Uploaded July 2019 | Updated September 2026, 5 hours ago
The CPT theorem says that any well-behaved QFT must be invariant under a combined reflection symmetry that reverses the direction of time, flips right- and left-handedness, and conjugates charge. The spin-statistics theorem connects particles' spin to statistical constraints governing collections of indistinguishable particles. Both theorems are puzzling. The physical chain of argument behind them is far from transparent, and despite being about apparently different things, they are in fact intimately related. In some proofs of the CPT theorem, the spin-statistics theorem appears as a lemma; in others the order of dependence is reversed. Moreover, the lack of analogous results for non-relativistic quantum theories and classical field theories strongly suggests that the theorems capture constraints essential for unifying relativity and quantum mechanics.
In recent work, I have argued that within the algebraic approach to QFT, CPT symmetry is best explained in terms of a certain global reflection operation on the theory's state space. In this talk I will explore the viability of extending this state space account to cover the spin-statistics connection. The ultimate goal is to crack a tricky chicken-and-egg problem: does the CPT theorem explain the spin-statistics connection, does the spin-statistics connection explain the CPT theorem, or is there an underlying common explanation?
Foundations of Quantum Field Theory: 2019 Annual Philosophy of Physics Conference
June 12 - 14, 2019
Noel Swanson, University of Delaware
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The CPT theorem says that any well-behaved QFT must be invariant under a combined reflection symmetry that reverses the direction of time, flips right- and left-handedness, and conjugates charge. The spin-statistics theorem connects particles' spin to statistical constraints governing collections of indistinguishable particles. Both theorems are puzzling. The physical chain of argument behind them is far from transparent, and despite being about apparently different things, they are in fact intimately related. In some proofs of the CPT theorem, the spin-statistics theorem appears as a lemma; in others the order of dependence is reversed. Moreover, the lack of analogous results for non-relativistic quantum theories and classical field theories strongly suggests that the theorems capture constraints essential for unifying relativity and quantum mechanics.
In recent work, I have argued that within the algebraic approach to QFT, CPT symmetry is best explained in terms of a certain global reflection operation on the theory's state space. In this talk I will explore the viability of extending this state space account to cover the spin-statistics connection. The ultimate goal is to crack a tricky chicken-and-egg problem: does the CPT theorem explain the spin-statistics connection, does the spin-statistics connection explain the CPT theorem, or is there an underlying common explanation?
Foundations of Quantum Field Theory: 2019 Annual Philosophy of Physics Conference
June 12 - 14, 2019
Noel Swanson, University of Delaware
Visit the Rotman website for more information on applications, events, project descriptions, and openings. rotman.uwo.ca
Follow The Rotman Institute on Twitter: twitter.com/rotmanphilo
Like The Rotman Institute on Facebook: facebook.com/rotmanphilosophy
Subscribe to our channel: youtube.com/user/rotmanphilosophy
