scholarly journals Perturbative algebraic field theory, and deformation quantization

2001 ◽  
pp. 151-160 ◽  
Author(s):  
Michael Dütsch ◽  
Klaus Fredenhagen
Keyword(s):  
Field Theory ◽  
Deformation Quantization ◽  
Algebraic Field

scholarly journals Localization in algebraic field theory

1982 ◽  
Vol 85 (1) ◽  
pp. 87-98 ◽  
Author(s):  
John E. Roberts
Keyword(s):  
Field Theory ◽  
Algebraic Field

DISSIPATIVE SCALAR FIELD THEORY VIA DEFORMATION QUANTIZATION

2013 ◽  
Vol 28 (16) ◽  
pp. 1350068
Author(s):  
ILIANA CARRILLO-IBARRA ◽  
HUGO GARCÍA-COMPEÁN ◽  
FRANCISCO J. TURRUBIATES
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Deformation Quantization ◽  
Star Product ◽  
Quantum Mechanical ◽  
Expectation Values ◽  
Scalar Field Theory ◽  
Oscillation Modes ◽  
Quantization Formalism ◽  
Damped Oscillation

The dissipative scalar field theory by means of the deformation quantization formalism is studied. Following the ideas presented by G. Dito and F. J. Turrubiates [Phys. Lett. A352, 309 (2006)] for quantum mechanics, a star product which contains the dissipative effect for the damped oscillation modes of the field is constructed. Employing this approach the expectation values of some observables in the quantum mechanical case as well as certain correlation functions for the field case are obtained under a particular dissipative process.

scholarly journals Coloring Operads for Algebraic Field Theory

2019 ◽  
Vol 67 (8-9) ◽  
pp. 1910004
Author(s):  
Simen Bruinsma
Keyword(s):  
Field Theory ◽  
Algebraic Field

A Poincaré covariant noncommutative spacetime

2018 ◽  
Vol 15 (09) ◽  
pp. 1850159 ◽  
Author(s):  
Albert Much ◽  
J. David Vergara
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Deformation Quantization ◽  
Deformation Theory ◽  
Relativistic Quantum ◽  
Minimal Length ◽  
Quantum Field ◽  
Relativistic Quantum Field Theory ◽  
Ball Problem ◽  
Noncommutative Spacetime

We interpret, in the realm of relativistic quantum field theory, the tangential operator given by Coleman and Mandula [All possible symmetries of the [Formula: see text] matrix, Phys. Rev. 159 (1967) 1251–1256] (see also [Much, Pottel and Sibold, Preconjugate variables in quantum field theory and their applications, Phys. Rev. D 94(6) (2016) 065007]) as an appropriate coordinate operator. The investigation shows that the operator generates a Snyder-like noncommutative spacetime with a minimal length that is given by the mass. By using this operator to define a noncommutative spacetime, we obtain a Poincaré invariant noncommutative spacetime and in addition solve the soccer-ball problem. Moreover, from recent progress in deformation theory we extract the idea of how to obtain, in a physical and mathematically well-defined manner, an emerging noncommutative spacetime. This is done by a strict deformation quantization known as Rieffel deformation (or warped convolutions). The result is a noncommutative spacetime combining a Snyder and a Moyal-Weyl type of noncommutativity that in addition behaves covariant under transformations of the whole Poincaré group.

scholarly journals Peierls brackets in non-Lagrangian field theory

2014 ◽  
Vol 29 (27) ◽  
pp. 1450157 ◽  
Author(s):  
A. A. Sharapov
Keyword(s):  
Field Theory ◽  
Poisson Bracket ◽  
Path Integral ◽  
Deformation Quantization ◽  
Equations Of Motion ◽  
Integral Approach ◽  
Lagrangian Dynamics ◽  
Path Integral Approach ◽  
Lagrangian Field Theory

The concept of Lagrange structure allows one to systematically quantize the Lagrangian and non-Lagrangian dynamics within the path-integral approach. In this paper, I show that any Lagrange structure gives rise to a covariant Poisson bracket on the space of solutions to the classical equations of motion, be they Lagrangian or not. The bracket generalize the well-known Peierls' bracket construction and make a bridge between the path-integral and the deformation quantization of non-Lagrangian dynamics.

ALGEBRAIC FIELD THEORY: RECOLLECTIONS AND THOUGHTS ABOUT THE FUTURE

1992 ◽  
Vol 04 (spec01) ◽  
pp. 159-166
Author(s):  
DANIEL KASTLER
Keyword(s):  
Field Theory ◽  
Space Time ◽  
Cyclic Cohomology ◽  
Algebraic Field ◽  
The Future ◽  
Commutative Space

Anecdotal description of Rudolf Haag’s discovery of algebraic field theory. Remarks on field theoretic invariants versus cyclic cohomology, and articulation of algebraic field theory with theories based on non-commutative space-time.

scholarly journals Algebraic field theory operads and linear quantization

2019 ◽  
Vol 109 (11) ◽  
pp. 2531-2570 ◽  
Author(s):  
Simen Bruinsma ◽  
Alexander Schenkel
Keyword(s):  
Field Theory ◽  
Algebraic Field
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