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Mar
6
answered Trick for deriving the stress tensor in any theory
Mar
6
awarded  Critic
Mar
5
answered A Book about the Bohr-Einstein debate?
Mar
5
answered Violation of Lorentz invariance (Lagrangian for particle)
Mar
3
comment Is there a Lagrangian formulation of statistical mechanics?
@Nathaniel. You are correct, the differentials in the Hamilton-Jacobi equation should be with respect to the end point. Also, the time dependence that I wrote is not the most general. In the case of an explicitely time varying Hamiltonian, the phase function depends on $t_0$ and $t_1$ and not only on their difference. In this case the time differetiation is also with respect to the end point. In fact you may choose either one of the boundary points.
Mar
1
comment Is there a Lagrangian formulation of statistical mechanics?
@Nathaniel cont. In this case instead of an iterative procedure of guessing the initial momenta and checking the second end boundary condition, we can solve the Hamilton-Jacobi equation. The price is that it is a partial differential equation. A second applications is in the discrete formulation of mechanics (we can imagine that the time "t" to be a small time step). I haven't seen an application to statistical mechanics. This is why I thought that the question is very original. But I haven't searched hard enough.
Mar
1
comment Is there a Lagrangian formulation of statistical mechanics?
@Nathaniel when $x_0$ and $x_1$ are the boundary points of a classical trajectory (satisfying the Hamilton's equations), then $S$ is the value of the classical action. Of course we can use this function for any two points on the configuration space not necessary along a classical trajectory. In this case the Hamilton Jacobi-phase function generates canonical transformations (for this reason, some authors call it the generating function). The basic application that I know of this function is in the solution of the Hamilton's equations given boundary and not initial conditions.
Mar
1
comment Is there a Lagrangian formulation of statistical mechanics?
@Vibert Spin systems can also be formulated on phase space, for example a single spin phase space can be chosen to be a 2-sphere (the collection of all spin directions). This description can also be generalized to the case of many spins, which can be formulated on "non-flat" phase spaces. The phase space is just the collection of initial data of an evolving mechanical system; The Hamiltonian contains the information about the interaction. Thus, the same description applies for both the weakly and the strongly interacting cases.
Mar
1
awarded  Revival
Feb
28
answered Is there a Lagrangian formulation of statistical mechanics?
Feb
27
answered Form of the Classical EM Lagrangian
Feb
27
answered Topological Charge. What is it Physically?
Feb
24
awarded  Yearling
Feb
18
answered Spontaneous breaking of Lorentz invariance in gauge theories
Feb
1
awarded  research-level
Jan
26
awarded  Enlightened
Jan
26
awarded  Nice Answer
Dec
30
comment Path integral with zero energy modes
@Greg I can't see your E-mail, instead I placed the copy in a file exchange server, fileconvoy.com/… where it will be abailable in the next 7 days
Dec
28
comment Path integral with zero energy modes
@Greg, 1) The unitary transformation U does not need to preserve $\mathrm{ker}(D)$, sorry for not emphasizing that one must project on the top form after performing the action, because the top form subspace is one dimensional. I'll try to add in a few days an explicit computation of the scalar multiple and the cocycle condition. 2) I'll be happy to help if you need me to send a copy of the article.
Dec
26
answered Path integral with zero energy modes