Fundamentals on the Noncommutative Plane

Abstract

Abstract:We consider the addition of charged matter ("fundametals") to noncommutative Yang-Mills theory and noncommutative QED, derive Feynman rules and tree-level potentials for them, and study the divergence structure of the theory. These particles behave very much as they do in the commutative theory, except that (1) they occupy bound-state wavefunctions which are essentially those of charged particles in magnetic fields, and (2) there is slight momentum nonconservation at vertices. There is no reduction in the degree of divergence of charged fermion loops like that which affects nonplanar noncommutative Yang-Mills diagrams.

Heisenberg Quantization for Systems of Identical Particles and the Pauli Exclusion Principle in Noncommutative Spaces

“…Recently there have been notable studies on the formulation and possible experimental consequences of extensions of the standard (usual) quantum mechanics in the noncommutative spaces [1][2][3][4][5][6][7][8][9][10][11][12][13]. Many physical problems have been studied in the framework of the noncommutative quantum mechanics (NCQM), see e.g.…”

Berry’s Phase in Noncommutative Spaces

“…Many physical problems have been studied in the framework of noncommutative quantum mechanics (NCQM), see e.g., [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. NCQM is formulated in the same way as standard quantum mechanics SQM (quantum mechanics in commutative spaces), that is in terms of the same dynamical variables represented by operators in a Hilbert space and a state vector that evolves according to the Schro¨dinger equation:…”