Re: Non-lagrangian from lagrangian
- From: Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>
- Date: Sun, 17 Sep 2006 13:37:51 +0000 (UTC)
wandering.the.cosmos@xxxxxxxxx wrote:
Given some lagrangian, when we integrate out degress of freedom either
in quantum or classical field theory, we usually obtain an effective
one. Are there cases where, upon integrating out degrees of freedom,
one no longer has a lagrangian description of the dynamics?
Essentially always, since the contraction process introduces some dissipation. If the latter can be neglected, one gets again a
Lagrangian system.
An excellent book for how to get reduced descriptions of a physical system (though from the hamiltonian rather than Lagrangian point of
view) is
H Grabert,
Projection Operator Techniques in Nonequilibrium
Statistical Mechanics,
Springer Tracts in Modern Physics, Berlin 1982.
Arnold Neumaier
.
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