Homework Statement
Consider an arbitrary rigid body with an axis of rotational symmetry, which we'll call ## \hat z ##
a.) Prove that the axis of symmetry is a principal axis. (b) Prove that any two directions ##\hat x## and ##\hat y ## perpendicular to ##\hat z ## and each other are also...
I understand there are quite a few GUT candidates. I also understand that among these candidates some are considered by the theoretical physics community to be more likely to be correct than others.
I am curious about what each of the various GUT candidates predicts as the time (relative to...
If I have a periodic wave x(t) with half-wave symmetry, it means that:
x(t + T0/2) = -x(t)
where T0 is the period of the wave. Would this automatically lead to the conclusion that
X(t + T0/2) = -X(t)
where X'(t) = x(t), i.e X(t) is the integral of x(t).
?
The source I'm using is:
http://inperc.com/wiki/index.php?title=Homology_classes
And they say
Symmetry: A∼B⇒B∼A . If path q connects A to B then p connects B to A ; just pick p(t)=q(1−t),∀t .
Transitivity: A∼B , B∼C⇒A∼C . If path q connects A to B and path p connects B to C then...
Homework Statement
Show that if a transformation ##\Phi \rightarrow \Phi + \alpha \partial \Phi/ \partial \alpha## is not a symmetry of the Lagrangian, then the Noether current is no longer conserved, but rather ##\partial_{\mu}J^{\mu} = \partial L/ \partial \alpha##. Use this result to show...
Can there be interactions that are symmetric under low temperatures but exhibit spontaneous symmetry breaking under extremely low temperatures? (Maybe that symmetry breaking temperature is so low that it couldn't be discovered in experiments)
Does electromagnetism split into electricity and...
As I understand it a Green's function ##G(x,y)## for a translationally invariant differential equation satisfies $$G(x+a,y+a)=G(x,y)\qquad\Rightarrow\qquad G(x,y)=G(x-y)$$ (where ##a## is an arbitrary constant shift.)
My question is, given such a translationally invariant system, how does one...
The Hamiltonian is not always equal to the total energy. In fact the Hamiltonian for a system of particles could be defined as
##H=L-\sum \dot{q_i}\frac{\partial L}{\partial \dot{q_i}}##
Which is the total energy only if the potential energy is a function of ##q_i## and if the kinetic energy...
Hi folks,
I know nothing about groups or symmetry. Could anyone recommend a good introduction that defines groups and explains their notation and operations? I am particularly interested in general, orthogonal, and unitary groups.
Thanks in advance. Kevin
There are problems in classical electromagnetism where they ask you to find the electrical displacement given some geometry (like a sphere or a cylinder) and the dielectric constant ##\epsilon_r##.
The solution to these problems typically employs symmetry arguments along with Gauss' laws for...
Hi guys,
i have been confused by one statement on the spatial correlation funciton in the statistical physics textbook. They say for a spatial correlation function f(x1,x2), where x1 and x2 are the coordinate of particle 1 and 2, if the system has translational symmetry, then f depends only...
I completely have no idea what time-reversal mean.
Why does, by substituting -t into an equation and if the result is the same as the original equation, then the equation is said to be time-reversal symmetry?
Also, what does that 'symmetry' mean there? An even function?
SO(3) is subgroup of Poicare group.Does Relativistic Quantum Mechanics obey rotational symmetry.If it is,why we do not still keep the non-relativistic concept of angular momentum(orbit angular momentum plus spin) for relativistic concept of angular momentum,but we instead replace the concept by...
Homework Statement
Given L (q, dq/dt, t).
translation: q ---> q + e (e is infinitesimal constant)
show that if ∂L/∂q = 0, then L is symmetry under the above translation.
then find conserved quantity.
Homework Equations
S = ∫ L dt
The Attempt at a Solution
My attempt is nothing... because I...
Thinking aloud.
Most descriptions of chiral symmetry breaking nowadays present it as something happening in QCD. But it was defined well before of the quark theory, and then it was something related to isospin symmetry.
It is a bit puzzling because it seems as if pion mass were originated...
Hi,
I am learning classical mechanics right now, Particularly Noether's theorem. What I understood was that those kinds of transformations under which the the Hamiltonian framework remains unchanged, were the key to finding constants of motion.
But here are my Questions:
1. What is...
First by "this derivation" I'm referring to an online tutorial: http://farside.ph.utexas.edu/teaching/336L/Fluidhtml/node9.html
It's said in the above tutorial that the ##i-th## component of the total torque acting on a fluid element is
##\tau_i = \int_V \epsilon_{ijk} \cdot x_{j} \cdot F_{k}...
