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

2001 ◽  
Vol 13 (02) ◽  
pp. 125-198 ◽  
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).

scholarly journals The locality axiom in quantum field theory and tensor products of C*-algebras

2014 ◽  
Vol 26 (06) ◽  
pp. 1450010 ◽  
Author(s):  
Romeo Brunetti ◽  
Klaus Fredenhagen ◽  
Paniz Imani ◽  
Katarzyna Rejzner
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Local Observable ◽  
Quantum Field ◽  
Covariant Quantum ◽  
C Algebras ◽  
Local Algebras ◽  
Globally Hyperbolic Spacetimes ◽  
Split Property ◽  
Hyperbolic Spacetimes

The prototypes of mutually independent systems are systems which are localized in spacelike separated regions. In the framework of locally covariant quantum field theory, we show that the commutativity of observables in spacelike separated regions can be encoded in the tensorial structure of the functor which associates unital C*-algebras (the local observable algebras) to globally hyperbolic spacetimes. This holds under the assumption that the local algebras satisfy the split property and involves the minimal tensor product of C*-algebras.

scholarly journals ON THE QUANTUM THEORY OF MASSLESS SPIN-3/2 FIELD IN MINKOWSKI SPACETIME

2006 ◽  
Vol 03 (07) ◽  
pp. 1303-1312 ◽  
Author(s):  
WEIGANG QIU ◽  
FEI SUN ◽  
HONGBAO ZHANG
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Casimir Effect ◽  
Minkowski Spacetime ◽  
Quantum Field ◽  
Explicit Result ◽  
Massless Spin ◽  
The Many ◽  
The One

From the modern viewpoint and by the geometric method, this paper provides a concise foundation for the quantum theory of massless spin-3/2 field in Minkowski spacetime, which includes both the one-particle's quantum mechanics and the many-particle's quantum field theory. The explicit result presented here is useful for the investigation of spin-3/2 field in various circumstances such as supergravity, twistor programme, Casimir effect, and quantum inequality.

scholarly journals Galilean covariance, Casimir effect and Stefan–Boltzmann law at finite temperature

2017 ◽  
Vol 32 (16) ◽  
pp. 1750094 ◽  
Author(s):  
S. C. Ulhoa ◽  
A. F. Santos ◽  
Faqir C. Khanna
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Finite Temperature ◽  
Temperature Effects ◽  
Casimir Effect ◽  
Quantum Field ◽  
Covariant Quantum ◽  
Thermo Field Dynamics ◽  
Boltzmann Law ◽  
Galilean Covariance

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.

scholarly journals Locally covariant quantum field theory and the spin–statistics connection

2016 ◽  
Vol 25 (06) ◽  
pp. 1630015 ◽  
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.

scholarly journals Locally Covariant Quantum Field Theory with External Sources

2014 ◽  
Vol 16 (10) ◽  
pp. 2303-2365 ◽  
Author(s):  
Christopher J. Fewster ◽  
Alexander Schenkel
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Covariant Quantum ◽  
External Sources

THE PRINCIPLE OF LOCALITY AND QUANTUM FIELD THEORY ON (NON GLOBALLY HYPERBOLIC) CURVED SPACETIMES

1992 ◽  
Vol 04 (spec01) ◽  
pp. 167-195 ◽  
Author(s):  
BERNARD S. KAY
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Field Algebra ◽  
Massless Field ◽  
Globally Hyperbolic ◽  
Local Algebras ◽  
Hyperbolic Spacetime ◽  
Globally Hyperbolic Spacetimes ◽  
Hyperbolic Spacetimes

In the context of a linear model (the covariant Klein Gordon equation) we review the mathematical and conceptual framework of quantum field theory on globally hyperbolic spacetimes, and address the question of what it might mean to quantize a field on a non globally hyperbolic spacetime. Our discussion centres on the notion of F-locality which we introduce and which asserts there is a net of local algebras such that every neighbourhood of every point contains a globally hyperbolic subneighbourhood of that point for which the field algebra coincides with the algebra one would obtain were one to regard the subneighbourhood as a spacetime in its own right and quantize — with some choice of time-orientation — according to the standard rules for quantum field theory on globally hyperbolic spacetimes. We show that F-locality is a property of the standard field algebra construction for globally hyperbolic spacetimes, and argue that it (or something similar) should be imposed as a condition on any field algebra construction for non globally hyperbolic spacetimes. We call a spacetime for which there exists a field algebra satisfying F-locality F-quantum compatible and argue that a spacetime which did not satisfy something similar to this condition could not arise as an approximate classical description of a state of quantum gravity and would hence be ruled out physically. We show that all F-quantum compatible spacetimes are time orientable. We also raise the issue of whether chronology violating spacetimes can be F-quantum compatible, giving a special model — a massless field theory on the “four dimensional spacelike cylinder” — which is F-quantum compatible, and a (two dimensional) model — a massless field theory on Misner space — which is not. We discuss the possible relevance of this latter result to Hawking’s recent Chronology Protection Conjecture.

Is Algebraic Lorentz-Covariant Quantum Field Theory Stochastic Einstein Local?

1994 ◽  
Vol 61 (3) ◽  
pp. 457-474 ◽  
Author(s):  
F. A. Muller ◽  
Jeremy Butterfield
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Covariant Quantum
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