Related papers: Two deformations of a fermionic solution to pentag…
The theoretical treatment of Fermi systems consisting of particles with unequal masses is challenging. Even in one spatial dimension analytic solutions are limited to special configurations and numerical progress with Monte Carlo…
Functional renormalization group (FRG) is applied to the three-body scattering problem in the two-component fermionic system with an attractive contact interaction. We establish a new and correct flow equation on the basis of FRG and show…
We find a system of two polynomial equations in two unknowns, whose solution allows to give an explicit expression of the conformal representation of a simply connected three sheeted compact Riemann surface onto the extended complex plane.…
We consider three Ginibre ensembles (real, complex and quaternion-real) with a deformed measure and relate them to the known integrable systems via presenting partition functions of these ensembles in form of fermionic expectation values.…
This note is purely expositional and is a complement to math review MR2730150 to the paper Bel'kov, S. I.; Korepanov, I. G. Matrix solution of the pentagon equation with anticommuting variables, Teoret. i Matemat. Fizika, 163:3 (2010),…
Non-homogeneous gauge ground state solutions in a six-dimensional gauge model in the presence of non-zero extended fermionic charge density fluctuations are reviewed and fully reinterpreted.
Conventional descriptions of higher-spin fermionic gauge fields appear in two varieties: the Aragone-Deser-Vasiliev frame-like formulation and the Fang-Fronsdal metric-like formulation. We review, clarify and elaborate on some essential…
Unitary transformations play a fundamental role in many-body physics, and except for special cases, they are not expressible in closed form. We present closed-form expressions for unitary transformations generated by a single fermionic…
We find an explicit form of weak solutions to a Riemann problem for a degenerate semilinear parabolic equation with piecewise constant diffusion coefficient. It is demonstrated that the phase transition lines (free boundaries) correspond to…
Spin asymmetry of the ground states is studied for the trapped spin-degenerate (two-component) gases of the fermionic atoms with the repulsive interaction between different components, and, for large particle number, the asymmetric…
The two-dimensional Ising model is representable as a lattice free-fermion field theory in terms of the integral over anticommuting Grassmann variables. The exact solution in a zero magnetic field then follows by evaluating Gaussian…
We deduce the structure of the Dirac field on the lattice from the discrete version of differential geometry and from the representation of the integral Lorentz transformations. The analysis of the induced representations of the Poincare…
To solve the spinor-spinor Bethe-Salpeter equation in Euclidean space we propose a novel method related to the use of hyperspherical harmonics. We suggest an appropriate extension to form a new basis of spin-angular harmonics that is…
We propose a nonlinear forward Feynman-Kac type equation, which represents the solution of a non-conservative semilinear parabolic Partial Differential Equations (PDE). We show in particular existence and uniqueness. The solution of that…
In this work we present a formal solution of the extended version of the Friedrichs Model. The Hamiltonian consists of discrete and continuum bosonic states, which are coupled to fermions. The simultaneous treatment of the couplings of the…
Systems of fermions with multiple internal states, such as quarks in quantum chromodynamics and nucleons in nuclear matter, are at the heart of some of the most complex quantum many-body problems. The stability of such many-body…
An estimate on the operator norm of an abstract fermionic renormalization group map is derived. This abstract estimate is applied in another paper to construct the thermodynamic Green's functions of a two dimensional, weakly coupled fermion…
We consider imbalanced Fermi gases with strong attractive interactions, for which Cooper-pair formation plays an important role. The two-component mixtures consist either of identical fermionic atoms in two different hyperfine states, or of…
Berezin integration over fermionic degrees of freedom as a standard tool of quantum field theory is analysed from the viewpoint of noncommutative geometry. It is shown that among the variety of contradictory integration prescriptions…
We investigate composite models of gravity and explore how dynamical tensor fields can emerge within the functional renormalization group framework. We consider two prototype models: a fermionic theory and a scalar theory. In both cases, an…