Abstract
In the Luttinger model, right-hand-going particles moving at a constant velocity c in 1D maintain a constant distance apart. Therefore their interaction energy should be a trivial constant of the motion whereas, in fact it is not. This interaction affects the dispersion of all the elementary excitations in the model, hence the dynamics and thermodynamics. (Identical remarks hold for the left-hand-goers.) The present paper explores the meaning of this interesting facet of Luttinger's model.
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REFERENCES
W. Thirring, A soluble relativistic field theory, Ann. Phys. (NY) 3:91 (1958).
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A partial bibliography can be found in Chap. 4 of D. Mattis, The Many-Body Problem (World Scientific, Singapore, 1994). 28 related papers are reprinted in M. Stone, Bosonization (World Scientific, Singapore, 1994).
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Mattis, D.C. Luttinger's Model and the Matter of Dispersion. Journal of Statistical Physics 103, 503–507 (2001). https://doi.org/10.1023/A:1010385131170
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DOI: https://doi.org/10.1023/A:1010385131170