Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10, випуск за цей рікhttp://dspace.nbuv.gov.ua:80/handle/123456789/1460242024-03-28T15:47:51Z2024-03-28T15:47:51ZWhy Do the Relativistic Masses and Momenta of Faster-than-Light Particles Decrease as their Speeds Increase?Madarász, J.X.Stannett, M.Székely, G.http://dspace.nbuv.gov.ua:80/handle/123456789/1468522019-02-11T23:24:06Z2014-01-01T00:00:00ZWhy Do the Relativistic Masses and Momenta of Faster-than-Light Particles Decrease as their Speeds Increase?
Madarász, J.X.; Stannett, M.; Székely, G.
It has recently been shown within a formal axiomatic framework using a definition of four-momentum based on the Stückelberg-Feynman-Sudarshan-Recami ''switching principle'' that Einstein's relativistic dynamics is logically consistent with the existence of interacting faster-than-light inertial particles. Our results here show, using only basic natural assumptions on dynamics, that this definition is the only possible way to get a consistent theory of such particles moving within the geometry of Minkowskian spacetime. We present a strictly formal proof from a streamlined axiom system that given any slow or fast inertial particle, all inertial observers agree on the value of m⋅√|1−v²|, where m is the particle's relativistic mass and v its speed. This confirms formally the widely held belief that the relativistic mass and momentum of a positive-mass faster-than-light particle must decrease as its speed increases.
2014-01-01T00:00:00ZThe Master T-Operator for Inhomogeneous XXX Spin Chain and mKP HierarchyZabrodin, A.http://dspace.nbuv.gov.ua:80/handle/123456789/1468512019-02-11T23:23:55Z2014-01-01T00:00:00ZThe Master T-Operator for Inhomogeneous XXX Spin Chain and mKP Hierarchy
Zabrodin, A.
Following the approach of [Alexandrov A., Kazakov V., Leurent S., Tsuboi Z., Zabrodin A., J. High Energy Phys. 2013 (2013), no. 9, 064, 65 pages, arXiv:1112.3310], we show how to construct the master T-operator for the quantum inhomogeneous GL(N) XXX spin chain with twisted boundary conditions. It satisfies the bilinear identity and Hirota equations for the classical mKP hierarchy. We also characterize the class of solutions to the mKP hierarchy that correspond to eigenvalues of the master T-operator and study dynamics of their zeros as functions of the spectral parameter. This implies a remarkable connection between the quantum spin chain and the classical Ruijsenaars-Schneider system of particles.
2014-01-01T00:00:00ZSymmetries and Special Solutions of Reductions of the Lattice Potential KdV EquationOrmerod, C.M.http://dspace.nbuv.gov.ua:80/handle/123456789/1468502019-02-11T23:24:13Z2014-01-01T00:00:00ZSymmetries and Special Solutions of Reductions of the Lattice Potential KdV Equation
Ormerod, C.M.
We identify a periodic reduction of the non-autonomous lattice potential Korteweg-de Vries equation with the additive discrete Painlevé equation with E₆⁽¹⁾ symmetry. We present a description of a set of symmetries of the reduced equations and their relations to the symmetries of the discrete Painlevé equation. Finally, we exploit the simple symmetric form of the reduced equations to find rational and hypergeometric solutions of this discrete Painlevé equation.
2014-01-01T00:00:00ZThe (n,1)-Reduced DKP Hierarchy, the String Equation and W ConstraintsJohan van de Leurhttp://dspace.nbuv.gov.ua:80/handle/123456789/1468492019-02-11T23:24:00Z2014-01-01T00:00:00ZThe (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints
Johan van de Leur
The total descendent potential of a simple singularity satisfies the Kac-Wakimoto principal hierarchy. Bakalov and Milanov showed recently that it is also a highest weight vector for the corresponding W-algebra. This was used by Liu, Yang and Zhang to prove its uniqueness. We construct this principal hierarchy of type D in a different way, viz. as a reduction of some DKP hierarchy. This gives a Lax type and a Grassmannian formulation of this hierarchy. We show in particular that the string equation induces a large part of the W constraints of Bakalov and Milanov. These constraints are not only given on the tau function, but also in terms of the Lax and Orlov-Schulman operators.
2014-01-01T00:00:00Z