The spin-1 equivalent homomorphism of group SU(2) to group SO(3) from observer’s mathematics point of view

Boris Khots; Dmitriy Khots

doi:10.1117/12.2591817

1 August 2021 The spin-1 equivalent homomorphism of group SU(2) to group SO(3) from observer’s mathematics point of view

Boris Khots, Dmitriy Khots

Author Affiliations +

Proceedings Volume 11805, Spintronics XIV; 118051R (2021) https://doi.org/10.1117/12.2591817
Event: SPIE Nanoscience + Engineering, 2021, San Diego, California, United States

Abstract

This paper considers homomorphism of the Lie group SU(2) to the Lie group SO(3) of all rotations of 3- dimensional Euclidean space from Observers Mathematics point of view. In our work, we proved that in Observers Mathematics the probability of spin-j transformation is a homomorphism (representation) of SU(2 ) to the set of matrix transformations of a linear space of polynomial functions is less than 1, and got corresponding results for elementary fermions and bosons. As a continuation of these results we proved here the following theorems: Theorem 1. In Observers Mathematics the probability of two-to-one transformation of SU(2) to SO(3) is Lie groups homomorphism (representation) is less than 1. Theorem 2. The probability of two-to-one transformation and spin-j transformation (j = 1) are equivalent in Observers Mathematics is less than 1.

Conference Presentation

Citation Download Citation

Boris Khots and Dmitriy Khots "The spin-1 equivalent homomorphism of group SU(2) to group SO(3) from observer’s mathematics point of view", Proc. SPIE 11805, Spintronics XIV, 118051R (1 August 2021); https://doi.org/10.1117/12.2591817

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available