We reconsider the Mott transition in the context of a two-dimensional fermion model with density-density coupling. We exhibit a Hilbert space mapping between the original model and the Double Lattice Chern-Simons theo...We reconsider the Mott transition in the context of a two-dimensional fermion model with density-density coupling. We exhibit a Hilbert space mapping between the original model and the Double Lattice Chern-Simons theory at the critical point by use of the representation theory of the q-oscillator and Weyl algebras. The transition is further characterized by the ground state modification. The explicit mapping provides a new tool to further probe and test the detailed physical properties of the fermionic lattice model considered here and to enhance our understanding of the Mott transition(s).展开更多
In this article, we revisit some aspects of the computation of the cohomology class of H2 (Witt, C)?using some methods in two-dimensional conformal field theory and conformal algebra to obtain the one-dimensional cent...In this article, we revisit some aspects of the computation of the cohomology class of H2 (Witt, C)?using some methods in two-dimensional conformal field theory and conformal algebra to obtain the one-dimensional central extension of the Witt algebra to the Virasoro algebra. Even though this is well-known in the context of standard mathematical physics literature, the operator product expansion of the energy-momentum tensor in two-dimensional conformal field theory is presented almost axiomatically. In this paper, we attempt to reformulate it with the help of a suitable modification of conformal algebra (as developed by V. Kac), and apply it to compute the representative element of the cohomology class which gives the desired central extension. This paper was written in the scope of an undergraduate’s exploration of conformal field theory and to gain insight on the subject from a mathematical perspective.展开更多
Fermion mass is modeled as an analogue of Weyl curvature, which by hypothesis emerges when closed, spin-2 strings sweep out closed world tubes. Second order curvature classes result when closed world tubes circulate a...Fermion mass is modeled as an analogue of Weyl curvature, which by hypothesis emerges when closed, spin-2 strings sweep out closed world tubes. Second order curvature classes result when closed world tubes circulate and themselves sweep out closed tubes etc. Gauge invariance distinguishes admissible curvature classes from the larger set that would constitute an infinite continuum of possibilities. Admissible curvature classes account for known quark masses and predict a new quark of mass 30 GeV/c2. Super-symmetric interactions among prescribed fermions and super-partners conserve electrical charge, I3, color and generation and are therefore regarded by hypothesis as preserving a minimal irreducible representation of a super-symmetric SU(5).展开更多
AdS/CFT correspondence is adopted and fermion masses are modeled as analogues of Weyl curvature states, which occur by hypothesis when closed spin-2 strings sweep out closed world tubes. Admissible curvature states ar...AdS/CFT correspondence is adopted and fermion masses are modeled as analogues of Weyl curvature states, which occur by hypothesis when closed spin-2 strings sweep out closed world tubes. Admissible curvature states are established by gauge invariance and fundamental mass is attributed to admissible curvature. A consequent spectrum of masses forms an SU(3) symmetry that is invariant under appropriate realizations of the SUGRA GUT interaction. Finally the spin-h/2 nature of the masses that are attributed to curvature emerges as a necessary condition for the relevant SUGRA GUT realizations. Calibration of the proposed model reveals a spectrum of fermion masses that corresponds approximately to observation. Moreover, the proposed model predicts a new quark that is characterized by I3 = -1/2 and by a mass of about 30 GeV/c2.展开更多
Conformational elasticity theory recently developed has been used to explore the internal energy contribution to the elastic force f(e)/f as a function of strain for poly(cis-1,4-isoprene) and poly(trans-1,4-isoprene)...Conformational elasticity theory recently developed has been used to explore the internal energy contribution to the elastic force f(e)/f as a function of strain for poly(cis-1,4-isoprene) and poly(trans-1,4-isoprene). Calculated f(e)/f values are in good agreement with those obtained experimentally. Results show that behavior of f(e)/f is mainly contributed by chemical structure, or intramolecular interaction, supporting the experimental observations, and that the internal energy contribution is strain dependent.展开更多
Conformational elasticity theory recently developed has been used to explore the internal energy contribution to the elastic force fe/f as a function of strain for polyethylene (PE). Calculated fe/f values are in good...Conformational elasticity theory recently developed has been used to explore the internal energy contribution to the elastic force fe/f as a function of strain for polyethylene (PE). Calculated fe/f values are in good agreement with those obtained experimentally. Results show that the behavior of fe/f is mainly contributed from intramolecular interaction of chemical structure, and that the internal energy contribution is strain-dependent.展开更多
