Related papers: A novel general mapping for bosonic and fermionic …
Transfer operators offer linear representations and global, physically meaningful features of nonlinear dynamical systems. Discovering transfer operators, such as the Koopman operator, require careful crafted dictionaries of observables,…
We explore a generalization of nonrelativistic fermionic statistics that interpolates between bosons and fermions, in which up to $K$ particles may occupy a single-particle state. We show that it can be mapped exactly to $K$ flavors of…
Two-component spinors are the basic ingredients for describing fermions in quantum field theory in four space-time dimensions. We develop and review the techniques of the two-component spinor formalism and provide a complete set of Feynman…
We find a representation for the determinant of a Dirac operator in an even number $D= 2 n$ of Euclidean dimensions as an overlap between two different vacua, each one corresponding to a bosonic theory with a quadratic action in $2 n + 1$…
We derive general form of finite-dimensional approximations of path integrals for both bosonic and fermionic canonical systems in terms of symbols of operators determined by operator ordering. We argue that for a system with a given quantum…
We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…
We address the problem of the bosonization of finite fermionic systems with two different approaches. First we work in the path integral formalism, showing how a truly bosonic effective action can be derived from a generic fermionic one…
The topology of two-dimensional movement allows for existing of anyons -- particles obeying statistics intermediate between that of bosons and fermions. In this article, the functional form of the occupation numbers of free anyons is…
The generalized massive Thirring model (GMT) with $N_{f}$[=number of positive roots of $su(n)$] fermion species is bosonized in the context of the functional integral and operator formulations and shown to be equivalent to a generalized…
We present a strategy for mapping the dynamics of a fermionic quantum system to a set of classical dynamical variables. The approach is based on imposing the correspondence relation between the commutator and the Poisson bracket, preserving…
We introduce analogs of creation and annihilation operators, related to involutive and Hecke symmetries R, and perform bosonic and fermionic realization of the modified Reflection Equation algebras in terms of the so-called Quantum Doubles…
Particles made of two fermions can in many cases be treated as elementary bosons, but the conditions for this treatment to be valid are nontrivial. The so-called "coboson formalism" is a powerful tool to tackle compositeness effects…
We describe coherent states and associated generalized Grassmann variables for a system of $m$ independent $q$-boson modes. A resolution of unity in terms of generalized Berezin integrals leads to generalized Grassmann symbolic calculus.…
We prove the formula for the traces of certain class of operators in bosonic and fermionic Fock spaces. Vertex operators belong to this class. Traces of vertex operators can be used for calculation of correlation functions and formfactors…
Compact representations of fermionic Hamiltonians are necessary to perform calculations on quantum computers that lack error-correction. A fermionic system is typically defined within a subspace of fixed particle number and spin while…
We study statistical signatures of composite bosons made of two fermions using a new many-body approach. Extending number-states to composite bosons, two-particle correlations as well as the dispersion of the probability distribution are…
We realize the Weil representation of infinite dimensional symplectic group and spinor representation of infinite-dimensional group $GL$ by linear operators in the space of symmetric functions in infinite number of variables.
We propose a new unified theoretical framework to construct equivalent representations of the multi-state Hamiltonian operator and present several approaches for the mapping onto the Cartesian phase space. After mapping an F-dimensional…
Dynamical and non-dynamical components of the 20-component wave function are separated in the generalized Dirac equation of the first order, describing fermions with spin 1/2 and two mass states. After the exclusion of the non-dynamical…
Integrable sl(N) spin chains, which we consider in this paper, are not only the prototypical example of quantum integrable systems but also systems with a wide range of applications. For these models we use the Functional Separation of…