Related papers: Superbosonisation, Riesz superdistributions, and h…
There has been substantial calculational progress in the last few years for gauge theory amplitudes which involve massless four dimensional particles. One of the central ingredients in this has been the ability to keep precise track of the…
We study the hardness of classically simulating Gaussian boson sampling at nonzero photon distinguishability. We find that similar to regular boson sampling, distinguishability causes exponential attenuation of the many-photon interference…
This paper describes the expected characteristic polynomial of the commutator of randomly rotated matrices, in the context of the finite free probability theory initiated by Marcus, Spielman, and Srivastava. The key technical features are…
We describe two distinct approaches for bosonization in higher dimensions; one is based on a direct comparison of current correlation functions while the other relies on a Master lagrangean formalism. These are used to bosonise the Massive…
We present a new formulation of Lagrangian perturbation theory which allows accurate predictions of the real- and redshift-space correlation functions of the mass field and dark matter halos. Our formulation involves a non-perturbative…
We show that abelian bosonization of 1+1 dimensional fermion systems can be interpreted as duality transformation and, as a conseguence, it can be generalized to arbitrary dimensions in terms of gauge forms of rank $d-1$, where $d$ is the…
We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract…
In the first part of my talk I will explain a solution to the extension of Lie's problem on classification of "local continuous transformation groups of a finite-dimensional manifold" to the case of supermanifolds. (More precisely, the…
We introduce sparse polynomial zonotopes, a new set representation for formal verification of hybrid systems. Sparse polynomial zonotopes can represent non-convex sets and are generalizations of zonotopes, polytopes, and Taylor models.…
This paper combines algebraic and Lagrangian geometry to construct a special basis in every space of conformal blocks, the Bohr-Sommerfeld (BS) basis. We use the method of [D. Borthwick, T. Paul and A. Uribe, Legendrian distributions with…
We study the ultraviolet problem for models of a finite-dimensional quantum mechanical system linearly coupled to a bosonic quantum field, such as the (many-)spin boson model or its rotating-wave approximation. If the state change of the…
Quantum integrable models that possess $N=2$ supersymmetry are investigated on the half-space. Conformal perturbation theory is used to identify some $N=2$ supersymmetric boundary integrable models, and the effective boundary…
We review the relation between compact asymptotic spectral measures and certain positive asymptotic morphism on locally compact spaces via asymptotic Riesz representation theorem, as introduced by Martinez and Trout [3]. Applications to…
A free boson on a lattice is the simplest field theory one can think of. Its partition function can be easily computed in momentum space. However, this straightforward solution hides its integrability properties. Here, we use the methods of…
We investigate light propagation through materials with periodically modulated gain/loss profile in both transverse and longitudinal directions, i.e. in material with two-dimensional modulation in space. We predict effects of…
The first part of this paper explains what super-integrability is and how it differs in the classical and quantum cases. This is illustrated with an elementary example of the resonant harmonic oscillator. For Hamiltonians in "natural form",…
Assuming that there exist operators which form an irreducible representation of the q-superoscillator algebra, it is proved that any two such representations are equivalent, related by a uniquely determined superunitary transformation. This…
Quantum integrable models that possess $N=2$ supersymmetry are investigated on the half-space. Conformal perturbation theory is used to identify some $N=2$ supersymmetric boundary integrable models, and the effective boundary…
Relativistic resonances and decaying states are described by representations of Poincar\'e transformations, similar to Wigner's definition of stable particles. To associate decaying state vectors to resonance poles of the $S$-matrix, the…
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…