## Quantum Mechanics Where Spin is SO(3)

**Authors:** Carl A. Brannen

In 2014 Steven Weinberg noted that quantum mechanics can avoid various difficulties, such as the many worlds hypothesis, by taking the quantum states to be density matrices without reference to state vectors. An immediate consequence of Weinberg's idea is that electron spin can be taken to follow SO(3) instead of SU(2). This radical departure from present understanding motivates our exploration of density matrices as a method of going beyond the Standard Model.
An important tool for Standard Model calculations is the Feynman path integral formulation of quantum field theory. When the path integral is Wick rotated from time to imaginary time or temperature it becomes a method of cooling down density matrices. While this does not show that one goes beyond the Standard Model by Wick rotation, it does show a close relation between this method of cooling density matrices and quantum field theory of the Standard Model. We explore these ideas and exhibit toy models with particle content and symmetry similar to the Standard Model.

**Comments:** 23 Pages.

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### Submission history

[v1] 2019-03-29 11:50:58

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