94
13 Non-Fock Representations
quantum electrodynamics. The charged (scattering) states define non-Fock coherent
representations of the asymptotic electromagnetic algebra.
69 If this type of states are
used to define the scattering amplitudes one gets finite results, when the infrared
cutoff is removed, also in (the correspondingly adapted) perturbation theory.
70
Other examples of non-Fock representations are provided by models with a nonvanishing ground state expectation value of the scalar field
ϕ(x, 0) =
dk e
ik·x
[a(k) + a
∗
(−k)](2ω(k))
−1/2
,
since, if the representation is Fock for the canonical variables a, a
∗ , by Haag’s
argument the ground state must coincide with the Fock vacuum and the latter gives
vanishing expectation of a and a
∗ .
69 V. Chung, Phys. Rev. 140B, 1110 (1965); J. Fröhlich, G. Morchio and F. Strocchi, Ann. Phys.
119, 241 (1979); G. Morchio and F. Strocchi, Nucl. Phys. B211, 471 (1984); for a review see G.
Morchio and F. Strocchi, Erice Lectures, in Fundamental Problems of Gauge Field Theory, G. Velo
and A.S. Wightman eds., Plenum 1986; and G. Morchio and F. Strocchi, Annales H. Poincaré, 17,
2699–2739 (2016).
70 T. W. Kibble, Phys. Rev. 173, 1527; 174, 1882; 175, 1624 (1968) and references therein.
13 Non-Fock Representations
quantum electrodynamics. The charged (scattering) states define non-Fock coherent
representations of the asymptotic electromagnetic algebra.
69 If this type of states are
used to define the scattering amplitudes one gets finite results, when the infrared
cutoff is removed, also in (the correspondingly adapted) perturbation theory.
70
Other examples of non-Fock representations are provided by models with a nonvanishing ground state expectation value of the scalar field
ϕ(x, 0) =
dk e
ik·x
[a(k) + a
∗
(−k)](2ω(k))
−1/2
,
since, if the representation is Fock for the canonical variables a, a
∗ , by Haag’s
argument the ground state must coincide with the Fock vacuum and the latter gives
vanishing expectation of a and a
∗ .
69 V. Chung, Phys. Rev. 140B, 1110 (1965); J. Fröhlich, G. Morchio and F. Strocchi, Ann. Phys.
119, 241 (1979); G. Morchio and F. Strocchi, Nucl. Phys. B211, 471 (1984); for a review see G.
Morchio and F. Strocchi, Erice Lectures, in Fundamental Problems of Gauge Field Theory, G. Velo
and A.S. Wightman eds., Plenum 1986; and G. Morchio and F. Strocchi, Annales H. Poincaré, 17,
2699–2739 (2016).
70 T. W. Kibble, Phys. Rev. 173, 1527; 174, 1882; 175, 1624 (1968) and references therein.