Correlation functions of charged free boson and fermion systems
Bibliographic record
Abstract
Abstract Using the idea of the quantum inverse scattering method, we introduce the operators B ( x ), C ( x ) and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi mathvariant="bold">B</mml:mi> </mml:mrow> <mml:mo>̃</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mi>x</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mo>,</mml:mo> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi mathvariant="bold">C</mml:mi> </mml:mrow> <mml:mo>̃</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mi>x</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> corresponding to the off-diagonal entries of the monodromy matrix T for the phase model and i -boson model in terms of bc fermions and neutral fermions respectively, thus giving alternative treatment of the KP and BKP hierarchies. We also introduce analogous operators B *( x ) and C *( x ) for the charged free boson system and show that they are in complete analogy to those of bc fermionic fields. It is proved that the correlation function ⟨0| C ( x N )⋯ C ( x 1 ) B ( y 1 )⋯ B ( y N )|0⟩ in the bc fermionic fields is the inverse of the correlation function ⟨0| C *( x N )⋯ C *( x 1 ) B *( y 1 )⋯ B *( y N )|0⟩ in the charged free bosons.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".