A closed string splits into two closed strings, which then merge again into a single closed string. The overall string worldsheet has ...
4
votes
1answer
70 views
How can we have massive states of strings and CFT on the string worldsheet at the same time?
Ok, so we can have conformal invariance on a string world sheet. However, it is well known that to preserve conformal symmetry we require states to be massless. So how is it that string theories ...
2
votes
2answers
218 views
Scale invariance symmetry as a simple argument in an electrostatics problem
In the comments to this post, it was hinted that proving that the force acting on a charge at a vertical distance from a uniformly charged plane is independent of that distance can be done by ...
2
votes
2answers
206 views
Invariance of Maxwell's Equations under inverting variables - Reference and use
Some months ago, an ArXiv paper mentioned in passing that Maxwell's Equations were invariant under reciprocating the variables, or at least this results in a dual set of Maxwell Equations. (Actually I ...
1
vote
1answer
144 views
Symmetry and Conservation
According to Noether's theorem, "Every conservation law corresponds to an underlying symetry or vice-versa" . For example, conservation of linear momentum corresponds to translational symmetry, ...
1
vote
0answers
111 views
Breaking of conformal symmetry
I am wondering something about the breaking of conformal symmetry: I know that it can be broken at the quantum level, anomalously, but I never encountered or heard about a model where it is broken "à ...
3
votes
1answer
331 views
Even and Odd States of a 1D finite potential well
Is it possible for a particle trapped in a 1D finite potential well to evolve from a even state to an odd state and vice-versa? Why?
3
votes
1answer
280 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
277 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 ...
3
votes
3answers
280 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?
1
vote
1answer
80 views
Excitations implied by symmetries
I read that in condensed matter field theory a symmetry implies not only a conserved current (through the well-known Noether theorem) but some kind of "low energy excitation". I am familiar with the ...
5
votes
3answers
190 views
Representation of phase in quantum mechanics
[Note: My discussion of the three answers can be found just after the question.]
Imagine three points in space that differ only by a phase angle of "something" (what doesn't really matter).
One way ...
1
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2answers
377 views
Lorentz Invariance of Maxwell Equations
I am curious to see a simple demonstration of how special relativity leads to Lorentz Invariance of the Maxwell Equations. Differential form will suffice.
0
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0answers
54 views
Working principle of symmetry operations of a system with given physical situations
In the book I read some explanations about symmetry of a system.
We can make an experiment using lambda particle, A^. A^ can disintegrate into one proton and one pion - A^ and proton have same spin ...
1
vote
2answers
232 views
Symmetries, Generators, Commutators and Observables
I'm learning about generators and conservation laws and have derived the equation (1)
$$[Q,A]=-i\hbar f(A)$$
which is satisfied by the observable generator $Q$ for a transformation group with ...
1
vote
1answer
243 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 ...
1
vote
1answer
95 views
Cyclic co-ordinates implying the constant velocity motion of center of mass of a system of particles
I'm reading the section on Central Force in my textbook (Goldstein's Classical Mechanics has a similar argument in the chapter titled "The Central Force Problem", first section), where we have the ...
0
votes
0answers
108 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?
...
6
votes
1answer
367 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
1answer
245 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 ...
1
vote
1answer
122 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 ...
1
vote
1answer
103 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 ...
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 ...
1
vote
1answer
102 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 ...
3
votes
1answer
192 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 ...
6
votes
1answer
107 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
209 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
214 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, ...
14
votes
3answers
812 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 ...
