相关论文: Simplification Rules for Birdtrack Operators
I gently introduce the diagrammatic birdtrack notation, first for vector algebra and then for permutations. After moving on to general tensors I review some recent results on Hermitian Young operators, gluon projectors, and multiplet bases…
In this paper, we give a generic algorithm of the transition operators between Hermitian Young projection operators corresponding to equivalent irreducible representations of SU(N), using the compact expressions of Hermitian Young…
In this paper, we describe a compact and practical algorithm to construct Hermitian Young projection operators for irreducible representations of the special unitary group SU(N), and discuss why ordinary Young projection operators are…
We present an efficient preconditioner for the orbital minimization method when the Hamiltonian is discretized using planewaves (i.e., pseudospectral method). This novel preconditioner is based on an approximate Fermi operator projection by…
This paper presents the main features of a system that aims to transform regular expressions into shorter equivalent expressions. The system is also capable of computing other operations useful for simplification, such as checking the…
We describe the shape of the symplectic Dirac operators on Hermitian symmetric spaces. For this, we consider these operators as families of operators that can be handled more easily than the original ones.
Starting from conventional Young operators we construct Hermitian operators which project orthogonally onto irreducible representations of the (special) unitary group.
Sequential model synchronisation is the task of propagating changes from one model to another correlated one to restore consistency. It is challenging to perform this propagation in a least-changing way that avoids unnecessary deletions…
Harmonic oscillators with a centrifugal spike are analysed, via a non-Hermitian regularization, within a complexified SUSY quantum mechanics. The formalism enables us to construct the factorized creation and annihilation operators. We show…
Using the framework of operator or Calder\'on preconditioning, uniform preconditioners are constructed for elliptic operators discretized with continuous finite (or boundary) elements. The preconditioners are constructed as the composition…
The recently introduced concept of a spectral shift operator is applied in several instances. Explicit applications include Krein's trace formula for pairs of self-adjoint operators, the Birman-Solomyak spectral averaging formula and its…
The paper presents a REDUCE program for the simplification of tensor expressions that are considered as formal indexed objects. The proposed algorithm is based on the consideration of tensor expressions as vectors in some linear space. This…
We present a simple way to discretize and precondition mixed variational formulations. Our theory connects with, and takes advantage of, the classical theory of symmetric saddle point problems and the theory of preconditioning symmetric…
The idea that symmetries simplify or reduce the complexity of a system has been remarkably fruitful in physics, and especially in quantum mechanics. On a mathematical level, symmetry groups single out a certain structure in the Hilbert…
The theory of symmetric, non-selfadjoint operators has several deep applications to the complex function theory of certain reproducing kernel Hilbert spaces of analytic functions, as well as to the study of ordinary differential operators…
Exact diagonalization and other numerical studies of quantum spin systems are notoriously limited by the exponential growth of the Hilbert space dimension with system size. A common and well-known practice to reduce this increasing…
Retraction maps have been generalized to discretization maps in (Barbero Li\~n\'an and and Mart\'{\i}n de Diego, 2022). Discretization maps are used to systematically derive numerical integrators that preserve the symplectic structure, as…
Recently a perturbative theory has been constructed, starting from the Feynman rules of the nonlinear sigma model at the tree level in the presence of an external vector source coupled to the flat connection and of a scalar source coupled…
Constraint propagation is a general algorithmic approach for pruning the search space of a CSP. In a uniform way, K. R. Apt has defined a computation as an iteration of reduction functions over a domain. He has also demonstrated the need…
Suzuki-Trotter decompositions of exponential operators like $\exp(Ht)$ are required in almost every branch of numerical physics. Often the exponent under consideration has to be split into more than two operators, for instance as local…