Related papers: Systematic study of the completeness of two-dimens…
In a seminal paper (Weitz, 2006), Weitz gave a deterministic fully polynomial approximation scheme for count- ing exponentially weighted independent sets (equivalently, approximating the partition function of the hard-core model from…
An investigation of classical fields with fractional derivatives is presented using the fractional Hamiltonian formulation. The fractional Hamilton's equations are obtained for two classical field examples. The formulation presented and the…
We exploit a recently constructed mapping between quantum circuits and graphs in order to prove that circuits corresponding to certain planar graphs can be efficiently simulated classically. The proof uses an expression for the Ising model…
An effective quantum field theory of the 2D Hubbard model on a square lattice near half-filling is presented and studied. This effective model describes so-called nodal and antinodal fermions, and it is derived from the lattice model using…
We give a general definition of classical and quantum groups whose representation theory is "determined by partitions" and study their structure. This encompasses many examples of classical groups for which Schur-Weyl duality is described…
Classical (maximal) superintegrable systems in $n$ dimensions are Hamiltonian systems with $2n-1$ independent constants of the motion, globally defined, the maximum number possible. They are very special because they can be solved…
There are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries. We study the finite and infinite irreducible…
It is widely believed that the parity of the partition function $p(n)$ is ``random.'' Contrary to this expectation, in this note we prove the existence of infinitely many congruence relations modulo 4 among its values. For each square-free…
This paper is a sequel to one in which we examined the affine symmetry algebras of arbitrary classical principal chiral models and symmetric space models in two dimensions. It examines the extension of those results in the presence of…
We compute the partition function and specific heat for a quantum mechanical particle under the influence of a quartic double-well potential non-perturbatively, using the semiclassical method. Near the region of bounded motion in the…
The spherical field formalism---a nonperturbative approach to quantum field theory---was recently introduced and applied to phi^4 theory in two dimensions. The spherical field method reduces a quantum field theory to a finite-dimensional…
We introduce a new notation for representing labeled regular bipartite graphs of arbitrary degree. Several enumeration problems for labeled and unlabeled regular bipartite graphs have been introduced. A general algorithm for enumerating all…
The notion of quantum-mechanical completeness is adapted to situations where the only adequate description is in terms of quantum field theory in curved space-times. It is then shown that Schwarzschild black holes, although geodesically…
The exactly solvable four-vertex model with the fixed boundary conditions in the presence of inhomogeneous linearly growing external field is considered. The partition function of the model is calculated and represented in the determinantal…
The partition function for a system of non-interacting $N-$particles can be found by summing over all the states of the system. The classical partition function for an ideal gas differs from Bosonic or Fermionic partition function in the…
Standard Model with a classical conformal invariance holds the promise to give a better understanding of the hierarchy problem and could pave the way for beyond the standard model physics. So, we give here a mathematical treatment of a…
Duality theorems play a fundamental role in convex optimization. Recently, it was shown how duality theorems for countable probability distributions and finite-dimensional quantum states can be leveraged for building relatively complete…
In a previous work, we established perturbative renormalizability to all orders of the massive $\phi^4_4$-theory on a half-space also called the semi-infinite massive $\phi^4_4$-theory. Five counter-terms which are functions depending on…
In a sequence of four papers, we prove the following results (via a unified approach) for all sufficiently large $n$: (i) [1-factorization conjecture] Suppose that $n$ is even and $D \geq 2\lceil n/4\rceil -1$. Then every $D$-regular graph…
The free Schroedinger theory in d space dimensions is a non-relativistic conformal field theory. The interacting non-linear theory preserves this symmetry in specific numbers of dimensions at the classical (tree) level. This holds in…