Individual Particles, Properties and Quantum Statistics

Matteo Morganti

Moorad Alexanian, Arnulfo Zepeda

Matteo Morganti

Robert C. Hilborn, Candice L. Yuca

The treatment of identical particles in quantum mechanics rests on two (related) principles: the spin‐statistics connection and the Symmetrization Postulate. In light of recent theories (such as q‐deformed commutators) that allow for ‘small’ violations of the spin‐statistics connection and the Symmetrization Postulate, we revisit the issue of how quantum mechanics deals with identical particles and how it supports or fails to support various philosophical stances concerning individuality. As a consequence of the expanded possibilities for quantum statistics, we argue that permutation symmetry is best formulated as a formal property of the state function describing the system of particles rather than as a property of the individual particles.1 Introduction2 Philosophical background2.1 Important terminology2.1.1 Identity2.1.2 Indistinguishability2.1.3 Indiscernibility2.2 When are particles indistinguishable?2.3 The Principle of the Identity of Indiscernibles and quantum mechanics2.4 The Principle of the Identity of Indiscernibles and logic2.5 Particle history2.6 Transcendental individuality3 Some quantum formalism3.1 The Principle of Permutation Invariance and the Symmetrization Postulate3.2 The configuration‐space approach3.3 Commutators and anticommutators, and identical particle statistics3.4 Q‐mutators4 Identical particle statistics: a holistic point of view5 Conclusions

Elliot W. Montroll, John Ward

Samina Masood

This chapter introduces fundamental laws of thermodynamics and statistical mechanics. It offers concise overviews of thermodynamics, probability theory, and statistical mechanics, which are crucial for studying multi-particle systems. A comprehensive discussion of the statistical behavior of many-particle systems in terms of thermodynamics and statistical mechanics is included. The significance of probability in quantum mechanics is emphasized in terms of all the (multiple) states available to a single particle. Definitions of thermodynamic variables and statistical parameters are necessary for understanding quantum statistical field theories, which bridge individual particle behavior and averaged thermodynamic properties.