Related papers: Fermionic determinant for SU(N) caloron with nontr…
In contrast to the determinant, no algorithm is known for the exact determination of the permanent of a square matrix that runs in time polynomial in its dimension. Consequently, non interacting fermions are classically efficiently…
We consider path integration of a fermionic oscillator with a one-parameter family of boundary conditions with respect to the time coordinate. The dependence of the fermion determinant on these boundary conditions is derived in a closed…
We consider the determination of the finite temperature phase transition in the Yang--Mills SU(3) gauge theory. We compute the difference of the spatial and temporal energy density at a physical Wilson flow time. This difference is zero in…
We compute the multiplicity of the irreducible representations in the decomposition of the tensor product of an arbitrary number $n$ of fundamental representations of $SU(N)$, and we identify a duality in the representation content of this…
Recently, we found the supersymmetric counterpart of the spectral triple. When we restrict the representation space to the fermionic functions of matter fields, the counterpart which we name "the triple" reduces to the original spectral…
We study the topological structure of QCD by cluster analysis. The fermionic topological charge density is constructed from low lying modes of overlap Dirac operator for three types of temporal boundary conditions for fermion field. This…
We investigate experimental consequences of the postulate that fundamentally photon propagation is governed by an SU(2) rather than a U(1) gauge principle. In the context of thermodynamics the SU(2) Yang-Mills theory is assumed to be in its…
We review several fermionic-type character formulae for the characters of the integrable highest weight modules of sl(n)^ at level l=1, and explain how they arise from a spinon basis for these modules. We also review how the Yangian…
The general conditions for the Chern-Simons action to be induced as a nonuniversal contribution of fermionic determinant are formulated in the finite temperature lattice QCD. The dependence of the corresponding action coefficient on…
Based on the chiral symmetry breaking pattern and the corresponding low-energy effective lagrangian, we determine the fermion mass dependence of the partition function and derive sum rules for eigenvalues of the QCD Dirac operator in finite…
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 $2 n + 1$…
Functional determinants of differential operators play a prominent role in theoretical and mathematical physics, and in particular in quantum field theory. They are, however, difficult to compute in non-trivial cases. For one dimensional…
Cosmological solutions with a homogeneous Yang-Mills field which oscillates and passes between topologically distinct vacua are discussed. These solutions are used to model the collapsing Bartnik-McKinnon gravitational sphaleron and the…
An analytical and nonperturbative approach to SU(2) and SU(3) Yang-Mills thermodynamics is developed and applied. Each theory comes in three phases: A deconfining, a preconfining, and a confining one. We show how macroscopic and inert…
We perform a lattice calculation of the Schr\"odinger functional running coupling in SU(2) Yang-Mills theory with six massless Wilson fermions in the fundamental representation. The aim of this work is to determine whether the above theory…
As well as arising naturally in the study of non-intersecting random paths, random spanning trees, and eigenvalues of random matrices, determinantal point processes (sometimes also called fermionic point processes) are relatively easy to…
The framework of shifted boundary conditions has proven to be a very powerful tool for the non-perturbative investigation of thermal quantum field theories. For instance, it has been successfully considered for the determination of the…
The aim of this paper is to offer an algebraic construction of infinite-dimensional Grassmannians and determinant bundles (and therefore valid for arbitrary base fields). As an application we construct the $\tau$-function and formal…
The integral of a function $f$ defined on a symmetric space $M \simeq G/K$ may be expressed in the form of a determinant (or Pfaffian), when $f$ is $K$-invariant and, in a certain sense, a tensor power of a positive function of a single…
A representation for the fermionic determinant of the massive Schwinger model, or $QED_2$, is obtained that makes a clean separation between the Schwinger model and its massive counterpart. From this it is shown that the index theorem for…