We say that something is symmetric if there is some transformation we can perform on that object that leaves some property unchanged. The set of symmetry transformations of an object form a group, and the name of this group is used as the name of the symmetry of the object.

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419 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 ...
9
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1answer
104 views

Confusion about two definitions of anomalies

As I am currently studying for an exam about quantum field theory and string theory, I got confused about the notion of "anomalies" and how they are actually defined. Similar questions have already ...
9
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1answer
382 views

Why does a transformation to a rotating reference frame NOT break temporal scale invariance?

Naively, I thought that transforming a scale invariant equation (such as the Navier-Stokes equations for example) to a rotating reference frame (for example the rotating earth) would break the ...
9
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1answer
277 views

Invariance of Functional Integration Measure

Let us consider the functional integral: \begin{equation} \int \mathcal{D} A e^{iS[A]} \end{equation} where $S[A]$ is the action for $U(1)$ gauge field and \begin{equation} \mathcal{D}A\equiv ...
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3answers
255 views

What are particle multiplets in the Standard Model?

The particles of the standard model are often displayed in groupings known as multiplets. I know that this somehow relates to the underlying symmetries of the standard model, which can be viewed as ...
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2answers
1k views

What does “soft” in “soft symmetry breaking” mean?

For example it is stated that if supersymmetry breaking is soft then stability of gauge hierarchy can be still maintained.
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89 views

When do phase space functions' Poisson brackets inherit the Lie algebra structure of a symmetry?

I've seen several examples of phase space functions whose Poisson brackets (or Dirac brackets) have the same algebra as the Lie algebra of some symmetry. For example, for plain old particle motion in ...
8
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1answer
426 views

Is Conformal Symmetry Local or Global?

I'm just brushing up on a bit of CFT, and I'm trying to understand whether conformal symmetry is local or global in the physics sense. Obviously when the metric is viewed as dynamical then the ...
8
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1answer
194 views

Boundary currents for Asymptotic Symmetry Group (ASG)

In the context of asymptotic symmetry groups, what is a boundary current? Why is it called a "current"? Context: I'm reading Strominger's recent paper on Asymptotic symmetry group of Yang-Mills ...
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3answers
601 views

What is kappa symmetry?

On page 180 David McMohan explains that to obtain a (spacetime) supersymmetric action for a GS superstring one has to add to the bosonic part $$ S_B = -\frac{1}{2\pi}\int d^2 \sigma ...
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2answers
724 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 ...
8
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2answers
183 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 ...
8
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1answer
219 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 ...
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1answer
446 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 ...
8
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1answer
189 views

How does the electron electric dipole moment (EDM) depend on supersymmetry?

I have read a recent paper that says that limit on the EDM of the electron has now been measured to 12 times better accuracy. According to that paper, as I understood, there should be a difference in ...
8
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3answers
183 views

Seeking a quality plain-language description of the Wigner-Eckart theorem

I'm a third year physics undergrad with a very cursory knowledge of quantum mechanics and the formalism involved. For instance, I understand roughly how tensors work and what it means for a tensor to ...
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2answers
2k views

Galilean invariance of the Schrodinger equation

I am only asking this question so that I can write an answer myself with the content found here: http://en.wikipedia.org/wiki/User:Likebox/Schrodinger#Galilean_invariance and here: ...
7
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2answers
784 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 ...
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3answers
524 views

Noether theorem with semigroup of symmetry instead of group

Suppose You have semigroup instead of typical group construction in Noether theorem. Is this interesting? In fact there is no time-reversal symmetry in the nature, right? At least not in the same ...
7
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3answers
454 views

What sort of experiment would directly test time reversal invariance?

I guess the title says it all: how could/would you experimentally test whether our universe is truly time reversal invariant, without relying on the CPT theorem? What experiments have been proposed to ...
7
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2answers
226 views

Particles mass determined by SO(D-2) vs SO(D-1)

I've recently come across this statement that massless particles arise from $SO(D-2)$ symetry and massive particles from $SO(D-1)$. I would have guessed that it would be the exact opposite way, but ...
7
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2answers
517 views

How can one see that the Hydrogen atom has $SO(4)$ symmetry?

For solving hydrogen atom energy level by $SO(4)$ symmetry, where does the symmetry come from? How can one see it directly from the Hamiltonian?
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2answers
671 views

Lorentz invariance of the 3 + 1 decomposition of spacetime

Why is allowed decompose the spacetime metric into a spatial part + temporal part like this for example $$ds^2 ~=~ (-N^2 + N_aN^a)dt^2 + 2N_adtdx^a + q_{ab}dx^adx^b$$ ($N$ is called lapse, $N_a$ is ...
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2answers
115 views

Why are these two definitions for symmetries in the Lagrangian equivalent?

I have heard the following two definitions for a symmetry of the Lagrangian: If under a coordinate transformation the form of the Lagrangian remains unchanged then there is a symmetry. If $\delta ...
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1answer
314 views

Precise statement of Mermin–Wagner theorem

Roughly speaking, Mermin-Wagner theorem states that continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions ...
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2answers
1k views

Can someone give a simple expose on Coleman Mandula theorem and what Mandelstam variables are?

