4
votes
On the physical meaning of functionals and the interpretation of their output numbers
What does "the action of the process" mean here physically?
The action $S$ is the integral of the Lagrangian:
$$
S[q] = \int_{t_1}^{t_2}dt L(q(t),\dot q(t), t)\;,
$$
where the Lagrangian is ...
- 17.6k
3
votes
Accepted
Potential energy of a particle inside a magnetic vector potential
$
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- 15.3k
2
votes
Understanding a supersymmetric quantum mechanical gauge theory model
1. Gauge Reduction and Fermions
Dimensional Reduction involves reducing the number of spatial dimensions. When reducing to 1 + 0 dimensions, the spatial component of $A_\mu$ is reinterpreted as a ...
- 730
2
votes
Accepted
2-point correlation function between two different fields
The story for a (connected) 2-point function of 2 different fields is very similar to what goes on for a 1-point function, cf. e.g. this & this related Phys.SE posts:
Either a symmetry ensures ...
- 196k
1
vote
Potential energy of a particle inside a magnetic vector potential
To call this quantity the potential energy is misleading. When a particle is subject to an external (non-dynamical) field we can define a potential energy $U$ for the particle if doing so gives a ...
- 6,226
1
vote
Derivation of Hamiltonian by constraining $L(q, v, t)$ with $v = \dot{q}$
This 3-way extended action principle is precisely the topic of my Phys.SE answer here. Concerning OP's main question, the
Hamiltonian is defined as the Legendre transform
$$ H(q,p)~:=~ \sup_v (p_i v^i-...
- 196k
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