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 ...
hft's user avatar
  • 17.6k
3 votes
Accepted

Potential energy of a particle inside a magnetic vector potential

$ \newcommand{\bl}[1]{\boldsymbol{#1}} \newcommand{\e}{\bl=} \newcommand{\p}{\bl+} \newcommand{\m}{\bl-} \newcommand{\mb}[1]{\mathbf {#1}} \newcommand{\mbh}[1]{\mb{\hat #1}} \newcommand{\mbwh}[1]{\mb{...
Frobenius's user avatar
  • 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 ...
MrDBrane's user avatar
  • 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 ...
Qmechanic's user avatar
  • 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 ...
Brian Bi's user avatar
  • 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-...
Qmechanic's user avatar
  • 196k

Only top scored, non community-wiki answers of a minimum length are eligible