Abstract Using the Coleman (‐Fröhlich‐Seiler) theorem we have mapped chargeless sectors of some (generalized) Yukawa‐Thirring‐(Schwinger) two‐dimensional models onto pure Bose theories. Discussion of certain correlation inequalities in this framework is made. In particular, we proved that the first and second Griffiths‐Kelly‐Shermann correlation inequalities hold. Correlation inequalities suggest that there is on phase transition of the first order in scalar versions of these models. Some results on the D‐L‐R equations for these models are established, confirming previous suggestion.Abstract Using the Coleman (‐Fröhlich‐Seiler) theorem we have mapped chargeless sectors of some (generalized) Yukawa‐Thirring‐(Schwinger) two‐dimensional models onto pure Bose theories. Discussion of certain correlation inequalities in this framework is made. In particular, we proved that the first and second Griffiths‐Kelly‐Shermann correlation inequalities hold. Correlation inequalities suggest that there is on phase transition of the first order in scalar versions of these models. Some results on the D‐L‐R equations for these models are established, confirming previous suggestion.

Fortschritte der PhysikJan 1, 19861 citation

Properties of ideal fermion systems

Erhard Hantzsche

Jan 1, 19950 citations

Reflection positivity and quantum Griffiths' inequalities

Tadahiro Miyao

We propose a new method of constructing the quantum Griffiths inequality. From a viewpoint of operator inequalities, we first study the quantum rotor model. This viewpoint clarifies important connections between the reflection positivity and the Griffiths inequality. Next we apply our method to the spin- $1/2$ quantum Heisenberg model. Finally we point out a model-independent structure which governs the correlation inequalities.We propose a new method of constructing the quantum Griffiths inequality. From a viewpoint of operator inequalities, we first study the quantum rotor model. This viewpoint clarifies important connections between the reflection positivity and the Griffiths inequality. Next we apply our method to the spin-$1/2$ quantum Heisenberg model. Finally we point out a model-independent structure which governs the correlation inequalities.

arXiv:1504.06676Apr 25, 20150 citations

Comment on "Nonlocality claims are inconsistent with Hilbert-space quantum mechanics"

Justo Pastor Lambare

The view exists that the Bell inequality is a mere inconsistent application of classical concepts to a well-established quantum world. In the article, ``Nonlocality claims are inconsistent with Hilbert-space quantum mechanics'' [Phys. Rev. A, 101, 022117, (2020)], Robert B. Griffiths advocates for quantum theory's locality. Although R. B. Griffiths presents valuable insights in favor of quantum mechanics' local character, he argues the Bell inequality is an inconsistent application of classical physics to quantum mechanics. We explain why a correct assessment of the Bell inequality does not in fact conflict with Griffiths's views of quantum locality and, on the contrary, it already contemplates them. Hence, Bell inequality inconsistency is not necessary for Griffiths's quantum locality to hold.The view exists that the Bell inequality is a mere inconsistent application of classical concepts to a well-established quantum world. In the article, ``Nonlocality claims are inconsistent with Hilbert-space quantum mechanics'' [Phys. Rev. A, 101, 022117, (2020)], Robert B. Griffiths advocates for quantum theory's locality. Although R. B. Griffiths presents valuable insights in favor of quantum mechanics' local character, he argues the Bell inequality is an inconsistent application of classical physics to quantum mechanics. We explain why a correct assessment of the Bell inequality does not in fact conflict with Griffiths's views of quantum locality and, on the contrary, it already contemplates them. Hence, Bell inequality inconsistency is not necessary for Griffiths's quantum locality to hold.

arXiv:2102.07524Feb 15, 20215 citations

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quantum Heisenberg model. Finally we point out a model-independent structure which governs the correlation inequalities.