Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1994-02-07
Phys.Rev.D50:5403-5408,1994
Physics
High Energy Physics
High Energy Physics - Phenomenology
10 pages, LaTeX, CCNY-HEP-94-5. Earlier submission had an email bug in transmission
Scientific paper
10.1103/PhysRevD.50.5403
The BP-FTW effective action is a good laboratory to study the nature of chiral symmetry at high $T$. It is invariant under a new Noether charge, $\Qbeta$. By explicit quantization, performed to order $\Tprime$ we show that the thermal vacuum is annihilated by $\Qbeta$, so that the new chiral symmetry is not broken spontaneously at high $T$. This high $T$ Noether charge is, however, different from the usual zero temperature chirality, $\Q$. Our quantization also shows that the thermal vacuum is not annihilated by $\Q$, so that the old chiral symmetry remains broken at high $T$. The thermal vacuum is thus every bit as `structured' and `complex' as the Nambu-Jona-Lasinio vacuum at zero temperature. We exhibit the relation between the normal mode expansion for $\Qbeta$ versus the usual expansion for $\Q$. In an appendix, we point out the analyticity properties of the fermion propagator in real time formalism, and verify the canonical nature of the thermal Green function.
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