scholarly journals BPHZ renormalization and its application to non-commutative field theory

2013 ◽  
Vol 73 (9) ◽  
Author(s):  
Daniel N. Blaschke ◽  
François Gieres ◽  
Franz Heindl ◽  
Manfred Schweda ◽  
Michael Wohlgenannt
Keyword(s):  
Field Theory ◽  
Commutative Field

TWISTED POINCARE GROUP AND SPIN-STATISTICS

2005 ◽  
Vol 20 (27) ◽  
pp. 6268-6277 ◽  
Author(s):  
ALEKSANDR PINZUL
Keyword(s):  
Field Theory ◽  
Tensor Product ◽  
Poincaré Group ◽  
Commutative Field ◽  
Poincare Group ◽  
Quantized Fields

Recently it has been shown that it is possible to retain the Lorentz-invariant interpretation of the non-commutative field theory.1,2,3 This was achieved by the means of the twisted action of the Poincaré group on the tensor product of the fields. We investigate the consequences of this approach for the quantized fields.

scholarly journals NON-COMMUTATIVE EINSTEIN EQUATIONS AND SEIBERG–WITTEN MAP

2011 ◽  
Vol 03 ◽  
pp. 143-149 ◽  
Author(s):  
PAOLO ASCHIERI ◽  
ELISABETTA DI GREZIA ◽  
GIAMPIERO ESPOSITO
Keyword(s):  
Field Theory ◽  
Einstein Equations ◽  
Action Functional ◽  
Field Equations ◽  
Commutative Field ◽  
First Order ◽  
Classical Geometry ◽  
Pure Gravity

The Seiberg–Witten map is a powerful tool in non-commutative field theory, and it has been recently obtained in the literature for gravity itself, to first order in non-commutativity. This paper, relying upon the pure-gravity form of the action functional considered in Ref. 2, studies the expansion to first order of the non-commutative Einstein equations, and whether the Seiberg–Witten map can lead to a solution of such equations when the underlying classical geometry is Schwarzschild. We find that, if one first obtains the non-commutative field equations by varying the action of Ref. 2 with respect to all non-commutative fields, and then tries to solve these equations by expressing the non-commutative fields in terms of the commutative ones via Seiberg–Witten map, no solution of these equations can be obtained when the commutative background is Schwarzschild.

scholarly journals NONCOMMUTATIVE QUANTIZATION FOR NONCOMMUTATIVE FIELD THEORY

2007 ◽  
Vol 22 (06) ◽  
pp. 1181-1200 ◽  
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.

scholarly journals Seiberg–Witten map and the axial anomaly in non-commutative field theory

2002 ◽  
Vol 533 (1-2) ◽  
pp. 162-167 ◽  
Author(s):  
Rabin Banerjee ◽  
Subir Ghosh
Keyword(s):  
Field Theory ◽  
Commutative Field ◽  
Axial Anomaly

scholarly journals Lorentz Invariance and the Unitarity Problem in Non-Commutative Field Theory

2003 ◽  
Vol 110 (5) ◽  
pp. 989-1001 ◽  
Author(s):  
K. Morita ◽  
Y. Okumura ◽  
E. Umezawa
Keyword(s):  
Field Theory ◽  
Lorentz Invariance ◽  
Commutative Field

scholarly journals NONCOMMUTATIVITY FROM THE SYMPLECTIC POINT OF VIEW

2006 ◽  
Vol 21 (26) ◽  
pp. 5359-5369 ◽  
Author(s):  
E. M. C. ABREU ◽  
C. NEVES ◽  
W. OLIVEIRA
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
String Theory ◽  
Point Of View ◽  
Field Theories ◽  
Lagrangian Description ◽  
Moyal Product ◽  
Commutative Field ◽  
Background Magnetic Field

The great deal in noncommutative (NC) field theories started when it was noted that NC spaces naturally arise in string theory with a constant background magnetic field in the presence of D-branes. In this work we explore how NC geometry can be introduced into a commutative field theory besides the usual introduction of the Moyal product. We propose a nonperturbative systematic new way to introduce NC geometry into commutative systems, based mainly on the symplectic approach. Further, as example, this formalism describes precisely how to obtain a Lagrangian description for the NC version of some systems reproducing well-known theories.

scholarly journals Non-Commutative Field Theory on S4

2004 ◽  
Vol 112 (5) ◽  
pp. 883-894 ◽  
Author(s):  
R. Nakayama ◽  
Y. Shimono
Keyword(s):  
Field Theory ◽  
Commutative Field
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