We calculate the contributions of a general non-vacuum conformal family to R′enyi entropy in twodimensional conformal field theory（CFT）. The primary operator of the conformal family can be either non-chiral or chir...We calculate the contributions of a general non-vacuum conformal family to R′enyi entropy in twodimensional conformal field theory（CFT）. The primary operator of the conformal family can be either non-chiral or chiral, and we denote its scaling dimension by ？. For the case of two short intervals on a complex plane, we expand the R′enyi mutual information by the cross ratio x to order x^（2△＋2）. For the case of one interval on a torus with low temperature, we expand the R′enyi entropy by q = exp（-2πβ/L）, with β being the inverse temperature and L being the spatial period, to order q^（△＋2）. To make the result meaningful, we require that the scaling dimension ？ cannot be too small. For two intervals on a complex plane we need △ 〉 1, and for one interval on a torus we need △ 〉 2.We work in the small Newton constant limit on the gravity side and so a large central charge limit on the CFT side,and find matches of gravity and CFT results.展开更多
Conformational elasticity theory of chain molecule" proposed by our group was used to explore the contribution of internal energy to elastic force( f e/f ). 1,4 Polybutadiene( cis and tran ) were studied. The cal...Conformational elasticity theory of chain molecule" proposed by our group was used to explore the contribution of internal energy to elastic force( f e/f ). 1,4 Polybutadiene( cis and tran ) were studied. The calculated f e/f for cis polymer is consistent with experimental data, while a little difference for the trans polymer, which needs more experimental data to support. The results also show that f e/ f is dependent on chemical structure and strain.展开更多
This paper shows how increased entropy values from an initially low big bang level can be measured experimentally by counting relic gravitons. Furthermore the physical mechanism of this entropy increase is explained v...This paper shows how increased entropy values from an initially low big bang level can be measured experimentally by counting relic gravitons. Furthermore the physical mechanism of this entropy increase is explained via analogies with early-universe phase transitions. The role of Ng’s revised infinite quantum statistics in the physics of gravitational wave detection is acknowledged. Ng’s infinite quantum statistics can be used to show that is a starting point to the increasing net universe cosmological entropy. Finally, in a nod to similarities with zero point energy (ZPE) analysis, it is important to note that the resulting in fact is much lower, allowing for evaluating initial graviton production as an emergent field phenomena, which may be similar to how ZPE states can be used to extract energy from a vacuum if entropy is not maximized. The rapid increase in entropy so alluded to without near sudden increases to 10<sup>88</sup> may be enough to allow successful modeling of relic graviton production for entropy in a manner similar to zero point energy (ZPE) energy extraction from a vacuum state. This entropy count is akin to quantum information models used to tell how much “information” may be stored in initial conditions, and transferred from a prior to the present展开更多
文摘We reconsider the Mott transition in the context of a two-dimensional fermion model with density-density coupling. We exhibit a Hilbert space mapping between the original model and the Double Lattice Chern-Simons theory at the critical point by use of the representation theory of the q-oscillator and Weyl algebras. The transition is further characterized by the ground state modification. The explicit mapping provides a new tool to further probe and test the detailed physical properties of the fermionic lattice model considered here and to enhance our understanding of the Mott transition(s).
文摘In this article, we revisit some aspects of the computation of the cohomology class of H2 (Witt, C)?using some methods in two-dimensional conformal field theory and conformal algebra to obtain the one-dimensional central extension of the Witt algebra to the Virasoro algebra. Even though this is well-known in the context of standard mathematical physics literature, the operator product expansion of the energy-momentum tensor in two-dimensional conformal field theory is presented almost axiomatically. In this paper, we attempt to reformulate it with the help of a suitable modification of conformal algebra (as developed by V. Kac), and apply it to compute the representative element of the cohomology class which gives the desired central extension. This paper was written in the scope of an undergraduate’s exploration of conformal field theory and to gain insight on the subject from a mathematical perspective.
文摘Fermion mass is modeled as an analogue of Weyl curvature, which by hypothesis emerges when closed, spin-2 strings sweep out closed world tubes. Second order curvature classes result when closed world tubes circulate and themselves sweep out closed tubes etc. Gauge invariance distinguishes admissible curvature classes from the larger set that would constitute an infinite continuum of possibilities. Admissible curvature classes account for known quark masses and predict a new quark of mass 30 GeV/c2. Super-symmetric interactions among prescribed fermions and super-partners conserve electrical charge, I3, color and generation and are therefore regarded by hypothesis as preserving a minimal irreducible representation of a super-symmetric SU(5).
