The Quantum Nature of Lorentz Invariance

• Main Author: Richard Kerner
• Format: Article
• Language: English
• Published: MDPI AG 2018-12-01
• Series: Universe
• Subjects: quark model; Z3-graded algebras; color dynamics; Dirac’s equation; Loretnz invariance
• Online Access: https://www.mdpi.com/2218-1997/5/1/1

If the reality underlying classical physics is quantum in nature, then it is reasonable to assume that the transformations of fields, currents, energy, and momentum observed macroscopically are the result of averaging of symmetry groups acting in the Hilbert space of quantum states of elementary constituents of which classical material bodies are formed. We show how Pauli&#8217;s exclusion principle based on the discrete <inline-formula> <math display="inline"> <semantics> <msub> <mi>Z</mi> <mn>2</mn> </msub> </semantics> </math> </inline-formula> symmetry group generates the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>S</mi> <mi>L</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mi mathvariant="bold">C</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula> symmetry of the space of states of an electron endowed with spin. Then, we generalize this reasoning in the case of quark colors and the corresponding <inline-formula> <math display="inline"> <semantics> <msub> <mi>Z</mi> <mn>3</mn> </msub> </semantics> </math> </inline-formula> symmetry. A ternary generalization of Dirac&#8217;s equation is proposed, leading to self-confined quarks states. It is shown how certain cubic or quadratic combinations can form freely-propagating entangled states. The entire symmetry of the standard model, <inline-formula> <math display="inline"> <semantics> <mrow> <mi>S</mi> <mi>U</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>&#215;</mo> <mi>U</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>&#215;</mo> <mi>S</mi> <mi>U</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>, is naturally derived, as well.