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Invariance of general equations under Lorentz Transformation

I'll try to answer this. It might be inadequate but maybe a little useful. If there is an equation $A^\mu = B^\mu$ then the equation holds true in any frame, which is a postulate of special relativity....
SX849's user avatar
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How to calculate the Hodge dual of a two-form defined in self-dual BF theory?

I found the solution thanks to the comments. There seems to be a factor of $\frac{1}{2}$ missing from the second term in the reference as well. Adding this factor will resolve the issue. \begin{align}\...
mortimer's user avatar
1 vote

Does the Wigner little group classification of particles have consequences for classical field theory?

Depending on how you look at quantization, you could say there are consequences for classical field theory; whether there was first classical fields then they get quantized, or they were quantum all ...
Mateo's user avatar
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1 vote

How does Diagonalizing Mass Terms Affect the Lagrangian?

This is a response to the first part of your question, not related to the neutrino physics specifically. Suppose we start with a generic Lagrangian with $N$ scalar fields where both the kinetic and ...
Andrew's user avatar
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2 votes

Difference in definition of conserved current in Quantum Field Theory

Comparing the two resulting currents you see that they only differ by the addition of the $-F^\mu$ term. (The replacement of $X_a $ by $\delta \phi / \delta \alpha$ is only due to a different ...
Thomas Tappeiner's user avatar
2 votes
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Was the singularity a boson?

No. Within our best theories, this is incorrect. In general relativity, a singularity is a hole in spacetime (which is properly defined by means of geodesic incompleteness). It is not a particle and ...
Níckolas Alves's user avatar
6 votes

Theorem in mechanics relating energy flow and momentum

It comes from the theory of relativity, not Newtonian mechanics, and it is not a theorem, but more of a generalization of what holds for energy and momentum of ordinary matter and EM field, to other ...
Ján Lalinský's user avatar
7 votes

Theorem in mechanics relating energy flow and momentum

It is simply the statement that in General relativity the energy-momentum tensor $T^{\mu\nu}$ is symmetric: $T^{\mu\nu}=T^{\nu\mu}$. The quantity $T^{0\mu}$ is the density of the $\mu$-th ...
mike stone's user avatar
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Conjugate momenta in field theory

TL;DR: The EOM of classical field theory are not those of classical mechanics because a field is a function of both space and time coordinates. Also, in field theory, space and time should be treated ...
Gabriel Ybarra Marcaida's user avatar
-1 votes

Conjugate momenta in field theory

This isn't my area, but my understanding is that the difference is the difference between a Lagrangian $L$ and a Lagrangian density $\cal L$: $$L=\int{\cal L}d^3x.$$ The Euler-Lagrange equations for $...
Greg Henderson's user avatar
1 vote
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Lagrange Multipliers in ADM formalism

On one hand in the Lagrangian formalism, the lapse and shift functions $(N,N_i)$ are given in terms of the $g_{0\mu}$-components, and vice-versa, cf. eq. (5.10). $(N,N_i)$ may appear non-linearly in ...
Qmechanic's user avatar
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Lagrange Multipliers in ADM formalism

The idea of the Hamiltonian formalism to express everything in terms of the fields $\phi$ and momenta $\Pi$ and use those as your fundamental variables. Once you do that, the Hamiltonian has the ...
Andrew's user avatar
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A question involving chiral transformations and gamma matrices

Really this holds even for finite $\beta$, by splitting the exponential: \begin{align} \exp\left(-i\beta\gamma_5\right)\gamma^0 &= \cos\left(\beta\gamma_5\right)\gamma^0 -i\sin\left(\beta\gamma_5\...
QLQ's user avatar
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1 vote
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What is the difference between field and disturbance?

They’re just using more reminiscent words. A ‘field’, to a lay-person means the place where you plant crops/fruits/vegetables… this is obviously not what we mean in Physics. So, they’re trying to give ...
peek-a-boo's user avatar
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Effect of gauge-fixing via Lagrange multipliers on Euler-Lagrange equations

The answer is 'yes' under the condition that $\lambda$ is independent of $x^\mu$. If $\lambda$ depends on $x^\mu$ it contributes in the equations of motion and the conservation laws. Note that $\...
my2cts's user avatar
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2 votes
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Effect of gauge-fixing via Lagrange multipliers on Euler-Lagrange equations

OP has correctly identified the mechanism in their example: In order for OP's action (4) to be gauge invariant, we must assume the continuity equation (3). Eq. (3) in turn implies that the Lagrange ...
Qmechanic's user avatar
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