Related papers: A note on supersymmetry and stochastic differentia…
We give the classification of second-order polynomial SUSY Quantum Mechanics in one and two dimensions. The particular attention is paid to the irreducible supercharges which cannot be built by repetition of ordinary Darboux…
Sequences of canonical conservation laws and generalized symmetries for the lattice Boussinesq and the lattice modified Boussinesq systems are successively derived. The interpretation of these symmetries as differential-difference equations…
We present evidence that the supersymmetric matrix model of Marinari and Parisi represents the world-line theory of N unstable D-particles in type II superstring theory in two dimensions. This identification suggests that the matrix model…
We propose the symmetry reduction method of partial differential equations to the system of differential equations with fewer number of independent variables. We also obtain generalized sufficient conditions for the solution found by…
We discuss the interrelations between symmetry of an Ito stochastic differential equations (or systems thereof) and its integrability, extending in party results by R. Kozlov [J. Phys. A ${\bf 43}$ (2010) \& ${\bf 44}$ (2011)]. Together…
Real-valued differential forms on Berkovich analytic spaces were introduced by Chambert-Loir and Ducros in 'Formes diff\'erentielles r\'eelles et courants sur les espaces de Berkovich' using superforms on polyhedral complexes. We prove a…
In this paper, a supersymmetric extension of the polytropic gas dynamics equations is constructed through the use of a superspace involving two independent fermionic variables and two bosonic superfields. A superalgebra of symmetries of the…
Nous presentons une introduction aux concepts de la supersymetrie par l'intermediaire de trois exemples: (i) Mecanique quantique supersymetrique, (ii) Superalgebres de Lie, (iii) Superconnexions de Quillen. Les points communs a toutes ces…
We introduce a new class of numerical methods for solving McKean-Vlasov stochastic differential equations, which are relevant in the context of distribution-dependent or mean-field models, under super-linear growth conditions for both the…
In this paper, a supersymmetric extension of a system of hydrodynamic type equations involving Riemann invariants is formulated in terms of a superspace and superfield formalism. The symmetry properties of both the classical and…
New formulations of the solutions of N=1 and N=2 super Toda field theory are introduced, using Hamiltonian Reduction of the N=1 and N=2 super WZNW Models to the super Toda Models. These parameterisations are then used to present the…
After recalling basic features of the theory of symmetric quasi regular Dirichlet forms we show how by applying it to the stochastic quantization equation, with Gaussian space-time noise, one obtains weak solutions in a large invariant set.…
This paper is concerned with semi-linear backward stochastic partial differential equations (BSPDEs for short) of super-parabolic type. An $L^p$-theory is given for the Cauchy problem of BSPDEs, separately for the case of $p\in (1,2]$ and…
We introduce a class of second order backward stochastic differential equations and show relations to fully non-linear parabolic PDEs. In particular, we provide a stochastic representation result for solutions of such PDEs and discuss Monte…
We present the first example of an interacting Carroll supersymmetric field theory with both temporal and spatial derivatives, belonging to the Galileon class, where the non-linear field equation remains second-order in derivative. To…
An algorithm for studing the symmetrical properties of the partial differential equation of the type Lu=0 is proposed. By symmetry of this equation we mean the operators Q satisfying commutational relations of order p more than p=1 on the…
The 2D Euler equations are a simple but rich set of non-linear PDEs that describe the evolution of an ideal inviscid fluid, for which one dimension is negligible. Solving numerically these equations can be extremely demanding. Several…
General issues concerning the regularization of supersymmetric theories using dimensional regularization and dimensional reduction are reviewed. Recent progress on problems of dimensional reduction related to factorization, supersymmetry,…
We study the hidden symmetries arising in the dimensional reduction of d=5, N=2 supergravity to three dimensions. Extending previous partial results for the bosonic part, we give a derivation that includes fermionic terms, shedding light on…
This set of lectures contain a brief review of some basic supersymmetry and its representations, with emphasis on superspace and superfields. Starting from the Poincar\'e group, the supersymmetric extensions allowed by the Coleman-Mandula…