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Where the b-vacuum state is defined by the condition b(t) |0; b >= 0. (67) Using these eigenvectors, one can construct the solution of the Schr¨odinger equation, as described above. In the DCC case, however, it is preferable to express the quantum state vector in terms of the pion creation and annihilation operators a+ , a. So we need a relation between two sets of the creation-annihilation operators a+ , a and b+ , b (the Bogoliubov transformation). The pionic modes correspond to the late time asymptotes ω(t) → ω(∞) = ω0 .
Larsson, Phys. Rev. D 56, 6942 (1997). [60] K. L. Kowalski and C. C. Taylor, hep-ph/9211282. [61] A. J. Leggett, Phys. Rev. Lett. 53, 1096 (1984). [62] A. J. Leggett, J. Low Temp. Phys. 87, 571 (1992); P. Schiffer, D. D. Osheroff and A. J. Leggett, Nucleation of the A-B transition in superfluid 3He: experimental and theoretical considerations, Prog. Low Temp. Phys. vol. XIV, ed. P. P. Pitaevskii, (Elsevier, Amsterdam, 1995), pp. 159-211. [63] Phys. Today 45N6, 20 (1992). [64] See, for example, S.
In QCD the baryon is represented by a gauge invariant, non-local, color singlet operator. In fact, the gauge invariance constraint severely restricts the possible forms of such composite operator, leaving only one possibility (α, β, γ are the color indices, the flavor indices are suppressed for simplicity) : B = ǫαβγ Tˆ(x1, x)q(x1) α Tˆ(x2, x)q(x2) β Tˆ(x3, x)q(x3) γ . Here Tˆ(xi, x) is the open string operator (the Wilson line), or parallel transporter of the quark field q(xi) from the point xi to the point x, where the three strings join.