Related papers: Bosonic formulas for (k,l)-admissible partitions
We obtain the fermionic formulas for the characters of (k, r)-admissible configurations in the case of r=2 and r=3. This combinatorial object appears as a label of a basis of certain subspace $W(\Lambda)$ of level-$k$ integrable highest…
We derive general formulae for computing the average spectrum for Bosonic or Fermionic massless emission from generic or particular sets of closed superstring quantum states, among the many occurring at a given large value of the number…
The divergences that arise in the regularized partition function for closed bosonic string theory in flat space lead to three types of perturbation series expansions, distinguished by their genus dependence. This classification of…
A new formalism for generation of solutions in the consistently truncated low-energy bosonic string theory is developed. This formalism gives a correspondence of the projection type between the theories toroidally compactified from the…
Quantum walks on lattices can give rise to relativistic wave equations in the long-wavelength limit, but going beyond the single-particle case has proven challenging, especially in more than one spatial dimension. We construct quantum…
We find nonlocal particle theories with two dimensional conformal symmetry, including examples equivalent to the bosonic open string and closed string. This work provides a new approach to construct solvable consistent backgrounds in string…
We produce graded monoidal categorifications of the quantum boson algebras in any symmetrizable Kac-Moody type. Our categories are defined in terms of diagrammatic generators and relations and have a faithful 2-representation on…
A class of rational solutions of Toda lattice satisfying certain Backlund transformations and a class of mixed rational-soliton solutions (quasisolitons) in wronskian formare obtained using the method of Ablowitz and Satsuma. Also an…
Four classes of three dimensional quadratic algebras of the type $\lsb Q_0 , Q_\pm \rsb$ $=$ $\pm Q_\pm$, $\lsb Q_+ , Q_- \rsb$ $=$ $aQ_0^2 + bQ_0 + c$, where $(a,b,c)$ are constants or central elements of the algebra, are constructed using…
We formulate the soliton equations on the lattice in terms of the reduced Moyal algebra which includes one parameter. The vanishing limit of the parameter leads to the continuous soliton equations.
Quantum simulation of quantum field theory is a flagship application of quantum computers that promises to deliver capabilities beyond classical computing. The realization of quantum advantage will require methods to accurately predict…
In many physical applications, bound states and/or resonances are observed, which raises the question whether these states are elementary or composite. Here we elaborate on several methods for calculating the compositeness $X$ of bound…
We present novel approaches to the dynamics of an open quantum system coupled linearly to a non-Markovian fermionic or bosonic environment. In the first approach, we obtain a hierarchy of stochastic evolution equations of the diffusion…
Categories of partitions are combinatorial structures arising from the representation theory of certain compact quantum groups and are linked to classical diagram algebras such as the Temperley-Lieb algebra. In this paper, we present…
In the paper, the authors present several new relations and applications for the combinatorial sequence that counts the possible partitions of a finite set with the restriction that the size of each block is contained in a given set. One of…
A formula which only involves a partition number and elementary functions is derived by applying Burnside's Lemma to the set of idempotent maps from a set to itself. One side involves a summation over a set closely related to the partition…
We describe a unified approach to calculating the partition functions of a general multi-level system with a free Hamiltonian. Particularly, we present new results for parastatistical systems of any order in the second quantized approach.…
For $n$ and $k$ integers we introduce the notion of some partition of $n$ being able to generate another partition of $n$. We solve the problem of finding the minimum size partition for which the set of partitions this partition can…
Using shift vector method we obtain a large class of self-dual lattices of dimension $(l,l)$, which has a one to one correspondence with modular invariants of free bosonic theory compactified on co-root lattice of a rank $l$ Lie group. Then…
Plane partitions naturally appear in many problems of statistical physics and quantum field theory, for instance, in the theory of faceted crystals and of topological strings on Calabi-Yau threefolds. In this paper a connection is made…