Hi,
I am running a finite element on a cylinder with that converges at the bottom for a opening, which is symmetrical in both directions so i modeled one quarter but the problem is my stresses are the same with when i compare with a full model that i also done but the deflections are different...
Homework Statement
determine whether the graph of the function has symmetry about the x-axis, the y-axis or the origin. Check work by graphing:
x^(2/3) + y^(2/3) = 1
Homework EquationsThe Attempt at a Solution
[ x^(2/3) + y^(2/3) = 1 ] ^(3/2)
y = -x+1
Its a straight line with y-intercept at...
Hi everyone,
my name is Vincenzo, i come from puglia in Italy and I'm studying physics at th university La Sapienza in rome.
I'm writing a dissertation about the discovery of the violation of CP symmetry in the neutral K mesons system.
I 'd love to discuss about these themes, and i hope i'll...
There are very results published about PT symmetry breaking in optical systems, with effects like anysotropical transmission resonance in waveguides.
But if PT symmetry is broken in a optical system and CPT symmetry must always be respected, then what C symmetry is broken in a optical system?
A friend of mine heard a popular science show on the radio. A caller asked what is better to wear on a hot day, white clothes or black clothes. The answer given was that it did not matter because although black absorbs more readily it also radiates it more readily. My friend said of course that...
As we know topological phases cannot be explained using spontaneous symmetry breaking and order parameter. But can they coexist? Suppose there is a system which is undergoing quantum phase transition to a anti-ferromagnetic phase from a disordered phase. So in the anti-ferromagnetic phase...
By fixing a gauge (thus breaking orspending the gauge symmetry), the model becomes something easier to analyse mathematically, such as a system of partial differential equations (in classical gauge theories) or a perturbative quantum field theory (in quantum gauge theories), though the...
Hello,
I have a problem in the search for symmetries in pde.
I would use Mathematica(c), does anyone know how to set up the code to obtain generators and then symmetries?
Thanks for all.
Homework Statement
Why does the symmetry ##\phi\rightarrow-\phi## mean that an amplitude can be written as
##\alpha + \beta p^2 + \gamma p^4 + ...##
without the odd terms in ##p##?
Homework Equations
I understand that, due to this symmetry, any diagram in ##\phi^4## has an even number of...
Homework Statement
Show Γ(ρ0→π0γ) = Γ(ρ+→π+γ)
Using G- and isospin symmetries, without exact calculating the matrix elements using additive quark model.
Homework Equations
L = jμAμ
G = CR1802
Mif ≅ <π|jμ|ρ>eμ
jμ=2/3 * (anti u)γμu - 1/3 * (andi d)γμd)
The Attempt at a Solution
Mif ≅...
There are two separate clocks, each set in a plane and on the ground. Assuming inertial reference frames, how can this be?
Perspective of the observer in motion:
The observer in motion on the plane will have recorded some time duration. Since the the world outside the plane is moving at a...
For details and to try to explain the above, the complex scalar field is a useful example. The complex scalar field has an action
S=∫d4x(∂μϕ∗)(∂μϕ)−V(|ϕ|).
There is a global, continuous symmetry to this action -- an overall phase. That is, if one replaces ϕ→eiαϕ, then the action does not change...
I would like to ask about the case of:
##SU(2)\otimes U(1) \rightarrow U(1)\otimes U(1),## spontaneous symmetry breaking.
It is given that the Wilson Loop:
##W \equiv exp[ig \oint dy H T^1]= diag(−1,−1,1).##
Where ##y## is the ##S^1/Z^2## fifth/extra dimension, ##H = \frac{1}{g R}## and...
Homework Statement
Assume that a ball of charged particles has a uniformly distributed negative charge density except for a narrow radial tunnel through its center, from the surface on one side to the surface on the opposite side. Also assume that we can position a proton anywhere along the...
Hi All,
Recently, in my earlier thread, I asked about the symmetry of Lorentz Factor (where +V == -V). I had several pointers about how to handle this (Thank you all those). However, it seemed unanimous that there was no explanation beyond the equation itself (math or physical).
Also, I...
Dear PF Forum,
Sorry if I ask (again) about twin paradox, after so many question about this topic here.
Supposed T is a star 100 ly from earth.
