Related papers: Free fermions and tau-functions
The Jordan-Wigner transformation is frequently utilised to rewrite quantum spin chains in terms of fermionic operators. When the resulting Hamiltonian is bilinear in these fermions, i.e. the fermions are free, the exact spectrum follows…
We introduce a novel approach for computing the twist operator correlators (TOC) in two-dimensional conformal field theories (2d CFT) and the closely related isomonodromic tau functions. The method stems from the formal path integral…
We derive the bosonization rules for free fermions on a half-line with physically sensible boundary conditions for Luttinger fermions. We use path-integral methods to calculate the bosonized fermionic currents on the half-line and derive…
Given a semisimple Frobenius manifold, we construct a class of integrable deformations of its hierarchy of topological type. We show that these integrable deformations have polynomial tau-structures, and conjecture that for the…
Parafermions that generalize (Majorana or usual) fermions appear as interacting quasi-particles because of their nature. Although attempts to develop models with free (non-interacting) parafermions have been undertaken, existing proposals…
In this paper combinatorial aspects of normal ordering arbitrary words in the creation and annihilation operators of the q-deformed boson are discussed. In particular, it is shown how by introducing appropriate q-weights for the associated…
We present exactly solvable modifications of the two-matrix Zinn-Justin-Zuber model and write it as a tau function. The grand partition function of these matrix integrals is written as the fermion expectation value. The perturbation theory…
The Clifford algebra of the endomorphisms of the exterior algebra of a countably dimensional vector space induces natural bosonic shadows, i.e. families of linear maps between the cohomologies of complex grassmannians. The main result of…
We construct theories of free fermions in $(2n-1)$-dimensions with $SU(1,n)$ spacetime symmetry from the null reduction of fermions on a $2n$-dimensional $\Omega$-deformed Minkowski background for $n=2$ and $n=3$. These play a role in the…
We compare different versions of a bosonic description for systems of interacting fermions, with particular emphasis on the free energy functional. The bosonic effective action makes the issue of symmetries particularly transparent and we…
We connect twisted vertex operator presentation of Hall-Littlewood polynomials with the action of charged free fermions, describe a boson-fermion correspondence that relates twisted vertex operators with classical Heisenberg algebra. We…
For the massless sine-Gordon model at the free fermion point, in infinite volume, we define the fractional (charge or vertex operator) correlation functions from the probabilistic path integral and prove that they are given by renormalized…
In a previous paper we have shown how, for bosonic fields, the generating functional in both relativistic quantum field theory and thermal field theory can be evaluated by use of a standard quantum mechanical path integral. In this paper we…
In this article we are concerned with finite dimensional Fermions, by which we mean vectors in a finite dimensional complex space embedded in the exterior algebra over itself. These Fermions are spinless but possess the characterizing…
The application of functional integral methods and the Hubbard--Stratonovich transformation to the Hubbard model is discussed. For the attractive case, using a simple gauge transformation of the superconducting order parameter field, the…
We consider the Itzykson-Zuber-Eynard-Mehta two-matrix model and prove that the partition function is an isomonodromic tau function in a sense that generalizes Jimbo-Miwa-Ueno's. In order to achieve the generalization we need to define a…
We carry out a systematic study of primary operators in the conformal field theory of a free Weyl fermion. Using SO(4,2) characters we develop counting formulas for primaries constructed using a fixed number of fermion fields. By…
A higher dimensional analogue of the dispersionless KP hierarchy is introduced. In addition to the two-dimensional ``phase space'' variables $(k,x)$ of the dispersionless KP hierarchy, this hierarchy has extra spatial dimensions…
We study a specific class of CFTs that involve coupled free fermions, arising from parafermion CFTs and lattice constructions. We analyse their representation spaces and the underlying exclusion statistics of coupled free fermions using…
Using the Weyl-Tetrode-Fock spinor formalism, the fermion triplet in the 't Hooft-Polyakov monopole field is examined all over again. Spherical solutions corresponding to the total conserved momentum J =l + S + T are constructed. The…