A theorem that relates continuous symmetries (continuous transformations that don't affect the value of the lagrangian) to quantities conserved in time.

learn more… | top users | synonyms

0
votes
1answer
23 views

How to define conserved charges in Euclidean field theory?

In a field theory with signature (1,d), conserved charges are obtained by integrating the time component of a conserved current over a spatial region. What are the corresponding equations and ...
1
vote
1answer
27 views

Conserved current in a complex relativistic scalar field

For my field theory class I have the following Lagrangian density $$\mathscr{L}=\frac{1}{2}\eta^{\mu\nu}\partial_\mu\phi^*\partial_\nu\phi-\frac{1}{2}m^2\phi^*\phi$$ Where $\eta^{\mu\nu}$ is the ...
2
votes
1answer
763 views

Can conservation of momentum be violated?

The law of the conservation of momentum was accepted for year-hundreds. Even in Quantum field theory every particle collision must be momentum-conserving if there is homogenity in space. Can this ...
1
vote
1answer
48 views

Given potentials, how does one find conserved quantities using Noether's theorem?

I've been asked to find the conserved quantities of the following 3D potentials: $U(\vec{r}) = U(x^2)$, $U(\vec{r}) = U(x^2 + y^2)$ and $U(\vec{r}) = U(x^2 + y^2 + z^2)$. For the first one, ...
2
votes
1answer
43 views

Basic QED - How are conserved charges expressions throught ladder operators derived?

I can't find this in similar questions, and I must be missing something very basilar since I can't find this in any textbook or online note: they just skip the passage. So, from my course's notes, we ...
0
votes
1answer
43 views

Wondering about Energy [duplicate]

Me and Energy I'm trying to move along with my study of non-advanced physics but not grasping what energy really is, is driving me nuts. Whenever i see anything about energy ( Kinetic, ...
8
votes
1answer
233 views

Noether currents in QFT

I am trying to organize my knowledge of Noether's theorem in QFT. There are several questions I would like to have an answer to. In classical field theory, Noether's theorem states that for each ...
3
votes
0answers
39 views

Conserved charge of a conformal transformation

From Becker, Becker and Schwarz String Theory and M-Theory: For the infinitesimal conformal transformation $$\tag{3.25}\delta z=\varepsilon(z)\quad\text{and}\quad \delta\bar ...
0
votes
0answers
20 views

Conserved quantities in the cart and pendulum problem

A problem on an assignment I'm doing deals with a cart of mass m1 which can slide frictionlessly along the x-axis. Suspended from the cart by a string of length l is a mass m2, which is constrained to ...
1
vote
0answers
47 views

Noether current scale transform of EM

I'm trying to solve a question about scale tranform of free EM. I got the next trnaform rules (these two line where EDITed later) $\delta x = -bx$ $\delta A = bA$ the current I got $D^\mu = ...
5
votes
1answer
158 views

Noether's Theorem: Lie algebra, Lie groups

I've had a brief look through similar threads on this topic to see if my question has already been answered, but I didn't find quite what I was looking for, perhaps it is because I'm finding it hard ...
0
votes
0answers
31 views

Symmetric energy-momentum tensor using derivative wrt. metric

I can find the Noether current for space time translation symmetry by demanding that the first order correction to the Lagrangian vanishes upon infinitesimal translations of coordinates. But in cases ...
0
votes
0answers
29 views

Can any global symmetry be promoted to the local symmetry? [duplicate]

Can any global symmetry be promoted to the local symmetry? Does there exist counterexample?
3
votes
2answers
93 views

Classical EM : clear link between gauge symmetry and charge conservation

In the case of classical field theory, Noether's theorem ensures that for a given action $$S=\int \mathrm{d}^dx\,\mathcal{L}(\phi_\mu,\partial_\nu\phi_\mu,x^i)$$ that stays invariant under the ...
2
votes
1answer
33 views

How to derive the conserved current of the Klein Gordon equation?

