Euclidean Quantum Field Theory on Commutative and Noncommutative Spaces

2008 ◽  
pp. 59-100
Author(s):  
R. Wulkenhaar
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Noncommutative Spaces ◽  
Euclidean Quantum Field Theory

scholarly journals NONLINEAR PHENOMENA IN CANONICAL STOCHASTIC QUANTIZATION

2008 ◽  
Vol 18 (09) ◽  
pp. 2787-2791
Author(s):  
HELMUTH HÜFFEL
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Gauge Field Theories ◽  
Higgs Mechanism ◽  
Nonlinear Phenomena ◽  
Quantum Field ◽  
Stochastic Quantization ◽  
Statistical System ◽  
Equilibrium Limit ◽  
Euclidean Quantum Field Theory

Stochastic quantization provides a connection between quantum field theory and statistical mechanics, with applications especially in gauge field theories. Euclidean quantum field theory is viewed as the equilibrium limit of a statistical system coupled to a thermal reservoir. Nonlinear phenomena in stochastic quantization arise when employing nonlinear Brownian motion as an underlying stochastic process. We discuss a novel formulation of the Higgs mechanism in QED.

scholarly journals INTERACTION MEASURES ON THE SPACE OF DISTRIBUTIONS OVER THE FIELD OF p-ADIC NUMBERS

2003 ◽  
Vol 06 (03) ◽  
pp. 389-411 ◽  
Author(s):  
ANATOLY N. KOCHUBEI ◽  
MUSTAFA R. SAIT-AMETOV
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Differential Operator ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Quantum Field ◽  
Pseudo Differential Operator ◽  
Schwartz Distributions ◽  
Space Of Distributions ◽  
Euclidean Quantum Field Theory

We construct measures on the space [Formula: see text], n≤4, of Bruhat–Schwartz distributions over the field of p-adic numbers, corresponding to finite volume polynomial interactions in a p-adic analog of the Euclidean quantum field theory. In contrast to earlier results in this direction, our choice of the free measure is the Gaussian measure corresponding to an elliptic pseudo-differential operator over [Formula: see text]. Analogs of the Euclidean P(φ)-theories with free and half-Dirichlet boundary conditions are considered.

scholarly journals Black Hole Radiation, Greybody Factors, and Generalised Wick Rotation

2021 ◽  
Author(s):  
◽  
Finnian Gray
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Hawking Temperature ◽  
Matrix Formalism ◽  
Quantum Field ◽  
Wick Rotation ◽  
Radiation Process ◽  
Black Hole Radiation ◽  
Euclidean Quantum Field Theory

<p>In this thesis we look at the intersection of quantum field theory and general relativity. We focus on Hawking radiation from black holes and its implications. This is done on two fronts. In the first we consider the greybody factors arising from a Schwarzschild black hole. We develop a new way to numerically calculate these greybody factors using the transfer matrix formalism and the product calculus. We use this technique to calculate some of the relevant physical quantities and consider their effect on the radiation process.  The second front considers a generalisation of Wick rotation. This is motivated by the success of Wick rotation and Euclidean quantum field theory techniques to calculate the Hawking temperature. We find that, while an analytic continuation of the coordinates is not well defined and highly coordinate dependent, a direct continuation of the Lorentzian signature metric to Euclidean signature has promising results. It reproduces the Hawking temperature and is coordinate independent. However for consistency, we propose a new action for the Euclidean theory which cannot be simply the Euclidean Einstein-Hilbert action.</p>

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