The symmetry tag has no wiki summary.
3
votes
2answers
72 views
What symmetries does a lattice calculation need to preserve?
I've heard that it is impossible to have a properly Lorentz-invariant lattice QFT simulation, as the Lorentz invariance is spoiled by the nonzero lattice distance $a$. I've also heard that there are ...
13
votes
1answer
215 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
1answer
146 views
How do we make symmetry assumptions rigorous?
I have, for instance, a problem with a spherically symmetric charge distribution. I deduce here, in order to solve the problem easily, that the corresponding electric field must be symmetric. How is ...
4
votes
0answers
59 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 ...
0
votes
0answers
29 views
Residual symmetries of the superposition of two fcc lattices
Fcc lattices are Bravais lattices and so are invariant under a set of discrete translations plus inversions over the 3 axis ($x\rightarrow -x$,$y\rightarrow -y$,$z\rightarrow -z$). When one superposes ...
4
votes
1answer
375 views
Physical significance of Killing vector field along geodesic
Let us denote by $X^i=(1,\vec 0)$ the Killing vector field and by $u^i(s)$ a tangent vector field of a geodesic, where $s$ is some affine parameter.
What physical significance do the scalar quantity ...
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 ...
0
votes
2answers
59 views
Why does isotropy principle require existence of inertial transformation when axes are reversed?
Assuming one spatial and one termporal dimension, let's assume an intertial transformation $A(v)$ as follows:
$$
\begin{pmatrix}
t' \\
x' \\
\end{pmatrix} = A(v)
\begin{pmatrix}
t \\
x \\
...
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 ...
2
votes
0answers
43 views
How does a snowflake “know” to form symmetrically? [duplicate]
Possible Duplicate:
Why are snowflakes symmetrical?
Under ideal situations, a snowflake forms into near perfect hexagonal symmetry. How? For instance, when a water molecule moves towards ...
7
votes
1answer
306 views
Do an action and its Euler-Lagrange equations have the same symmetries?
Assume a certain action $S$ with certain symmetries, from which according to the Lagrangian formalism, the equations of motion (EOM) of the system are the corresponding Euler-Lagrange equations.
Can ...
15
votes
4answers
494 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 ...
9
votes
1answer
64 views
Global symmetry in string theory
It is often stated that in quantum gravity only charges coupled to gauge fields can be conserved. This is because of the no hair theorem. If a charge is coupled to a gauge field then when it falls ...
16
votes
1answer
211 views
Why does charge conservation due to gauge symmetry only hold on-shell?
While deriving Noether's theorem or the generator(and hence conserved current) for a continuous symmetry, we work modulo the assumption that the field equations hold. Considering the case of gauge ...
19
votes
1answer
67 views
Any use for $F_4$ in hep-th?
In high energy physics, the use of the classical Lie groups are common place, and in the Grand Unification the use of $E_{6,7,8}$ is also common place.
In string theory $G_2$ is sometimes utilized, ...
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 ...
2
votes
1answer
73 views
Killing Vectors of BTZ black hole and their calculation in general
I was wondering what are the Killing vectors of BTZ black hole and how to guess them easily? Will it be the same as of AdS? What then will be Killing vectors for AdS-Schwarzschild e.g.?
8
votes
3answers
843 views
What is the symmetry which is responsible for preservation of electrical charges?
Another Noether's theorem question, this time about electrical charge.
According to Noether's theorem, all conservation laws originate from invariance of a system to shifts in a certain space. For ...
3
votes
1answer
190 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 ...
16
votes
2answers
89 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
3answers
196 views
Symmetries of a Free Massless Scalar in Two Dimensions
On p. 49 of Polchinski's book, he says: "Incidentally, the free massless scalar in two dimensions has a remarkably large amount of symmetry -- much more than we will have occasion to mention."
Does ...
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
...
2
votes
1answer
58 views
Obtaining the conserved current of the Lagrangian making the parameter depending on $x$
To calculate the conserved current due to an internal symmetry of the system (expressed by the Lagrangian density) we can proceed as follows: if it is invariant under
$\delta \phi = \alpha \phi$, ...
2
votes
3answers
184 views
Are the principles of space-time homogeneity and Isotropy independent of one another?
Einstein in deriving the Lorentz transformations, used the principles of space-time homogeneity and Isotropy. Does space-time isotropy follow from space-time homogeneity or are they completely ...
7
votes
2answers
93 views
Group of symmetries of Lagrange's equations
Consider the following statements, for a classical system whose configuration space has dimension $d$:
Lagrange equations admit a smaller group of "symmetries" (coordinate change under which ...
3
votes
1answer
192 views
Which kinds of Physics laws do and don't comply with the principle of relativity?
In Physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference.
However, according to this and ...
7
votes
2answers
188 views
How to model a symmetry using Lie Groups?
I have been reading lately about Lie groups, and although all books keep listing the groups, and talk about Lie algebras and all that, one thing I still don't know how is it made, and I guess it's the ...
6
votes
3answers
133 views
From Manifold to Manifold?
Tensor equations are supposed to stay invariant in form wrt coordinate transformations where the metric is preserved. It is important to take note of the fact that invariance in form of the tensor ...
2
votes
0answers
96 views
Who used the concept of symmetries first?
Who "invented" the concept of symmetries? This article is quite extensive, but it blurs the history with the modern understanding.
http://plato.stanford.edu/entries/symmetry-breaking/
Some of the ...
2
votes
0answers
217 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 ...
1
vote
1answer
81 views
Proper times of two observers in a three-torus
Consider two observer in a tree-torus space of size $L$. Observer $A$ is at rest, while observer $B$ moves in the $x$-direction with constant velocity $v$. $A$ and $B$ began at the same event, and ...
11
votes
1answer
66 views
Are possible gauge fields in a Lagrangian theory always determined by the structure of the charged degrees of freedom?
An elementary example to explain what I mean. Consider introducing a classical point particle with a Lagrangian $L(\mathbf{q} ,\dot{\mathbf{q}}, t)$. The most general gauge transformation is $L ...
0
votes
2answers
186 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})$, ...
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 ...
7
votes
2answers
274 views
Conjugate Variables, Noether's Theorem and QM
What is the underlying reason that the same pairs of conjugate variables (e.g. energy & time, momentum & position) are related in Noether's theorem (e.g. time symmetry implies energy ...
3
votes
2answers
163 views
Relativistic Hamiltonian Formulations [duplicate]
Possible Duplicate:
Hamiltonian mechanics and special relativity?
The Hamiltonian formulation is beautifully symmetric. It's a shame that the explicit time derivatives in Hamilton's ...
5
votes
2answers
97 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
96 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
123 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
306 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
66 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
128 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
124 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
118 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
318 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
79 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
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 ...
3
votes
2answers
305 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
829 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, ...
