Symmetry Definition and 907 Threads

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.

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...

What is more fundamental and why, the postulated time symmetry of QM tie evolution or the time asymmetry of the CPT theorem?

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...

Homework Statement The Attempt at a Solution I would guess it is -b/2a but I have gotten this incorrect. Maybe I have to figure out what the parabola equation is and apply it into the axis of symmetry. Assuming that is correct how would I find that? Thanks[/B]

Hello, I want to understand how bracket operations in general are related to symmetry and infinitesimal transformations (in hindsight of quantumfieldtheory), so I calculated an example with a particle that is moving on a circle with a generic potential. (I used simple polar coordinates in two...

Homework Statement Figure 23.52 gives the magnitude of the electric field inside and outside a sphere with a positive charge distributed uniformly throughout its volume. The scale of the vertical axis is set by Es = 5.0 x 10e7 N/C. What is the charge on the sphere? Homework Equations Net Flux...

Hello, I am looking for resources on scale symmetry including the persons who are at the forefront, arxiv preprints, history of the development of the idea, and any other sources you can think of. Thank you.

A twisted cylindrial rod has the cross sectional symmetry so that it's not posible to tell whether it is twisted or not without knowing if there is any torsional energy. now drawing a line on the surface of it can tell us whether or not it's twisted. It might not be a straight line.. there are...

Homework Statement A beam (e.g. a steel liner) of a length L is bent between two supports, as shown in fig (a). According to the Euler column, the shape is a half period of a sine. Now, a force P is applied at the axis of symmetry - fig (b). What is the shape of the liner? y=f(x) Instead of the...

Hello ! In the book Quantum Field for mathematician, there is this Wick diagram as an example to understand how to compute the symmetry factor (I am sorry, I draw it with paint...) This is about a hermitian field interacting with a complex field. The book says it has a symmetry factor of 2...

The question is to determine which decays are possible for: i) ##P^0## ## ->\prod## ##^+## ## \prod## ##^-## ii)##P^0## ## ->\prod## ##^0## ## \prod## ##^0## where ##J^p = 0^-, 1^- ## respectively for ## \prod## ##^+##, ## \prod## ##^-## , ## \prod## ##^0## and ##P^0## respectively. For...

In case it's relevant, the context of my question is finding the allowed states of an atom. For example, given a nitrogen atom with (1s)2(2s)22p3, how do we find the possible states in terms of total orbital angular momentum L, total spin S, and total angular momentum J = L + S. It seems that...

Spontaneous symmetry breaking refers to the solution of a system loses some symmetry in its Lagrangian. Consider a Simple Harmonic Oscillator, its lagrangian is time translationally invariant but its solution is periodic in time, thus not time-translational invariant. Is this Spontaneous...

Homework Statement Find the conserved Noether current j^\mu of the Dirac Lagrangian L = \bar{\psi} ( i \partial_\mu \gamma^\mu - m ) \psi under the transformation: \psi \rightarrow e^{i \alpha} \psi \,\,\,\,\,\,\,\,\,\, \bar{\psi} \rightarrow e^{-i \alpha} \bar{\psi} Homework Equations...

Homework Statement Consider the lagrangian L=\delta_\mu \phi \delta^\mu \phi^* - m^2 \phi \phi^* Show that the transformation: \phi \rightarrow \phi + a \,\,\,\,\,\,\,\,\,\, \phi^* \rightarrow \phi^* + a^* is symmetry when m=0. The attempt at a solution Substituting the transformation...

Hello, I am learning Feynman diagrams and I still do not understad quite well the symmetry factor idea. The equation is: $$ \frac{1}{O(G)} = \frac{M}{n!(4!)^n} $$ I was trying the next example: If I am not wrong it is O(G) = 10 taking care of the asymmetry of each pair of internal lines...

Homework Statement Let S = { (x,y) in Z | 5x+7y is divisible by 3 } Show that S is symmetrical. Homework Equations None apart from basic algebraic knowledge. The Attempt at a Solution [/B] The only thing I can think of is starting with 3a = 5x+7y and putting x (or y) into the...

Suppose we have some function f(x) with period L. My book states that if it is even around the point x=L/4, it satisfies f(L/4-x)=-f(x-L/4), whilst if it is odd it satisfies f(L/4-x)=f(x-L/4). Then we define s=x-L/4 so we have for the function to be odd or even about L/4 that f(s)=±f(-s)...

Hi guys, have a very tricky question on my HW to find compact group of global symmetry to this Lagrangian of 2 complex scalar fields L={\partial_\mu \phi_1^*}{\partial_\mu \phi_1}+{\partial_\mu \phi_2^*}{\partial_\mu \phi_2}-\lambda(\phi_1^* \phi_1 - \phi_2^* \phi_2 - v^2)^2 and I can't figure...

Anyone can explain me what is the physical meaning of azimuthal symmetry? Based on the book, azimuthal symmetry means when m=0. However how can we determine that a system is azimuthal symmetry or not? Like for example, I have a two concentric spheres with radius a and b and hold at different...