The quon algebra describes particles, ``quons,'' that are neither fermions nor bosons. The parameter $q$ attached to a quon labels a smooth interpolation between bosons ( $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}+1$ ) and fermions ( $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1$). Wigner and Ehrenfest and Oppenheimer showed that a composite system of identical bosons and fermions is a fermion if it contains an odd number of fermions and is a boson otherwise. We generalize this and show that ${q}_{\mathrm{composite}}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}q}_{\mathrm{constituent}}^{{n}^{2}}$ for a system of $n$ identical quons. Using this generalization, we find bounds on possible violations of the Pauli exclusion principle for nucleons and quarks based on such bounds for nuclei.The quon algebra describes particles, ``quons,'' that are neither fermions nor bosons. The parameter $q$ attached to a quon labels a smooth interpolation between bosons ( $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}+1$) and fermions ( $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1$). Wigner and Ehrenfest and Oppenheimer showed that a composite system of identical bosons and fermions is a fermion if it contains an odd number of fermions and is a boson otherwise. We generalize this and show that ${q}_{\mathrm{composite}}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}q}_{\mathrm{constituent}}^{{n}^{2}}$ for a system of $n$ identical quons. Using this generalization, we find bounds on possible violations of the Pauli exclusion principle for nucleons and quarks based on such bounds for nuclei.

arXiv:quant-ph/9903020Physical Review LettersNov 29, 199939 citations

Fermion Condensation: Theory and Experiment

VICTOR A. KHODEL, J. W. Clark, MIKHAIL V. ZVEREV

Fundamentals of fermion-condensation physics are outlined. Fermion condensation is a phase transition occurring in a strongly correlated Fermi system upon a topological reconstruction of the Landau ground state and leading to the formation of a fermion condensate that possesses the dispersionless single-particle spectrum $\epsilon({\mathbf{p}})=0$ in the momentum-space region adjacent to the Fermi surface and, accordingly, an anomalously enhanced density of single-particle states. A original method is developed for solving the set of nonlinear integral equations of fermion-condensation theory. This method makes it possible to analyze the problem of quantum chaos in strongly interacting multifermion systems. The computational technique used is demonstrated by applying it to superdense quark–gluon plasma, where the structure of exchange quark–quark interaction is well known. In electron systems featuring a fermion condensate, the magnitude of the gap appearing in the single-particle spectrum owing to Cooper pairing is shown to be much larger than that in Bardeen–Cooper–Schrieffer (BCS) theory. This explains both a high superconducting-transition temperature $T_{c}$ and, with allowance for $C_{4}$ crystal-lattice symmetry, the $D$ -wave pairing-gap structure observed in cuprates. It is found that, in addition to the BCS gap $\Delta$ , the spectrum of single-particle excitations of superconducting systems where a fermion condensate is present develops a nonsuperconducting gap $\Upsilon$ that owes its existence to the interaction of condensate particles with normal quasiparticles residing outside the condensate region in momentum space. The question of whether these results are pertinent to the two-gap structure recently unearthed in the excitation spectrum of cuprates upon analyzing ARPES data is addressed.Fundamentals of fermion-condensation physics are outlined. Fermion condensation is a phase transition occurring in a strongly correlated Fermi system upon a topological reconstruction of the Landau ground state and leading to the formation of a fermion condensate that possesses the dispersionless single-particle spectrum $$\epsilon({\mathbf{p}})=0$$ in the momentum-space region adjacent to the Fermi surface and, accordingly, an anomalously enhanced density of single-particle states. A original method is developed for solving the set of nonlinear integral equations of fermion-condensation theory. This method makes it possible to analyze the problem of quantum chaos in strongly interacting multifermion systems. The computational technique used is demonstrated by applying it to superdense quark–gluon plasma, where the structure of exchange quark–quark interaction is well known. In electron systems featuring a fermion condensate, the magnitude of the gap appearing in the single-particle spectrum owing to Cooper pairing is shown to be much larger than that in Bardeen–Cooper–Schrieffer (BCS) theory. This explains both a high superconducting-transition temperature $$T_{c}$$ and, with allowance for $$C_{4}$$ crystal-lattice symmetry, the $$D$$ -wave pairing-gap structure observed in cuprates. It is found that, in addition to the BCS gap $$\Delta$$ , the spectrum of single-particle excitations of superconducting systems where a fermion condensate is present develops a nonsuperconducting gap $$\Upsilon$$ that owes its existence to the interaction of condensate particles with normal quasiparticles residing outside the condensate region in momentum space. The question of whether these results are pertinent to the two-gap structure recently unearthed in the excitation spectrum of cuprates upon analyzing ARPES data is addressed.