Similarly to the probability current in non-relativistic quantum mechanics, there is a conserved current for the Klein Gordon equation, however a different one. I'm trying to calculate that. The KG ...
2
votes
1answer
57 views

Lagrangian under time transformation

Given a Lagrangian $$L(q,\dot{q},t)=\sum_{ij}a_{ij}(q)\dot{q}_i\dot{q}_j-V(q_1,q_2,\cdots,q_f)$$show that under a time transformation $t=\lambda T$ ($\lambda$ = constant), the invariance of ...
4
votes
2answers
71 views

Peskin and Schroeder passive and active translation

In peskin and Schroeder's qft book, in chapter two, they're discussing Noether's theorem with respect to translations of co-ordinates. They describe and "infinitesimal" translation $x^\mu\rightarrow ...
3
votes
1answer
106 views

Does time invariance conclude conservation of energy? [closed]

I find it hard to understand that time-translation invariance necessarily implies conservation of energy. As I understand it, Noether's theorem says that there is an energy conservation because the ...
0
votes
1answer
59 views

Scalar field gives spin $0$ particles

Related to this question. What needs to be shown is that the total angular momentum (derived from the Klein-Gordon lagrangian) acting on a ket with $0$ momentum, gives 0. This would mean that a ...
3
votes
1answer
61 views

Deriving the Canonical Energy Momentum Tensor

In the Mathematics for Physics of Stone and Goldbart the canonical energy momentum tensor is derived by the action principle as follows. To the action of the form $$ S=\int ...
3
votes
0answers
82 views

Does Noether's theorem apply to entropy?

Entropy appears to have a translation symmetry - adding some constant value to it doesn't appear to my fairly rudimentary understanding of physics alter the actual physics. Is this correct? Now ...
0
votes
1answer
26 views

Conservation of generalized energies in Newtonian and Relativistic Systems

I was considering the following problem: In a closed system, it is assumed that mass, momentum and energy is conserved. If we label the total mass of the System $M(i)$ at a time i, the total Momentum ...
0
votes
0answers
70 views

Why is electric charge the conserved quantity corresponding to global $U(1)$ symmetry? [duplicate]

An example of a symmetry transformation for certain Lagrangians (notably the canonical complex scalar field Lagrangian) is multiplication of the fields by a complex phase. When we multiply the fields ...
0
votes
1answer
82 views

Origin of momentum. Noether's theorem

My professor talked about Noether's theorem and how translation is the origin of momentum conservation. But why is it not velocity that is conserved but mass times velocity. And on the same note why ...
0
votes
4answers
79 views

Relationship between Energy and Time [closed]

Is there a relationship between energy and time? What is it?
5
votes
0answers
43 views

If weak isospin is not conserved in time, what does the Noether theorem tell us?

As far as I understand weak isospin is only conserved in interactions but not as time evolves. Nevertheless, we get from Noethers theorem, because of global $SU(2)$ invariance a conserved quantity ...
3
votes
0answers
79 views

Why is only the third component of weak isospin used as a conserved quantity?

Using Noether's theorem \begin{equation} \partial_0 \int d^3x \left(\frac{\partial L}{\partial(\partial_0\Psi)} \delta \Psi \right) = 0 \end{equation} we get three conserved quantites $Q_i$ from ...
2
votes
0answers
54 views

Is global gauge symmetry really a symmetry and local conserved current in gauge theories?

One way to define a gauge theory is that whenever the Lagrangian is invariant under some local transformations, we say these local transformations are local gauge transformations and the theory is a ...
1
vote
0answers
95 views

Derivation of correction to canonical stress energy tensor due to addition of total divergence to Lagrangian

It is mentioned in almost every text book that equations of motions are not modified if we add a total divergence of some vector $$\partial_\mu \ X^{\mu}$$ to Lagrangian but canonical stress energy ...
0
votes
6answers
539 views

Can energy be created and destroyed?

The indroduction of the principle of conservation of mechanical energy has been tremendously useful from the practical point of view. But .. Consider the case in which we shoot an electron up in the ...
0
votes
1answer
52 views

Complex scalar field

In his book on Quantum Field Theory, Ryder mentioned in p. 91 under the title Complex Scalar Fields and Electromagnetism, the following: He said that under a global phase transformation $$\phi ...
3
votes
1answer
113 views

How does conservation of energy manifest itself quantum mechanically?

We know that classically, if we have some theory $\mathcal{L}$ such that the action $\int d^4 x \mathcal{L}$ is invariant under time translation, then we can use Noether's theorem to find that (the ...
2
votes
1answer
60 views

Symmetries of the action of the free classical Klein-Gordon field

I've read that the action for the free classical Klein-Gordon field $$S = \int \mathrm{d}^4x~ \mathcal{L} = \frac{1}{2} \int \mathrm{d}x^4 \left(\partial_\mu \phi(x) \, \partial^\mu \phi(x) - ...
3
votes
1answer
228 views

Which transformations *aren't* symmetries of a Lagrangian?

