scholarly journals Singularity structure of the two-point function in quantum field theory in curved spacetime

1978 ◽  
Vol 63 (3) ◽  
pp. 257-264 ◽  
Author(s):  
Stephen A. Fulling ◽  
Mark Sweeny ◽  
Robert M. Wald
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Point Function ◽  
Curved Spacetime ◽  
Singularity Structure

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 ON THE 1-LOOP CALCULATIONS OF SOFTLY BROKEN FERMION-TORSION THEORY IN CURVED SPACE USING THE STÜCKELBERG PROCEDURE

2009 ◽  
Vol 24 (08n09) ◽  
pp. 1570-1573
Author(s):  
G. DE BERREDO-PEIXOTO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Gauge Symmetry ◽  
Torsion Theory ◽  
Quantum Calculations ◽  
Quantum Field ◽  
Curved Spacetime ◽  
Curved Space ◽  
Gauge Fixing ◽  
Additional Field

The soft breaking of gauge or other symmetries is the typical Quantum Field Theory phenomenon. In many cases one can apply the Stückelberg procedure, which means introducing some additional field (or fields) and restore the gauge symmetry. The original softly broken theory corresponds to a particular choice of the gauge fixing condition. In this paper we use this scheme for performing quantum calculations for fermion-torsion theory, softly broken by the torsion mass in arbitrary curved spacetime.

scholarly journals Exact four-point function and OPE for an interacting quantum field theory with space/time anisotropic scale invariance

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Hidehiko Shimada ◽  
Hirohiko Shimada
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scale Invariance ◽  
Asymptotic Series ◽  
Space Time ◽  
Quantum Field ◽  
Coupling Constant ◽  
Point Function ◽  
Calogero Model ◽  
Primary Operator

Abstract We identify a nontrivial yet tractable quantum field theory model with space/time anisotropic scale invariance, for which one can exactly compute certain four-point correlation functions and their decompositions via the operator-product expansion(OPE). The model is the Calogero model, non-relativistic particles interacting with a pair potential $$ \frac{g}{{\left|x-y\right|}^2} $$ g x − y 2 in one dimension, considered as a quantum field theory in one space and one time dimension via the second quantisation. This model has the anisotropic scale symmetry with the anisotropy exponent z = 2. The symmetry is also enhanced to the Schrödinger symmetry. The model has one coupling constant g and thus provides an example of a fixed line in the renormalisation group flow of anisotropic theories.We exactly compute a nontrivial four-point function of the fundamental fields of the theory. We decompose the four-point function via OPE in two different ways, thereby explicitly verifying the associativity of OPE for the first time for an interacting quantum field theory with anisotropic scale invariance. From the decompositions, one can read off the OPE coefficients and the scaling dimensions of the operators appearing in the intermediate channels. One of the decompositions is given by a convergent series, and only one primary operator and its descendants appear in the OPE. The scaling dimension of the primary operator we computed depends on the coupling constant. The dimension correctly reproduces the value expected from the well-known spectrum of the Calogero model combined with the so-called state-operator map which is valid for theories with the Schrödinger symmetry. The other decomposition is given by an asymptotic series. The asymptotic series comes with exponentially small correction terms, which also have a natural interpretation in terms of OPE.

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