文摘AdS/CFT correspondence is adopted and fermion masses are modeled as analogues of Weyl curvature states, which occur by hypothesis when closed spin-2 strings sweep out closed world tubes. Admissible curvature states are established by gauge invariance and fundamental mass is attributed to admissible curvature. A consequent spectrum of masses forms an SU(3) symmetry that is invariant under appropriate realizations of the SUGRA GUT interaction. Finally the spin-h/2 nature of the masses that are attributed to curvature emerges as a necessary condition for the relevant SUGRA GUT realizations. Calibration of the proposed model reveals a spectrum of fermion masses that corresponds approximately to observation. Moreover, the proposed model predicts a new quark that is characterized by I3 = -1/2 and by a mass of about 30 GeV/c2.
基金This project has been supported by the National Natural Science Foundation of China, 863 High Technology Project, Special Funds for Major State Basic Research Project (G1999064800).
文摘Conformational elasticity theory recently developed has been used to explore the internal energy contribution to the elastic force f(e)/f as a function of strain for poly(cis-1,4-isoprene) and poly(trans-1,4-isoprene). Calculated f(e)/f values are in good agreement with those obtained experimentally. Results show that behavior of f(e)/f is mainly contributed by chemical structure, or intramolecular interaction, supporting the experimental observations, and that the internal energy contribution is strain dependent.
基金This work was supported by the National Natural Science Foundation of China (Grant Nos. 29874035 and 20074041), the "863" High Technology Project, and the Special Funds for the State Major Basic Research Project (Grant No. G1999064800).
文摘Conformational elasticity theory recently developed has been used to explore the internal energy contribution to the elastic force fe/f as a function of strain for polyethylene (PE). Calculated fe/f values are in good agreement with those obtained experimentally. Results show that the behavior of fe/f is mainly contributed from intramolecular interaction of chemical structure, and that the internal energy contribution is strain-dependent.
基金Supported by ERC Starting Grant 637844-HBQFTNCER
文摘We calculate the contributions of a general non-vacuum conformal family to R′enyi entropy in twodimensional conformal field theory（CFT）. The primary operator of the conformal family can be either non-chiral or chiral, and we denote its scaling dimension by ？. For the case of two short intervals on a complex plane, we expand the R′enyi mutual information by the cross ratio x to order x^（2△＋2）. For the case of one interval on a torus with low temperature, we expand the R′enyi entropy by q = exp（-2πβ/L）, with β being the inverse temperature and L being the spatial period, to order q^（△＋2）. To make the result meaningful, we require that the scaling dimension ？ cannot be too small. For two intervals on a complex plane we need △ 〉 1, and for one interval on a torus we need △ 〉 2.We work in the small Newton constant limit on the gravity side and so a large central charge limit on the CFT side,and find matches of gravity and CFT results.
文摘Conformational elasticity theory of chain molecule" proposed by our group was used to explore the contribution of internal energy to elastic force( f e/f ). 1,4 Polybutadiene( cis and tran ) were studied. The calculated f e/f for cis polymer is consistent with experimental data, while a little difference for the trans polymer, which needs more experimental data to support. The results also show that f e/ f is dependent on chemical structure and strain.
文摘This paper shows how increased entropy values from an initially low big bang level can be measured experimentally by counting relic gravitons. Furthermore the physical mechanism of this entropy increase is explained via analogies with early-universe phase transitions. The role of Ng’s revised infinite quantum statistics in the physics of gravitational wave detection is acknowledged. Ng’s infinite quantum statistics can be used to show that is a starting point to the increasing net universe cosmological entropy. Finally, in a nod to similarities with zero point energy (ZPE) analysis, it is important to note that the resulting in fact is much lower, allowing for evaluating initial graviton production as an emergent field phenomena, which may be similar to how ZPE states can be used to extract energy from a vacuum if entropy is not maximized. The rapid increase in entropy so alluded to without near sudden increases to 10<sup>88</sup> may be enough to allow successful modeling of relic graviton production for entropy in a manner similar to zero point energy (ZPE) energy extraction from a vacuum state. This entropy count is akin to quantum information models used to tell how much “information” may be stored in initial conditions, and transferred from a prior to the present