Can someone give a simple expose on Coleman Mandula theorem and what Mandelstam variables are? Coleman-Mandula is often cited as being the key theorem that leads us to consider Supersymmetry for ...
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1answer
142 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 ...
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129 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 ...
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1answer
160 views

Invariance of action $\Rightarrow$ covariance of field equations?

Invariance of action $\Rightarrow$ covariance of field equations? Is this statement true? I have only seen examples of this, like the invariance of Electromagnetic action under Lorentz ...
7
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2answers
169 views

Do the standard cosmology models spontaneously break Lorentz symmetry?

In standard cosmology models (Friedmann equations which your favorite choice of DM and DE), there exists a frame in which the total momenta of any sufficiently large sphere, centered at any point in ...
7
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1answer
302 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 ...
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3answers
99 views

Rotationally invariant body and principal axis

Suppose a rigid body is invariant under a rotation around an axis $\mathsf{A}$ by a given angle $0 \leq \alpha_0 < 2\pi$ (and also every multiple of $\alpha_0$). Is it true that in this case the ...
7
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2answers
513 views

Why are conformal transformations so prevalent in physics?

What is it about conformal transformations that make them so widely applicable in physics? These preserve angles, in other words directions (locally), and I can understand that might be useful. Also, ...
7
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1answer
155 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 ...
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4answers
455 views

What is meant by the phrase “the mass is protected by a symmetry”?

In a particle physics context I've heard this phrase used. I guess it means that the mass of a particle is less than you'd naively expect from $E=mc^2$ after computing the momentum uncertainty ...
7
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1answer
173 views

Symmetries in physics

Can you explain me some of the mathematical details of such concept as symmetries? In physics, we have some manifold, and fields are functions on this manifold. On the one hand, we have symmetries of ...
7
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1answer
230 views

Generator of local symmetries

Let us only consider classical field theories in this discussion. Noether's theorem states that for every global symmetry, there exists a conserved current and a conserved charge. The charge is the ...
7
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2answers
191 views

Tadpole symmetry factor

Can someone help me with symmetry factor of one-loop tadpole diagram (one loop correction to one point Green function in phi-3 theory)?
7
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1answer
571 views

Explaining chirality for spin 1/2 particle

I found the following explanation for chirality for spin 1/2 particles here What happens when you rotate a left- vs right-chiral fermion 360 degree about its direction of motion. Both ...
7
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2answers
141 views

Dirac spinors under Parity transformation or what do the Weyl spinors in a Dirac spinor really stand for?

My problem is understanding the transformation behaviour of a Dirac spinor (in the Weyl basis) under parity transformations. The standard textbook answer is $$\Psi^P = \gamma_0 \Psi = ...
7
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3answers
167 views

What is the symmetry associated with the local particle number conservation law for fluid?

According to Noether's theorem, every continuous symmetry (of the action) yields a conservation law. In fluid, there is a local particle number conservation law, which is ...
7
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0answers
275 views

Extended Born relativity, Nambu 3-form and ternary (n-ary) symmetry

Background: Classical Mechanics is based on the Poincare-Cartan two-form $$\omega_2=dx\wedge dp$$ where $p=\dot{x}$. Quantum mechanics is secretly a subtle modification of this. By the other hand, ...
6
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3answers
193 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 ...
6
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3answers
1k views

Noether's current expression in Peskin and Schroeder

In the second chapter of Peskin and Schroeder, An Introduction to Quantum Field Theory, it is said that the action is invariant if the Lagrangian density changes by a four-divergence. But if we ...
6
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2answers
266 views

Quantum Anomalies in Non-Gauge Theories?

I'm reading about quantum anomalies in QFT and all the examples seem to arise in gauge theories. Is it true that theories without a local gauge invariance don't have quantum anomalies? I can't think ...
6
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2answers
279 views

Must every isometry have an associated Killing vector?

I understand that the flows of Killing vector fields are isometries, and that one-parameter groups of isometries have an associated Killing vector which generates them, but are your Killing vectors ...
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4answers
1k views

Symmetry in resistor circuits

Given 6 points that are connected with each other with a resistor of resistance $R$, find the resistance between any two points. (Answer: $R/3$) (All the conducting wires have the same ...
6
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2answers
198 views

Galilean, SE(3), Poincare groups - Central Extension

After having learnt that the Galilean (with its central extension) with an unitary operator $$ U = \sum_{i=1}^3\Big(\delta\theta_iL_i + \delta x_iP_i + \delta\lambda_iG_i +dtH\Big) + ...
6
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1answer
2k 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
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163 views

How can we differentiate between matter and antimatter? [duplicate]

For instance if there was a galaxy, assume it to be made up of antimatter (isolated from other "normal" galaxies), how would we, or rather, would we be able to distinguish if it was made up of matter ...