Statistical mechanics of free particles on space with Lie type noncommutativity

Abstract

Effects of Lie type noncommutativity on thermodynamic properties of a system of free identical particles are investigated. A definition for finite volume of the configuration space is given, and the grandcanonical partition function in the thermodynamic limit is calculated. Two possible definitions for the pressure are discussed, which are equivalent when the noncommutativity vanishes. The thermodynamic observables are extracted from the partition function. Different limits are discussed where either the noncommutativity or the quantum effects are important. Finally specific cases are discussed where the group is SU(2) or SO(3), and the partition function of a nondegenerate gas is calculated.

1+14 pages; no figs

References in corpus (26)

• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• D-branes and the Noncommutative Torus
• Gauge Theory on Noncommutative Spaces
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• Quantum $\kappa$-Poincare in Any Dimensions
• Coproduct and star product in field theories on Lie-algebra non-commutative space-times
• Local D=4 Field Theory on $\kappa$--Deformed Minkowski Space
• Mixed Boundary Conditions and Brane-String Bound States
• Enlarged Bound on the Measurability of Distances and Quantum $\kappa$-Poincarè Group
• On $\kappa$-Deformation and UV/IR Mixing
• The UV/IR Interplay in Theories with Space-time Varying Non-commutativity
• Scalar field theories in a Lorentz-invariant three-dimensional noncommutative space-time
• Space-time uncertainty relation and Lorentz invariance
• Thermodynamics of Fuzzy Spheres in PP-wave Matrix Model
• Thermodynamics of a non-commutative fermion gas
• Field theories on spaces with linear fuzziness
• Field theory amplitudes in a space with SU(2) fuzziness
• Loop diagrams in space with SU(2) fuzziness
• Poisson structure on a space with linear SU(2) fuzziness
• Quantum mechanics on space with SU(2) fuzziness
• Thermodynamics on Fuzzy Spacetime
• TeV-photon paradox and space with SU(2) fuzziness

Cited by in corpus (8)

• Noncommutative spaces and covariant formulation of statistical mechanics
• The entropy of dense non-commutative fermion gases
• Closedness of orbits in a space with SU(2) Poisson structure
• Entropy bound for the photon gas in noncommutative spacetime
• Dirac theory on a space with linear Lie type fuzziness
• Gauge theory on a space with linear Lie type fuzziness
• Eigenvalue problem for radial potentials in space with SU(2) fuzziness
• Thermodynamics Properties of Confined Particles on Noncommutative Plane