# Tag Info

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### Pauli-Lubanski vector for Maxwell's equation

I will attempt to give an answer to your question and if there are any points for which something is not clear, please let me know in the comments... First of all, we shall note that under ...

### How is the Feynman propagator (Green's function) connected with the field?

The Feynman propagator is the time-ordered two point correlation function of the field \begin{equation} \langle 0 | T\phi(x)\phi(y) | 0 \rangle = D_F(x,y) \end{equation} Because $D_F$ obeys the ...

### How is the Feynman propagator (Green's function) connected with the field?

You were right in your comment that what I had suggested, i.e. choosing $u(x)=\phi(x)$ was trivial and could not be used to infer any useful results. A more insightful choice would be $f(y)=\phi(y)$. ...
Accepted

### Equal-time Canonical Commutation Relation for a scalar field

You can write the integrals in question as $$\int_{\mathbb{R}^3} f(\vec{p}) d^3 p = \int_{-\infty}^\infty\!\!\int_{-\infty}^\infty\!\!\int_{-\infty}^\infty\!\! f(p_x,p_y,p_z) dp_x dp_y,dp_z$$ where ...
Accepted

### A wind tunnel and 2 strong magnets in the wind tunnel creating a very strong field, how would the wind & magnetic force interact?

Magnetic fields exert a force on charged objects and magnetic objects. Air is usually neither. If a charged particle moves in a magnetic field it experiences a force proportional to the charge, field ...

### What is the problem with classical fermionic field?

Note that the soul-part of a supernumber [and in particular a Grassmann-odd variable] is an indeterminate/a placeholder/has no value. This is fine as long as we make manipulations within the framework ...

### Calculation of Lagrangian from Hamiltonian $\frac{1}{2}(-i\partial_\phi -A)^2$

We start with the Lagrangian $$L_M~=~\frac{m}{2}\left(\frac{d\vec{r}}{dt_M}\right)^2 + q \vec{A}\cdot\frac{d\vec{r}}{dt_M}-q\phi_M,$$ for a non-relativistic point particle in Minkowski space ...

1 vote

### Why does the Lagrangian have $O(4)$ symmetry after Wick rotating (previously Lorentz symmetry)?

As long as the Minkowski action is constructed from Lorentz-covariant tensors, then under Wick rotation [where the contravariant and covariant $0$-components of the tensors are Wick-rotated in ...
1 vote
Accepted

### Expression of a Lagrangian in other form

What you need to use are so-called null-Lagrangians, i.e. terms that are a divergence and can be dropped in the Lagrangian because in the action integral they only contribute a surface term, or, to ...

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