Internal supersymmetry and unification.

Area of Science:

• Mathematical Physics
• High Energy Physics

Background:

• Superalgebraic representations are crucial for theoretical physics models.
• Understanding particle charges requires specific algebraic structures.

Purpose of the Study:

• To construct finite-dimensional representations of the superalgebra sl(n/m).
• To model elementary particles and their charges using these representations.
• To identify parameter choices that yield known quark and lepton charges.

Main Methods:

• Constructing representations of sl(n/m) superalgebras.
• Defining particle models based on commuting operators for weak isospin (I(3)) and hypercharge (U).
• Applying the electric charge formula Q = I(3) + (1/2)U.

Main Results:

• Developed representations dependent on integer or complex parameters.
• Identified two specific parameter sets for sl(n/1) that exactly reproduce all 32 quark and lepton charges.
• Demonstrated a general construction for sl(n/1) representations yielding particle generations.

Conclusions:

• The superalgebra sl(n/1) provides a framework for generating particle generations.
• Specific choices of weak isospin and hypercharge operators within this framework precisely account for observed particle charges.
• This work offers a unified approach to particle charge quantization.