LeClair-Mussardo series for two-point functions in Integrable QFT

We develop a well-defined spectral representation for two-point functions in relativistic Integrable QFT in finite density situations, valid for space-like separations. The resulting integral series is based on the infinite volume, zero density form factors of the theory, and certain statistical functions related to the distribution of Bethe roots in the finite density background. Our final formulas are checked by comparing them to previous partial results obtained in a low-temperature expansion. It is also show that in the limit of large separations the new integral series factorizes into the product of two LeClair-Mussardo series for one-point functions, thereby satisfying the clustering requirement for the two-point function.Comment: 27 pages, v2: minor modifications, a note and a reference adde

New Fundamental Symmetries of Integrable Systems and Partial Bethe Ansatz

We introduce a new concept of quasi-Yang-Baxter algebras. The quantum quasi-Yang-Baxter algebras being simple but non-trivial deformations of ordinary algebras of monodromy matrices realize a new type of quantum dynamical symmetries and find an unexpected and remarkable applications in quantum inverse scattering method (QISM). We show that applying to quasi-Yang-Baxter algebras the standard procedure of QISM one obtains new wide classes of quantum models which, being integrable (i.e. having enough number of commuting integrals of motion) are only quasi-exactly solvable (i.e. admit an algebraic Bethe ansatz solution for arbitrarily large but limited parts of the spectrum). These quasi-exactly solvable models naturally arise as deformations of known exactly solvable ones. A general theory of such deformations is proposed. The correspondence ``Yangian --- quasi-Yangian'' and ``$XXX$ spin models --- quasi-$XXX$ spin models'' is discussed in detail. We also construct the classical conterparts of quasi-Yang-Baxter algebras and show that they naturally lead to new classes of classical integrable models. We conjecture that these models are quasi-exactly solvable in the sense of classical inverse scattering method, i.e. admit only partial construction of action-angle variables.Comment: 49 pages, LaTe

Electronic Journal of Theoretical Physics A New Procedure to Understanding Formulas of Generalized Quantum Mean Values for a Composite

Abstract: Herein is presented a research concerning to the calculation of quantum mean values, for a composite A + B, by using different formulas to expressions in Boltzmann-Gibbs-Shannon’s statistics. It is analyzed why matrix formulas with matrices EA and EB, in Hilbert subspaces, produce identical results to full Hilbert space formulas. In accord to former investigations, those matrices are the true density matrices, inside third version of nonextensive statistical mechanics. Those investigations were obtained by calculating the thermodynamical parameters of magnetization and internal energy for magnetic materials. This publication shows that it is not necessary postulate the mean value formulas in Hilbert subspaces, but they can be formally derived from full Hilbert space, taking into consideration the very statistical independence concept

Microscopic derivation of Ginzburg-Landau theories for hierarchical quantum Hall states

We propose a Ginzburg-Landau theory for a large and important part of the abelian quantum Hall hierarchy, including the prominently observed Jain sequences. By a generalized "flux attachment" construction we extend the Ginzburg-Landau-Chern-Simons composite boson theory to states obtained by both quasielectron and quasihole condensation, and express the corresponding wave functions as correlators in conformal field theories. This yields a precise identification of the relativistic scalar fields entering these correlators in terms of the original electron field.Comment: Submission to SciPost; added comments and reference

Theory of higher spin tensor currents and central charges

We study higher spin tensor currents in quantum field theory. Scalar, spinor and vector fields admit unique "improved" currents of arbitrary spin, traceless and conserved. Off-criticality as well as at interacting fixed points conservation is violated and the dimension of the current is anomalous. In particular, currents J^(s,I) with spin s between 0 and 5 (and a second label I) appear in the operator product expansion of the stress tensor. The TT OPE is worked out in detail for free fields; projectors and invariants encoding the space-time structure are classified. The result is used to write and discuss the most general OPE for interacting conformal field theories and off-criticality. Higher spin central charges c_(s,I) with arbitrary s are defined by higher spin channels of the many-point T-correlators and central functions interpolating between the UV and IR limits are constructed. We compute the one-loop values of all c_(s,I) and investigate the RG trajectories of quantum field theories in the conformal window following our approach. In particular, we discuss certain phenomena (perturbative and nonperturbative) that appear to be of interest, like the dynamical removal of the I-degeneracy. Finally, we address the problem of formulating an action principle for the RG trajectory connecting pairs of CFT's as a way to go beyond perturbation theory.Comment: Latex, 46 pages, 4 figures. Final version, to appear in NPB. (v2: added two terms in vector OPE

Lie-Nambu and beyond

Linear quantum mechanics can be regarded as a particular example of a nonlinear Nambu-type theory. Some elements of this approach are presented.Comment: revtex; an extended version of the talk given at the workshop "Actual problems in quantum mechanics", Peyresq, July, 199

Excitation Spectrum and Collective Modes of Composite Fermions

According to the composite fermion theory, the interacting electron system at filling factor $\nu$ is equivalent to the non-interacting composite fermion system at $\nu^*=\nu/(1-2m\nu)$, which in turn is related to the non-interacting electron system at $\nu^*$. We show that several eigenstates of non-interacting electrons at $\nu^*$ do not have any partners for interacting electrons at $\nu$, but, upon composite fermion transformation, these states are eliminated, and the remaining states provide a good description of the spectrum at $\nu$. We also show that the collective mode branches of incompressible states are well described as the collective modes of composite fermions. Our results suggest that, at small wave vectors, there is a single well defined collective mode for all fractional quantum Hall states. Implications for the Chern-Simons treatment of composite fermions will be discussed.Comment: Revtex. 25 pages. Postscript files of figures is appended to the pape

Variational Principle of Bogoliubov and Generalized Mean Fields in Many-Particle Interacting Systems

The approach to the theory of many-particle interacting systems from a unified standpoint, based on the variational principle for free energy is reviewed. A systematic discussion is given of the approximate free energies of complex statistical systems. The analysis is centered around the variational principle of N. N. Bogoliubov for free energy in the context of its applications to various problems of statistical mechanics and condensed matter physics. The review presents a terse discussion of selected works carried out over the past few decades on the theory of many-particle interacting systems in terms of the variational inequalities. It is the purpose of this paper to discuss some of the general principles which form the mathematical background to this approach, and to establish a connection of the variational technique with other methods, such as the method of the mean (or self-consistent) field in the many-body problem, in which the effect of all the other particles on any given particle is approximated by a single averaged effect, thus reducing a many-body problem to a single-body problem. The method is illustrated by applying it to various systems of many-particle interacting systems, such as Ising and Heisenberg models, superconducting and superfluid systems, strongly correlated systems, etc. It seems likely that these technical advances in the many-body problem will be useful in suggesting new methods for treating and understanding many-particle interacting systems. This work proposes a new, general and pedagogical presentation, intended both for those who are interested in basic aspects, and for those who are interested in concrete applications.Comment: 60 pages, Refs.25