If B travels to T from earth
A. Is the symmetry broken?
B. If B watches A's clock at Earth and A watches B's clock at T, do they see the other clock...
The standard spatially flat FRW metric in Cartesian co-moving co-ordinates is given by:
$$ds^2=dt^2-a(t)^2(dx^2+dy^2+dz^2)$$
As far as I understand it the fact that the metric can be written in a form that is independent of ##x,y,z## implies that the Universe has the physical qualities of being...
I would like to prove the following:
Suppose we have the diagonal matrix ##P = diag(1,\ldots,1, -1,\ldots, 1)##, with ##N_+## elements of ##1## and ##N_-## elements of ##-1## such as ##N_+ + N_- = N## and ##N_+, N_- \geq 1##.
This matrix is a non trivial parity matrix since it is not...
Is the expection value of expession in left hand side of motion equation of field(example: Klein-Gordon,Dirac...equations) equal zero or not?(left hand side of the equation equals zero when we put condition of mimimizing the action).If not,why we can say when expectation value of divergence of...
Homework Statement
Let Aijkl be a rank 4 square tensor with the following symmetries:
A_{ijkl} = -A_{jikl}, \qquad A_{ijkl} = - A_{ijlk}, \qquad A_{ijkl} + A_{iklj} + A_{iljk} = 0,
Prove that
A_{ijkl} = A_{klij}
Homework EquationsThe Attempt at a Solution
From the first two properties...
This is sort of a nebulous question, but I'm wondering if anyone knows of analysis of the EPR experiment from the point of view of crossing symmetry for Feynman diagrams?
In the above diagram, I've drawn a very simple particle interaction diagram. The same diagram can be interpreted in two...
Can someone confirm or refute my thinking regarding the diagonalizability of an orthogonal matrix and whether it's symmetrical?
A = [b1, b2, ..., bn] | H = Span {b1, b2, ..., bn}. Based on the definition of the span, we can conclude that all of vectors within A are linearly independent...
In peskin p. 192, they says that the denominator (that is equation 6.43) is symmetric under x<--> y. Thay all so say that you can see it in equation 6.44.
But one of the terms in the denominetor is y*q which dose not have that symmetry!
Looking at (6.43) and removing the summetric parts leave...
I stumbled upon this article: http://www.comsol.com/blogs/exploiting-symmetry-simplify-magnetic-field-modeling/
Since the article does not contain any mathematical formulations, I was wondering how the boundary conditions can be expressed in terms of magnetic vector potential.
From what I...
When can I do the following where ##h_{i}## is a function of ##(x_{1},...,x_{n})##?
\frac{\partial}{\partial x_{k}}\frac{\partial f(h_{1},...,h_{n})}{\partial h_{m}}\overset{?}{=}\frac{\partial}{\partial h_{m}}\frac{\partial f(h_{1},...,h_{n})}{\partial x_{m}}\overset{\underbrace{chain\...
Homework Statement
Consider the set of operations in the plane that includes rotations by an angle about the origin and reflections about an axis through the origin. Find a matrix representation in terms of 2x2 matrices of the group of transformations (rotations plus reflections) that leaves...
Refering to this paper "Theoretical Aspects of Massive Gravity" (http://arxiv.org/abs/1105.3735) about the spin-2 boson field and GR.
The author uses the Fierz-Pauli action ( I quote the massless part)
##-\frac{1}{2}\partial_\lambda h_{\mu\nu}\partial^\lambda h^{\mu\nu} + \partial_\mu...
Homework Statement
Consider the specific case of a point above the axis of a circular ring of charge, how do the calculations follow to cancel the radial components? I understand the concept of the symmetry but don't understand how to express it in the expression without just removing the term...
I have some questions or thoughts about EW symmetry breaking.
(1) Higgs mechanism gives mass to SM particles after the background higgs field rolls from ##h=0## to ##h=v## and symmetry is broken. We are talking about pole mass, aren't we? So pole mass changes continuously from ##0## to ##m##...
Hey
I have a tight binding Hamiltonian of a BCC lattice which is a 4x4 matrix in k space (the 4 elements correspond to 4 atoms that are in a unit cell)
I want to expand it for small k's around the symmetry points P or Gamma or H.
I'm looking at a paper by J. L. Ma˜nes, PHYSICAL REVIEW B 85...
Hi all,
Without first delving too deeply into the literature I wanted to ask if its is only permissible for FCC structures to have a coordination number of 12. In the case of lattice vacancies and/or distortion: wherein the atomic sites are slightly displaced; is there a kind of tolerence for...