# On the Spin-Statistics Connection in Curved Spacetimes

@article{Fewster2016OnTS, title={On the Spin-Statistics Connection in Curved Spacetimes}, author={Christopher J. Fewster}, journal={arXiv: Mathematical Physics}, year={2016}, pages={1-18} }

The connection between spin and statistics is examined in the context of locally covariant quantum field theory. A generalization is proposed in which locally covariant theories are defined as functors from a category of framed spacetimes to a category of ∗-algebras. This allows for a more operational description of theories with spin, and for the derivation of a more general version of the spin-statistics connection in curved spacetimes than previously available. The proof involves a “rigidity…

## 8 Citations

Locally covariant quantum field theory and the spin-statistics connection

- Physics, Mathematics
- 2016

The framework of locally covariant quantum field theory, an axiomatic approach to quantum field theory in curved spacetime, is reviewed. As a specific focus, the connection between spin and…

Algebraic Quantum Field Theory in Curved Spacetimes

- Mathematics, Physics
- 2015

This chapter sets out the framework of algebraic quantum field theory in curved spacetimes, based on the idea of local covariance. In this framework, a quantum field theory is modelled by a functor…

Algebraic Quantum Field Theory on Curved Spacetimes

- Physics
- 2016

In this chapter, we review all background material on algebraic quantum field theory on curved spacetimes which is necessary for understanding the cosmological applications discussed in the next…

An Analogue of the Coleman–Mandula Theorem for Quantum Field Theory in Curved Spacetimes

- Physics, Mathematics
- 2016

The Coleman–Mandula (CM) theorem states that the Poincaré and internal symmetries of a Minkowski spacetime quantum field theory cannot combine nontrivially in an extended symmetry group. We establish…

Quantum Field Theories on Categories Fibered in Groupoids

- Mathematics, Physics
- 2016

We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum…

Quantum field theory on curved spacetimes: Axiomatic framework and examples

- Physics, Mathematics
- 2016

In this review article, we want to expose a systematic development of quantum field theory on curved spacetimes. The leading principle is the emphasis on local properties. It turns out that this…

Deciphering the algebraic CPT theorem

- PhysicsStudies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
- 2019

The CPT theorem states that any causal, Lorentz-invariant, thermodynamically well-behaved quantum field theory must also be invariant under a reflection symmetry that reverses the direction of time…

Algebraic Approach to Quantum Theory

- Physics
- 2016

Before entering the realm of the quantum theory of fields, let’s have a look at something simpler and better understood, namely quantum mechanics (QM). To prepare the ground for what follows, we will…

## References

SHOWING 1-10 OF 46 REFERENCES

A Spin-Statistics Theorem for Quantum Fields¶on Curved Spacetime Manifolds¶in a Generally Covariant Framework

- Physics, Mathematics
- 2001

Abstract: A model-independent, locally generally covariant formulation of quantum field theory over four-dimensional, globally hyperbolic spacetimes will be given which generalizes similar, previous…

The locally covariant Dirac field

- Physics, Mathematics
- 2010

We describe the free Dirac field in a four-dimensional spacetime as a locally covariant quantum field theory in the sense of Brunetti, Fredenhagen and Verch, using a representation independent…

Algebraic Quantum Field Theory in Curved Spacetimes

- Mathematics, Physics
- 2015

This chapter sets out the framework of algebraic quantum field theory in curved spacetimes, based on the idea of local covariance. In this framework, a quantum field theory is modelled by a functor…

Statistics from dynamics in curved spacetime.

- Physics, MedicinePhysical review. D, Particles and fields
- 1989

The dynamical Bogolubov transformations associated with gravitationally induced particle creation imply the connection between spin and statistics, and it is shown in the same manner that parastatistics are consistent with the dynamical evolution of curved spacetime.

On the Notion of 'the Same Physics in All Spacetimes'

- Mathematics, Physics
- 2012

Brunetti, Fredenhagen and Verch (BFV) have shown how the notion of local covariance for quantum field theories can be formulated in terms of category theory: a theory being described as a functor…

The Split Property for Locally Covariant Quantum Field Theories in Curved Spacetime

- Physics, Mathematics
- 2015

The split property expresses the way in which local regions of spacetime define subsystems of a quantum field theory. It is known to hold for general theories in Minkowski space under the hypothesis…

Quantum energy inequalities and local covariance II: categorical formulation

- Physics, Mathematics
- 2007

We formulate quantum energy inequalities (QEIs) in the framework of locally covariant quantum field theory developed by Brunetti, Fredenhagen and Verch, which is based on notions taken from category…

Locally covariant quantum field theory and the problem of formulating the same physics in all space–times

- Medicine, PhysicsPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2015

The framework of locally covariant quantum field theory is discussed, motivated in part using ‘ignorance principles’. It is shown how theories can be represented by suitable functors, so that…

Existence of Local Covariant Time Ordered Products of Quantum Fields in Curved Spacetime

- Physics, Mathematics
- 2002

Abstract: We establish the existence of local, covariant time ordered products of local Wick polynomials for a free scalar field in curved spacetime. Our time ordered products satisfy all of the…

Renormalized Quantum Yang-Mills Fields in Curved Spacetime

- Mathematics, Physics
- 2008

We present a proof that the quantum Yang–Mills theory can be consistently defined as a renormalized, perturbative quantum field theory on an arbitrary globally hyperbolic curved, Lorentzian…