Related papers: S@M, a Mathematica Implementation of the Spinor-He…
Suppose that $\Sigma=\partial M$ is the $n$-dimensional boundary of a connected compact Riemannian spin manifold $( M,\langle\;,\;\rangle)$ with non-negative scalar curvature, and that the (inward) mean curvature $H$ of $\Sigma$ is…
We propose a "master" higher-spin (HS) particle system. The particle model relevant to the unfolded formulation of HS theory, as well as the HS particle model with a bosonic counterpart of supersymmetry, follow from the master model as its…
The Hilbert scheme $S^{[n]}$ of points on an algebraic surface $S$ is a simple example of a moduli space and also a nice (crepant) resolution of singularities of the symmetric power $S^{(n)}$. For many phenomena expected for moduli spaces…
We focus our attention on the spinor model proposed in an article by J. Magueijo et al. and we analyze it from the point of view of the cosmological background. We show that this model, under some conditions, can well-describe the…
We formalise the pi-calculus using the nominal datatype package, based on ideas from the nominal logic by Pitts et al., and demonstrate an implementation in Isabelle/HOL. The purpose is to derive powerful induction rules for the semantics…
Emerging computational paradigms, such as probabilistic and hybrid programming, introduce new primitive operations that often need to be combined with classic programming constructs. However, it still remains a challenge to provide a…
This work is a contribution to the area of Strict Quantization (in the sense of Rieffel) in the presence of curvature and non-Abelian group actions. More precisely, we use geometry to obtain explicit oscillatory integral formulae for…
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…
We describe TensoriaCalc, a tensor calculus package written to be smoothly consistent with the Wolfram Language, so as to ensure ease of usage. It allows multiple metrics to be defined in a given session; and, once a metric is computed,…
The article consists of the Russian and English variants of Ph.D. Thesis in which the answers is given on the following questions: 1. how to construct the spinor formalism for n=6; 2. how to construct the spinor formalism for n=8; 3. how to…
SMATASY is an interface for the ZFITTER package and may be used for the model independent description of the Z resonance at LEP 1 and SLC. It allows the determination of the Z mass and width and its resonance shape parameters r and j for…
For some research questions that involve Spin(p, q) representation theory, using symbolic algebra based techniques might be an attractive option for simplifying and manipulating expressions. Yet, for some such problems, especially as they…
This paper describes the design and implementation of mechanisms for light-weight inclusion of formal mathematics in informal mathematical writings, particularly in a Web-based setting. This is conceptually done in three stages: (i) by…
In this study, the properties of an oscillating system composed of a pendulum connected to a seesaw and placed on a moving platform with a certain slope are analyzed. Using complex numbers to collect the information contained in the system…
In this paper, we revisit the smoothness of the classical limit of inclusive observables in the formalism developed by Kosower, Maybee and O'Connell (KMOC). Building on the earlier work [1-3], we prove that the classical limit of three…
Same amplitudes evaluated independently using RNS and pure spinor formalism are expected to agree. While for massless states, this fact has been firmly established, for massive states such an explicit check has been lacking so far. We…
We present a program for the numerical evaluation of scalar integrals and tensor form factors entering the calculation of one-loop amplitudes which supports the use of complex masses in the loop integrals. The program is built on an earlier…
This paper contains a review of the theoretical foundations of Clifford algebras, spinors and spinor bundles in the so-called co-frame formalism. A compact index-free notation is introduced, along with a series of identities useful for…
We present a new variant of the spinor techniques for calculating the amplitudes of processes involving massive fermions with arbitrary polarization. It is relatively simple and leads to basic spinor products. Our procedure is not more…
The development of new electronic structure methods is a very time consuming and error prone process when done by hand. SpinAdaptedSecondQuantization is an open-source Julia package we have developed for working with automated electronic…