Physics of Atomic NucleiMar 1, 20200 citations

On the Relation between Fermions and Bosons

Morikazu TODA

Total mean curvature and submanifolds of finite typeOct 1, 19930 citations

When Can Two Fermions Be Characterized as a Boson

Christina Knapp

Bulletin of the American Physical SocietyNov 9, 20120 citations

Entangled Simultaneous Measurement and Elementary Particle Representations

Robert Y. Levin, Victor Dannon

We propose that the principles of relativistic quantum mechanics are incomplete for simultaneous measurement of non-commuting operators. Consistent joint measurement of incompatible observables at a single point in space-time requires that the system be in an entangled state with vacuum meters. We suggest that entagled simultaneous mesurement for noncommuting observables is the basis for the observed fermionic multiplets. This generalizes the standard spin representations for particles arising from Lorentz invariance. We show that operator entanglement for all quantum observables in the Poincare algebra, coupled with Fermi-Dirac statistics, mandates six fermions. We propose that the quark and lepton generations form a super-structure of the Poincare algebra based on the principles of entangled simultaneity. Mathematically, that super-structure is known as a Naimark extension. The required entanglement between particle generations for left-handed quarks is observed in the Cabbibo-Kobayashi-maskawa matrix. We show that the Naimark-extended von Neumann lattice is ditributive, thereby suggesting the principle of entangled simultaneity as a mechanism to avoid quantum non-locality. Keywords: enatangled simultaneous quantum measurement, Naimark extension, Lepton/quark generations. PACS Number: 03.65.BZWe propose that the principles of relativistic quantum mechanics are incomplete for simultaneous measurement of non-commuting operators. Consistent joint measurement of incompatible observables at a single point in space-time requires that the system be in an entangled state with vacuum meters. We suggest that entagled simultaneous mesurement for noncommuting observables is the basis for the observed fermionic multiplets. This generalizes the standard spin representations for particles arising from Lorentz invariance. We show that operator entanglement for all quantum observables in the Poincare algebra, coupled with Fermi-Dirac statistics, mandates six fermions. We propose that the quark and lepton generations form a super-structure of the Poincare algebra based on the principles of entangled simultaneity. Mathematically, that super-structure is known as a Naimark extension. The required entanglement between particle generations for left-handed quarks is observed in the Cabbibo-Kobayashi-maskawa matrix. We show that the Naimark-extended von Neumann lattice is ditributive, thereby suggesting the principle of entangled simultaneity as a mechanism to avoid quantum non-locality. Keywords: enatangled simultaneous quantum measurement, Naimark extension, Lepton/quark generations. PACS Number: 03.65.BZ

arXiv:hep-th/0005177May 19, 20001 citation

The quon algebra describes particles, ``quons,'' that are neither fermions nor bosons. The parameter

q

attached to a quon labels a smooth interpolation between bosons (

q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}+1

) and fermions ( $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1$). Wigner and Ehrenfest and Oppenheimer showed that a composite system of identical bosons and fermions is a fermion if it contains an odd number of fermions and is a boson otherwise. We generalize this and show that

{q}_{\mathrm{composite}}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}q}_{\mathrm{constituent}}^{{n}^{2}}

for a system of

n

identical quons. Using this generalization, we find bounds on possible violations of the Pauli exclusion principle for nucleons and quarks based on such bounds for nuclei.

\epsilon({\mathbf{p}})=0

in the momentum-space region adjacent to the Fermi surface and, accordingly, an anomalously enhanced density of single-particle states. A original method is developed for solving the set of nonlinear integral equations of fermion-condensation theory. This method makes it possible to analyze the problem of quantum chaos in strongly interacting multifermion systems. The computational technique used is demonstrated by applying it to superdense quark–gluon plasma, where the structure of exchange quark–quark interaction is well known. In electron systems featuring a fermion condensate, the magnitude of the gap appearing in the single-particle spectrum owing to Cooper pairing is shown to be much larger than that in Bardeen–Cooper–Schrieffer (BCS) theory. This explains both a high superconducting-transition temperature

T_{c}

and, with allowance for

C_{4}

crystal-lattice symmetry, the

D

-wave pairing-gap structure observed in cuprates. It is found that, in addition to the BCS gap

\Delta

, the spectrum of single-particle excitations of superconducting systems where a fermion condensate is present develops a nonsuperconducting gap

\Upsilon

that owes its existence to the interaction of condensate particles with normal quasiparticles residing outside the condensate region in momentum space. The question of whether these results are pertinent to the two-gap structure recently unearthed in the excitation spectrum of cuprates upon analyzing ARPES data is addressed.