Related papers: Fermion quadrature bases for Wigner functionals
We perform the complete bosonization of 2+1 dimensional QED with one fermionic flavor in the Hamiltonian formalism. The Fermi operators are explicitly constructed in terms of the vector potential and the electric field. We carefully specify…
The coupling of spin 0 and spin 1 external fields to Dirac fermions defines a theory which displays gauge chiral symmetry. Quantum mechanically, functional integration of the fermions yields the determinant of the Dirac operator, known as…
In a space of $d $ Grassmann coordinates two types of generators of Lorentz transformations can be defined, one of spinorial and the other of vectorial character. Both kinds of operators appear as linear operators in Grassmann space,…
In this paper we study dual bases functions in subspaces. These are bases which are dual to functionals on larger linear space. Our goal is construct and derive properties of certain bases obtained from the construction, with primary focus…
We formulate a general gauge invariant Lagrangian construction describing the dynamics of massive higher spin fermionic fields in arbitrary dimensions. Treating the conditions determining the irreducible representations of Poincare group…
The celebrated Jordan--Wigner transformation provides an efficient mapping between spin chains and fermionic systems in one dimension. Here we extend this spin-fermion mapping to arbitrary tree structures, which enables mapping between…
The probability distribution for finding a state of the radiation field in a particular phase is described by a multitude of theoretical formalisms; the phase-sensitivity of the Wigner quasi-probability distribution being one of them. We…
We further explore the idea that physics takes place in Clifford space which should be considered as a generalization of spacetime. Following the old observation that spinors can be represented as members of left ideals of Clifford algebra,…
Smoothed Wigner transforms have been used in signal processing, as a regularized version of the Wigner transform, and have been proposed as an alternative to it in the homogenization and / or semiclassical limits of wave equations. We…
We introduce the orthogonal Grassmannian as a novel kinematic space for describing correlators of massless spinning fields in de Sitter space. By automatically encoding the constraints of conformal symmetry and current conservation, the…
We consider macroscopic motion of quantum field systems. Zubarev statistical operator allows to describe several types of motion of such systems in thermal equilibrium. We formulate the corresponding effective theory on the language of…
We study the conformal bootstrap for a 4-point function of fermions $\langle\psi\psi\psi\psi\rangle$ in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in fermion 4-point functions.…
New time dependent Wigner functions for the quantum harmonic oscillator have been obtained in this work. The Moyal equation for the harmonic oscillator has been presented as the wave equation of a 2D membrane in the phase plane. The values…
The mathematical description of the quantum harmonic oscillator is essentially based on the Gaussian function. In the case of a quantum oscillator with finite-dimensional Hilbert space, the position space consists in a finite number of…
Exact characteristic trajectories are specified for the time-propagating Wigner phase-space distribution function. They are especially simple---indeed, classical---for the quantized simple harmonic oscillator, which serves as the…
Parafermions are emergent excitations which generalize Majorana fermions and are potentially relevant to topological quantum computation. Using the concept of Fock parafermions, we present a mapping between lattice $\mathbb{Z}_4$…
We use the fermionic construction of two-matrix model partition functions to evaluate integrals over rational symmetric functions. This approach is complementary to the one used in the paper ``Integrals of Rational Symmetric Functions,…
Spin chain Hamiltonians can be written in terms of complex differential operators using the Bargmann representation of the Jordan-Schwinger map. In this case, the eigenfunctions are expressed as the product of orthonormal monomials of the…
This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions and star-products, following a technique developed earlier, {\it viz\/,} using the unitary…
In this article, we explore the inconsistencies in the physics of fermionic oscillators and propose potential solutions to address them. By rigorously deriving the Hamiltonian and Lagrangian from first principles, we aim to provide a…