Canonical quantization of noncommutative field theory

We consider a Moyal plane and propose to make the noncommutativity parameter Θμν bifermionic, i.e. composed of two fermionic (Grassmann odd) parameters. The Moyal product then contains a finite number of derivatives, which avoid the difficulties of the standard approach. As an example, we construct a two-dimensional noncommutative field theory model based on the Moyal product with a bifermionic parameter and show that it has a locally conserved energy–momentum tensor. The model has no problem with the canonical quantization and appears to be renormalizable.

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NONCOMMUTATIVE QUANTIZATION FOR NONCOMMUTATIVE FIELD THEORY

International Journal of Modern Physics A ◽

10.1142/s0217751x07035239 ◽

2007 ◽

Vol 22 (06) ◽

pp. 1181-1200 ◽

Cited By ~ 11

Author(s):

YASUMI ABE

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Correlation Functions ◽

Canonical Quantization ◽

Noncommutative Space ◽

Quantization Scheme ◽

Quantum Field ◽

Noncommutative Field Theory ◽

Commutative Field ◽

Noncommutative Parameter

We present a new procedure for quantizing field theory models on a noncommutative space–time. Our new quantization scheme depends on the noncommutative parameter explicitly and reduces to the canonical quantization in the commutative limit. It is shown that a quantum field theory constructed by this quantization yields exactly the same correlation functions as those of the commutative field theory, that is, the noncommutative effects disappear completely after the quantization. This implies, for instance, that the noncommutativity may be incorporated in the process of quantization, rather than in the action as conventionally done.

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High-energy scattering in noncommutative field theory

Physical Review D ◽

10.1103/physrevd.73.025018 ◽

2006 ◽

Vol 73 (2) ◽

Cited By ~ 1

Author(s):

Jason Kumar ◽

Arvind Rajaraman

Keyword(s):

Field Theory ◽

High Energy ◽

Noncommutative Field Theory ◽

Energy Scattering ◽

High Energy Scattering

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LOCALITY, CAUSALITY AND NONCOMMUTATIVE GEOMETRY

International Journal of Modern Physics A ◽

10.1142/s0217751x06024876 ◽

2006 ◽

Vol 21 (01) ◽

pp. 67-82 ◽

Cited By ~ 16

Author(s):

CHONG-SUN CHU ◽

KO FURUTA ◽

TAKEO INAMI

Keyword(s):

Field Theory ◽

Noncommutative Geometry ◽

Light Cone ◽

Energy Condition ◽

Noncommutative Space ◽

Noncommutative Field Theory ◽

Causality Condition ◽

Usual Form ◽

New Form ◽

Lower Dimensional

We analyze the causality condition in noncommutative field theory and show that the nonlocality of noncommutative interaction leads to a modification of the light cone to the light wedge. This effect is generic for noncommutative geometry. We also check that the usual form of energy condition is violated and propose that a new form is needed in noncommutative space–time. On reduction from light cone to light wedge, it looks like the noncommutative dimensions are effectively washed out and suggests a reformulation of noncommutative field theory in terms of lower dimensional degree of freedom. This reduction of dimensions due to noncommutative geometry could play a key role in explaining the holographic property of quantum gravity.

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Noncommutative Field Theory and Lorentz Violation

Physical Review Letters ◽

10.1103/physrevlett.87.141601 ◽

2001 ◽

Vol 87 (14) ◽

Cited By ~ 621

Author(s):

Sean M. Carroll ◽

Jeffrey A. Harvey ◽

V. Alan Kostelecký ◽

Charles D. Lane ◽

Takemi Okamoto

Keyword(s):

Field Theory ◽

Lorentz Violation ◽

Noncommutative Field Theory

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Canonical quantization of free fields

Introduction to Quantum Field Theory with Applications to Quantum Gravity ◽

10.1093/oso/9780198838319.003.0005 ◽

2021 ◽

pp. 70-98

Author(s):

Iosif L. Buchbinder ◽

Ilya L. Shapiro

Keyword(s):

Field Theory ◽

Quantum Theory ◽

Electromagnetic Fields ◽

Classical Theory ◽

Canonical Quantization ◽

Classical Mechanics ◽

Scalar Fields ◽

Complex Scalar ◽

Spinor Fields ◽

Free Fields

This chapter discusses canonical quantization in field theory and shows how the notion of a particle arises within the framework of the concept of a field. Canonical quantization is the process of constructing a quantum theory on the basis of a classical theory. The chapter briefly considers the main elements of this procedure, starting from its simplest version in classical mechanics. It first describes the general principles of canonical quantization and then provides concrete examples. The examples include the canonical quantization of free real scalar fields, free complex scalar fields, free spinor fields and free electromagnetic fields.

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