Problems of dynamics in generally covariant quantum field theory

The Galilean covariance, formulated in 5-dimensions space, describes the nonrelativistic physics in a way similar to a Lorentz covariant quantum field theory being considered for relativistic physics. Using a nonrelativistic approach the Stefan–Boltzmann law and the Casimir effect at finite temperature for a particle with spin zero and 1/2 are calculated. The thermo field dynamics is used to include the finite temperature effects.

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Locally covariant quantum field theory and the spin–statistics connection

International Journal of Modern Physics D ◽

10.1142/s0218271816300159 ◽

2016 ◽

Vol 25 (06) ◽

pp. 1630015 ◽

Cited By ~ 2

Author(s):

Christopher J. Fewster

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Axiomatic Approach ◽

Quantum Field ◽

General Version ◽

Curved Spacetime ◽

New Approach ◽

Covariant Quantum ◽

Specific Focus ◽

Spin And Statistics

The framework of locally covariant quantum field theory (QFT), an axiomatic approach to QFT in curved spacetime (CST), is reviewed. As a specific focus, the connection between spin and statistics is examined in this context. A new approach is given, which 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 CSTs than previously available. This part of the text is based on [C. J. Fewster, arXiv:1503.05797.] and a forthcoming publication; the emphasis here is on the fundamental ideas and motivation.

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Locally Covariant Quantum Field Theory with External Sources

Annales Henri Poincaré ◽

10.1007/s00023-014-0372-y ◽

2014 ◽

Vol 16 (10) ◽

pp. 2303-2365 ◽

Cited By ~ 6

Author(s):

Christopher J. Fewster ◽

Alexander Schenkel

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Quantum Field ◽

Covariant Quantum ◽

External Sources

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CHARGED SECTORS, SPIN AND STATISTICS IN QUANTUM FIELD THEORY ON CURVED SPACETIMES

Reviews in Mathematical Physics ◽

10.1142/s0129055x01000557 ◽

2001 ◽

Vol 13 (02) ◽

pp. 125-198 ◽

Cited By ~ 34

Author(s):

D. GUIDO ◽

R. LONGO ◽

J. E. ROBERTS ◽

R. VERCH

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Black Holes ◽

Rotational Symmetry ◽

Minkowski Spacetime ◽

Rotation Group ◽

Quantum Field ◽

Covariant Quantum ◽

Killing Horizon ◽

Hyperbolic Spacetimes

The first part of this paper extends the Doplicher–Haag–Roberts theory of superselection sectors to quantum field theory on arbitrary globally hyperbolic spacetimes. The statistics of a superselection sector may be defined as in flat spacetime and each charge has a conjugate charge when the spacetime possesses non-compact Cauchy surfaces. In this case, the field net and the gauge group can be constructed as in Minkowski spacetime. The second part of this paper derives spin-statistics theorems on spacetimes with appropriate symmetries. Two situations are considered: First, if the spacetime has a bifurcate Killing horizon, as is the case in the presence of black holes, then restricting the observables to the Killing horizon together with "modular covariance" for the Killing flow yields a conformally covariant quantum field theory on the circle and a conformal spin-statistics theorem for charged sectors localizable on the Killing horizon. Secondly, if the spacetime has a rotation and PT symmetry like the Schwarzschild–Kruskal black holes, "geometric modular action" of the rotational symmetry leads to a spin-statistics theorem for charged covariant sectors where the spin is defined via the SU(2)-covering of the spatial rotation group SO(3).

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