Defining Spin in QFT in Curved Spacetime

In summary, spin in Quantum Field Theory can be defined as the generators of SO(3) in flat spacetime, but this definition does not hold in curved spacetime. In order to define spin in curved spacetime, we need to think in terms of fields rather than particles. In globally hyperbolic and stationary spacetime, spin can be defined by forming a bundle over the spacetime with the same fiber as in the Minkowski case. Mikio Nakahara's "Geometry, Topology and Physics, Second Edition" Section 11.6 provides a comprehensive explanation of how to define spin in curved spacetime and which types of manifolds do not allow for a spinor field.
  • #1
paweld
255
0
How one can define a spin in Qunatum Filed Theory in curved spacetime. If the
space is flat it's invarainat under Poincare group - so in particular it's invariant under SO(3).
Spin operators are simply generators of SO(3). If the space isn't flat we cannot define
spin in this way. I know that in curved spacetime we should think of fileds rather than particles,
because notion of particle is not always well defined. So maybe better question is
how we define spin in globally hyberbolic and stationary spacetime?
 
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  • #2
You just form a bundle over the spacetime with the same Fiber as in the Minkowski case.

See Mikio Nakahara "Geometry, Topology and Physics, Second Edition" Section 11.6

It not only tells you how to define it, but what sort of manifolds do not admit a spinor field.
 

1. What is spin in quantum field theory (QFT)?

Spin is a fundamental property of particles in quantum field theory that describes their intrinsic angular momentum. It is a quantum mechanical quantity that can take on discrete values based on the type of particle.

2. How is spin defined in QFT in curved spacetime?

In QFT in curved spacetime, spin is defined as the transformation properties of a quantum field under rotations of the local coordinate system. This is mathematically described using the spinor formalism.

3. Can spin change in curved spacetime?

Yes, spin can change in curved spacetime due to the effects of gravity. This is because the local coordinate system is no longer flat and inertial, so rotations of the local coordinate system can have different effects on the quantum field.

4. How does spin affect the behavior of particles in curved spacetime?

The spin of a particle can affect its behavior in curved spacetime through its coupling to gravity. This means that the gravitational field can interact differently with particles of different spin, leading to different trajectories and properties.

5. What is the significance of defining spin in QFT in curved spacetime?

Defining spin in QFT in curved spacetime allows us to understand the behavior of particles in the presence of gravity, which is essential for understanding the dynamics of the universe. It also helps us to develop more accurate and comprehensive theories, such as quantum gravity.

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