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Dec
30
revised “distinguishability” of 1D identical particles
deleted 1 character in body
Dec
30
comment How does one compute position and momentum in QFT?
@MarcusQuinnRodriguezTenes: Yes, in the 1-particle sector. Only the notation has changed.
Dec
30
comment Representations of SO(3) and the classification of relativistic massive particles as in Weinberg's “The Quantum Theory of Fields”
Weinberg discusses the need of projective representations in Chapter 2.7.
Dec
30
answered “distinguishability” of 1D identical particles
Dec
30
answered Why are one-particle states called representations of Poincaré group?
Dec
30
answered Modern relevance of canonical quantisation
Dec
30
comment Unsolved Potentials in Path Integral
The important potentials are the exactly solvable ones, as they are being used as starting point for a perturbative treatment of the others. It doesn't matter whether you do it via path integrals or via the Schroedinger equation.
Dec
30
answered How does one compute position and momentum in QFT?
Dec
30
answered Self Teaching QFT
Dec
16
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Dec
13
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Dec
10
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Dec
9
comment Extending the ergodic theorem to non-equilibrium systems
''did you mean that a turbulent flow would stay turbulent indefinitely?'' It depends on the boundary condition. Running water can well be turbulent indefinitely. A closed and isolated turbulent system with enough friction at the container will ultimately settle in an equilibrium state. Dissipation is represented by the parabolic terms in the Navier-Stokes equations. The corresponding conservative system would satisfy instead the Euler equations.
Dec
9
comment Extending the ergodic theorem to non-equilibrium systems
@user929304: In principle, the cell size is a free parameter on which the coarse-grained model depends. But for a macroscopic system, the result is nearly independent of it, if it is far away from both microscopic and macroscopic scales. In practice, its choice is therefore not critical, taking the geometric mean of microscopic and macroscopic scales works well. In phase space, things are more delicate as there is no canonical metric on it.
Dec
9
comment Density of states for the diffusion
You cannot get such a relation, as the variable that you make small disappears from the limiting formula. For the wave propagator it works since only the unphysical $\epsilon$ goes to zero.
Dec
9
comment Extending the ergodic theorem to non-equilibrium systems
@user929304: (i) For local equilibrium, one bins space-time (a short time average is also needed to account for contributions of very high frequencies). One can also bin in (macroscopic) phase space, but then gets Boltzmann-like kinetic equations rather than hydrodynamic equations, as all the fields then depend on position and momentum. Each cell has its own set of thermodynamic variables defining its macrostate. (ii) roughly, yes.
Dec
8
answered What happened with Hilbert's sixth problem (the axiomatization of physics) after Gödel's work?
Dec
8
comment Extending the ergodic theorem to non-equilibrium systems
A dissipative system doesn't need to tend to a fixed point. An important example is the case of turbulence in fluids satisfying the Navier-Stokes equations.
Dec
8
comment Extending the ergodic theorem to non-equilibrium systems
@josephf.johnson: If an open or closed system is in local equilibrium, ergodic arguments can (with caution) be applied to the individual cells. This is a way - and the only way - his question can be made sense of. He asked for ''[...] ergodic theory. Does this concept even extend to non-equilibrium? If yes, how is it interpreted?'', and my answer gives the only feasible interpretation.
Dec
8
answered Extending the ergodic theorem to non-equilibrium systems