Megascopic Quantum Phenomena
325
issue since there is no symmetry to break. In the latter case it is possible that the
discrete symmetry is spontaneously broken. But the usual argument for symmetry
breaking using the conserved Noether current does not apply. And while it is possible
that some completely different sort of construction will demonstrate the spontaneous
breakdown of the hypothesized discrete symmetry there are no extant demonstrations
that have more than a hand waving force.”
If we compare our analysis of the Goldstone theorem with the Earman’s multi-tier
reflection, it is obvious that the whole chain ends at the second tier, i.e. the Goldstone
bosons have not been suppressed after all. The rest is nothing but metaphysics. In fact
Higgs named his Nobel lecture “Evading the Goldstone theorem” [97], but this was
no evasion rather a total misreading of this theorem. Anderson’s stimulating paper
[95] was indeed an incorrect marking, misleading Higgs and his co-authors on a lost
course.
11 The Paradox of the Centre of Mass of Quantum Systems
In this section we will show an independent proof of the Goldstone theorem for condensed matter, molecules and solids. Since the original Goldstone-Salam-Weinberg
proof [92] is admittedly the most general, it is not, for the purpose of this study,
sufficiently transparent regarding the fundamental question of the one-to-one correspondence between broken symmetries and associated massless and spinless bosons.
The problem of translational and rotational symmetry violations in solids is a nice
example.
Solid state physics has adopted some adequate patterns from quantum electrodynamics. The quantum field electron-photon Feynman diagrammatic technique has
found many successful applications in solid state electron-phonon treatments. Many
years ago, when I finished my studies in solid state physics, I did start to work in
a quantum chemistry department. In this environment quantum field methods are
not so often exercised in comparison to its use in solid state physics, and moreover
mostly on the fermionic electron-hole level. At that time I was familiar with the works
of Czech emigrants Paldus and ˇ
Cížek, who were inspired by Goldstone’s revision
[98] of Brueckner’s many-body theory [99] with the solution expressed in a manner
that avoids the problem of unlinked clusters, introducing Goldstone’s diagrammatic
electron-hole mechanism into quantum chemistry [100].
The goal of my Ph.D. thesis [101] was to introduce, in a diagrammatic treatment, the full electron-phonon interactions into quantum chemistry, i.e. to elaborate
the mathematical framework for second quantization of the full electron-vibrational
Hamiltonian. Goldstone’s theorem was at first beyond my interest, since it was mostly
discussed in the domain of elementary particle physics, but hardly not mentioned
at the time in solid state physics and quantum chemistry. As a result, I thought that
electron-phonon mechanisms really constituted a complete description of solids, i.e.
exactly how we learned in school as it was described in all textbooks.
325
issue since there is no symmetry to break. In the latter case it is possible that the
discrete symmetry is spontaneously broken. But the usual argument for symmetry
breaking using the conserved Noether current does not apply. And while it is possible
that some completely different sort of construction will demonstrate the spontaneous
breakdown of the hypothesized discrete symmetry there are no extant demonstrations
that have more than a hand waving force.”
If we compare our analysis of the Goldstone theorem with the Earman’s multi-tier
reflection, it is obvious that the whole chain ends at the second tier, i.e. the Goldstone
bosons have not been suppressed after all. The rest is nothing but metaphysics. In fact
Higgs named his Nobel lecture “Evading the Goldstone theorem” [97], but this was
no evasion rather a total misreading of this theorem. Anderson’s stimulating paper
[95] was indeed an incorrect marking, misleading Higgs and his co-authors on a lost
course.
11 The Paradox of the Centre of Mass of Quantum Systems
In this section we will show an independent proof of the Goldstone theorem for condensed matter, molecules and solids. Since the original Goldstone-Salam-Weinberg
proof [92] is admittedly the most general, it is not, for the purpose of this study,
sufficiently transparent regarding the fundamental question of the one-to-one correspondence between broken symmetries and associated massless and spinless bosons.
The problem of translational and rotational symmetry violations in solids is a nice
example.
Solid state physics has adopted some adequate patterns from quantum electrodynamics. The quantum field electron-photon Feynman diagrammatic technique has
found many successful applications in solid state electron-phonon treatments. Many
years ago, when I finished my studies in solid state physics, I did start to work in
a quantum chemistry department. In this environment quantum field methods are
not so often exercised in comparison to its use in solid state physics, and moreover
mostly on the fermionic electron-hole level. At that time I was familiar with the works
of Czech emigrants Paldus and ˇ
Cížek, who were inspired by Goldstone’s revision
[98] of Brueckner’s many-body theory [99] with the solution expressed in a manner
that avoids the problem of unlinked clusters, introducing Goldstone’s diagrammatic
electron-hole mechanism into quantum chemistry [100].
The goal of my Ph.D. thesis [101] was to introduce, in a diagrammatic treatment, the full electron-phonon interactions into quantum chemistry, i.e. to elaborate
the mathematical framework for second quantization of the full electron-vibrational
Hamiltonian. Goldstone’s theorem was at first beyond my interest, since it was mostly
discussed in the domain of elementary particle physics, but hardly not mentioned
at the time in solid state physics and quantum chemistry. As a result, I thought that
electron-phonon mechanisms really constituted a complete description of solids, i.e.
exactly how we learned in school as it was described in all textbooks.