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Results tagged with field-theory
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user 322041
For questions where the dynamical variables are fields, that is, functions of several variables (typically, one time coordinate and several space coordinates). Comprises both classical field theory and quantum field theory. Use this tag when the question applies to both classical and quantum phenomena. Otherwise, use the specific tag instead.
0
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1
answer
54
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What is the vacuum solution of Dirac equation?
What am I generally asking is what solution of massive Dirac equation could be considered vacuum solution
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2
votes
1
answer
50
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A question on QED
In QED it's given a current of the particle described by wave function $\psi$
$$j^\mu=\bar{\psi}\gamma^\mu\psi.$$
If we substitute positive- and negative-energy solutions we get that
$$j_{+}^0=j^0_-,$ …
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votes
0
answers
25
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Dirac equation solution for a point particle
I want to solve a Dirac equation with a special condition for the probabillity
$\bar{\psi}\gamma^0\psi=\delta\left(\vec{r}\right)$
Since Dirac spinor is a $4\times 1$ matrix, I am not sure what compon …
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1
vote
0
answers
29
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How did scientists calculate the bounds of mass of Higgs boson without measurement [duplicate]
First of all, let us write out the lagrangian of the Higgs field
$\mathcal{L}=\partial_\mu\bar{\varphi}\partial^\mu\varphi-\lambda(\bar{\varphi}\varphi-\frac{v^2}{2})^2$
This yields $m^2=\lambda v^2$. …
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1
vote
1
answer
75
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Does single electron interact with its own electromagnetic field?
The QED equations are given by
$\square A^\mu=e\bar{\psi}\gamma^\mu\psi$
$i\gamma^\mu\partial_\mu\psi=(m+e\gamma^\mu A_\mu)\psi$
These equations suggest, that electrons interact with field created by …
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1
vote
0
answers
50
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What are the beta functions for electroweak and strong constants of interactions?
As the title says I want to find beta function for electroweak and strong constants ($g$ for W-boson, $g'$ for B-boson and $g_s$ for gluons)
Beta function is the function that describes change in cons …
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3
votes
3
answers
739
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A problem with QED
I have a small problem with the understanding of QED.
The equations of motion in QED are
$\square A^\mu=e\bar{\psi}\gamma^\mu\psi$
$\left(i\gamma^\mu\partial_\mu-m\right)\psi=e\gamma^\mu A_\mu\psi$
If …
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0
votes
1
answer
111
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Charge Conjugation of Dirac equation
In contituation of this question
In answers of this question people mentioned charged conjugation and formula below
$\bar{\psi}\gamma^\mu\psi=u^2-v^2$
With $u$ for particles and $v$ for antiparticles
…
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0
votes
1
answer
56
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Deriving equation describing fermion-antifermion field
We know the Lagrangian of massless interacting Dirac field
$\mathcal{L}=\bar{\psi}i\gamma^\mu(\partial_\mu-iA_\mu)\psi$
Now consider charge conjugation operator $C=i\gamma^2$
The Lagrangian for charge …
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0
votes
1
answer
44
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Gauge invariance to solve Dirac equation in external EM field
Consider a Dirac equation in external EM field $A_\mu$
$(i\gamma^\mu\partial_\mu-m)\psi=q\gamma^\mu A_\mu\psi$
Consider a solution without EM field $\psi_0$. Let us do the gauge transformation $\psi_0 …
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3
votes
2
answers
148
views
How do I derive the Dirac Lagrangian?
It's frequently said, that the Lagrangian of a Dirac field is
$$\mathcal{L}=i\bar{\psi}(\gamma^\mu\partial_\mu-m)\psi.$$
Applying the Euler-Lagrange equation we get the Dirac equation. Although, we ca …
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0
votes
1
answer
237
views
Proca equation gauge conditions
In massive case without any gauge conditions proca equation can be written as
$\partial_\nu(\partial^\nu A^\mu- \partial^\mu A^\nu)+\left(\frac{mc}{\hbar}\right)^2 A^\mu=0$
Since $A_\mu$ is a $n$-vect …
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-1
votes
1
answer
64
views
Problem with energy conservation in field theory
As it's known, for conservation of energy by Noether Theorem it's neccesery that equation below is satisfied
$\partial_\mu T^{\mu\nu}=0$
Where $T^{\mu\nu}=\frac{\partial\mathcal{L}}{\partial(\partial_ …
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1
vote
0
answers
43
views
Question on positronium lifetime
From Wikipedia I could get that lifetime of orthopositronium (spin of electron and positron point in same direction) is
$t=\frac{9h}{4m_ec^2\alpha^6(\pi^2-9)}$
And parapositronium
$t=\frac{h}{\pi m_ec …
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0
votes
1
answer
45
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Charge of a composite fermion
Suppose a fermion being a composite of two other fermions
$$\psi=\varphi\cos\theta+\chi\sin\theta.$$
If $\varphi$ and $\chi$ satisfy the Dirac equations
$$i\!\!\not\!\partial\varphi=e_{\varphi}\!\!\no …
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