The symmetry tag has no wiki summary.
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 ...
2
votes
2answers
142 views
Does a constant factor matter in the definition of the Noether current?
This is a very basic Lagrangian Field Theory question, it is about a definition convention. It takes much more time to typeset it than answering, but here it is:
Consider a field Lagrangian with only ...
6
votes
1answer
225 views
Coulomb gauge fixing and “normalizability”
The Setup
Let Greek indices be summed over $0,1,\dots, d$ and Latin indices over $1,2,\dots, d$. Consider a vector potential $A_\mu$ on $\mathbb R^{d,1}$ defined to gauge transform as
$$
A_\mu\to ...
4
votes
1answer
430 views
Physical significance of Killing vector field along geodesic
Let us denote by $X^i=(1,\vec 0)$ the Killing vector field and by $u^i(s)$ a tangent vector field of a geodesic, where $s$ is some affine parameter.
What physical significance do the scalar quantity ...
2
votes
0answers
43 views
How does a snowflake “know” to form symmetrically? [duplicate]
Possible Duplicate:
Why are snowflakes symmetrical?
Under ideal situations, a snowflake forms into near perfect hexagonal symmetry. How? For instance, when a water molecule moves towards ...
0
votes
2answers
61 views
Why does isotropy principle require existence of inertial transformation when axes are reversed?
Assuming one spatial and one termporal dimension, let's assume an intertial transformation $A(v)$ as follows:
$$
\begin{pmatrix}
t' \\
x' \\
\end{pmatrix} = A(v)
\begin{pmatrix}
t \\
x \\
...
7
votes
1answer
319 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
512 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 ...
2
votes
1answer
85 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.?
3
votes
1answer
205 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 ...
8
votes
3answers
200 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 ...
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
$\delta \phi = \alpha \phi$, ...
8
votes
1answer
131 views
Why do we classify states under covering groups instead of the group itself?
Why do we always classify states under covering group representations instead of the group itself? For example see the following picture I lifted from 'Symmetry in physics' by Gross
So in the first ...
3
votes
1answer
197 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
200 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 ...
2
votes
3answers
199 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 ...
2
votes
0answers
100 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 ...
1
vote
1answer
85 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 ...
0
votes
2answers
187 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 $\phi=\int dp^3\frac{1}{(2\pi)^3}\frac{1}{\sqrt{2\omega_p}}(a_p e^{ipx}+a^\dagger e^{-ipx})$, ...
7
votes
2answers
300 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
169 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
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.
...
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
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 ...
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
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, ...
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 ...
3
votes
2answers
330 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 ...
2
votes
3answers
457 views
Does high entropy means low symmetry?
According to Bogolubov postulate (various texts name it differently) in Non-equilibrium thermodynamics, the number of needed parameters to describe our system is decreasing with time, and finally at ...
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 $H_0$:
$$E_0 = ...
1
vote
0answers
105 views
Why does renormalization need an unbroken symmetry?
Common wisdom is that for a QFT to be renormalizable it must be invariant under a symmetry transformation. Why does renormalization need an unbroken symmetry? Which is the first publication that ...
1
vote
1answer
50 views
Testing covariance of an expression?
This is something I've been unsure of for a while but still don't quite get.
How does one tell whether an expression (e.g. the Dirac equation) is covariant or not? I get it for a single tensor, but ...
1
vote
1answer
131 views
Symmetries of spacetime and objects over it
I guess according to mathematical didactic, we first think of spacetime as a set and we reason about elements of its topology and then it's furthermore equipped with a metric. Appearently it is this ...
3
votes
1answer
166 views
What happens to the Lagrangian of the Dirac theory under charge conjugation?
Consider a charge conjugation operator which acts on the Dirac field($\psi$) as
$$\psi_{C} \equiv \mathcal{C}\psi\mathcal{C}^{-1} = C\gamma_{0}^{T}\psi^{*}$$
Just as we can operate the parity operator ...
4
votes
2answers
314 views
How to apply Noether's theorem
Say I have a point transformation:
$$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 ...
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
64 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 ...
2
votes
3answers
1k views
What are the applications of Gauss's law in technology? [closed]
Freshmen physics textbooks use Gauss's law plus symmetry to calculate the electric field.
I was wondering if this method of finding the electric field using a symmetry is used in real applications in ...
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, ...
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 ...
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
276 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 ...
8
votes
2answers
448 views
Deriving the action and the Lagrangian for a free point particle in Special Relativity
My question relates to
Landau & Lifshitz, Classical Theory of Field, Chapter 2: Relativistic Mechanics, Paragraph 8: The principle of least action.
As stated there, to determine the action ...
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
0answers
153 views
Symmetrizing the Canonical Energy-Momentum Tensor
The Canonical energy momentum tensor is given by
$$T_{\mu\nu} = \frac{\delta {\cal L}}{\delta (\partial^\mu \phi_s)} \partial_\nu \phi_s - g_{\mu\nu} {\cal L} $$
A priori, there is no reason to ...
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 ...