As far as I understand, Noether's theorem for fields works, as explained in David Tong's QFT lecture notes (page 14) for example, by saying that a transformation $\phi(x) \mapsto \phi(x) + \delta \phi ...
1
vote
0answers
65 views

What's the conserved stress energy tensor? [closed]

I've worked on this problem for forever and still don't really see the solution. Any help appreciated. Say we have the Lagrangian for a scalar field that's $U(1)$ charged,$$\mathcal{L} ...
0
votes
0answers
82 views

Conservation of kinetic energy on a moving inertial frame

The velocity of an object differs from the point of views of two different inertial observers standing at two different frame of reference. Assuming no gravity and acceleration = 0 for the object and ...
5
votes
1answer
230 views

Connection between conserved charge and the generator of a symmetry

I'm trying to understand the connection between Noether charges and symmetry generators a little better. In Schwartz QFT book, chapter 28.2, he states that the Noether charge $Q$ generates the ...
2
votes
1answer
94 views

Derivation of Baryon Number conservation?

The symmetry connected to Baryon/Lepton Number conservation is, as far as I understand, global U(1) symmetry (which is called here global gauge invariance). Does anyone know of an explicit ...
1
vote
1answer
86 views

Convenient coordinate systems and symmetries

I recall in my basic electromagnetism and quantum mechanics lectures that choosing one coordinate system over another may greatly simplify the equations involved in solving a problem (think about ...
2
votes
2answers
209 views

The variation of the Lagrangian density under an infinitesimal Lorentz transformation

I'm trying to introduce myself to QFT following these lectures by David Tong. I've started with lecture 1 (Classical Field Theory) and I'm trying to prove that under an infinitesimal Lorentz ...
1
vote
0answers
108 views

Spin tensor from Noether theorem and spin tensor from Pauli-Lubanski vector

Spin 3-vector directly from Noether theorem Let's have one of applications of Noether theorem: the invariance of action under Lorentz group transformations leads to conservation of tensor $$ \tag 1 ...
0
votes
2answers
122 views

Lorentz symmetry and Noether's theorem

I'm trying to overcome some misunderstanding that I have in Noether's theorem. There is formula in David Gross's Lectures on QFT for Noether's theorem: ...
2
votes
2answers
74 views

World-sheet energy-momentum tensor and OPE

On p43 of Polchinski's book, it says that under the world-sheet translation $\sigma^a\rightarrow\sigma^a+\epsilon v^a$, $X^\mu\rightarrow X^\mu-\epsilon v^a\partial_a X^\mu$. And $$j^a=iv^b T_{ab},$$ ...
0
votes
0answers
61 views

Conserved charge from conserved current associated with translational invariance

(c.f Di Francesco, 'Conformal Field Theory' P.45) Di Francesco calls the conserved charge arising from the conserved current associated with a translation invariant theory the 'four momentum'. While ...
2
votes
1answer
48 views

Deriving conserved currents by promoting parameter

I currently reading Tong's text on String Theory. In Chapter 4.1.1 he alludes to a technique to derive conserved currents Recall that we can usually derive conserved currents by promoting the ...
0
votes
1answer
102 views

Conserved current for a constant translation of a free massless scalar field

In Zinn-Justin's Quantum Field Theory and Critical Phenomena they start with an action for a free massless scalar field: $$S(\varphi) = \frac{1}{2}\int ...
1
vote
1answer
133 views

Subtlety in derivation of Noether's theorem by Di Francesco

In the book 'Conformal Field Theory' by Di Francesco et al, a derivation of Noether's theorem is demonstrated by imposing that, what I believe is said to be a more elegant approach, the parameter ...
4
votes
1answer
165 views

Noether's Theorem: Foundations

I'm wondering on what principles Noether's theorem foots. More precisely: The action is a functional on the fields only. Why do we consider then variations of the space time too? In principle careful ...
2
votes
0answers
88 views

Constructing Ward identity associated with conserved currents

Consider constructing the Ward identity associated with Lorentz invariance. It is possible to find a 3rd rank tensor $B^{\rho \mu \nu}$ antisymmetric in the first two indices, then the stress-energy ...
3
votes
1answer
313 views

Hamiltonian Noether's theorem in classical mechanics

How does one think about, and apply, Noether's theorem in the classical mechanical Hamiltonian formalism? From the Lagrangian perspective, Noether's theorem (in 1-D) states that the quantity ...