Discretization in Noncommutative Field Theory

2019 ◽  
pp. 65-78
Author(s):  
Ciprian Sorin Acatrinei ◽  
Keyword(s):  
Field Theory ◽  
Noncommutative Field Theory

scholarly journals LOCALITY, CAUSALITY AND NONCOMMUTATIVE GEOMETRY

2006 ◽  
Vol 21 (01) ◽  
pp. 67-82 ◽  
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.

scholarly journals Noncommutative Field Theory and Lorentz Violation

2001 ◽  
Vol 87 (14) ◽  
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

scholarly journals A consistent noncommutative field theory: the Wess–Zumino model

2000 ◽  
Vol 587 (1-3) ◽  
pp. 299-310 ◽  
Author(s):  
H.O. Girotti ◽  
M. Gomes ◽  
V.O. Rivelles ◽  
A.J. da Silva
Keyword(s):  
Field Theory ◽  
Noncommutative Field Theory ◽  
Zumino Model

scholarly journals ON THE CORRESPONDENCE BETWEEN NONCOMMUTATIVE FIELD THEORY AND GRAVITY

2007 ◽  
Vol 22 (16) ◽  
pp. 1119-1132 ◽  
Author(s):  
HYUN SEOK YANG
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Gauge Fields ◽  
Noncommutative Field Theory ◽  
Basic Reason ◽  
New Development ◽  
Collective Phenomenon ◽  
Darboux Theorem ◽  
Theory Of Gravity

In this brief review, we summarize the new development on the correspondence between noncommutative (NC) field theory and gravity, shortly referred to as the NCFT/Gravity correspondence. We elucidate why a gauge theory in NC spacetime should be a theory of gravity. A basic reason for the NCFT/Gravity correspondence is that the Λ-symmetry (or B-field transformations) in NC spacetime can be considered as a par with diffeomorphisms, which results from the Darboux theorem. This fact leads to a striking picture about gravity: Gravity can emerge from a gauge theory in NC spacetime. Gravity is then a collective phenomenon emerging from gauge fields living in fuzzy spacetime.

scholarly journals Discussion on Lorentz invariance violation of noncommutative field theory and neutrino oscillation

2017 ◽  
Vol 32 (06n07) ◽  
pp. 1750040 ◽  
Author(s):  
Cui-Bai Luo ◽  
Song Shi ◽  
Yi-Lun Du ◽  
Yong-Long Wang ◽  
Hong-Shi Zong
Keyword(s):  
Field Theory ◽  
Neutrino Oscillation ◽  
Lorentz Invariance ◽  
Noncommutative Field Theory ◽  
Atmospheric Neutrinos ◽  
Moyal Product ◽  
Invariance Violation ◽  
Lorentz Invariance Violation ◽  
Massless Neutrino ◽  
Canonical Anticommutation Relations

Depending on deformed canonical anticommutation relations, massless neutrino oscillation based on Lorentz invariance violation in noncommutative field theory is discussed. It is found that the previous studies about massless neutrino oscillation within deformed canonical anticommutation relations should satisfy the condition of new Moyal product and new nonstandard commutation relations. Furthermore, comparing the Lorentz invariant violation parameters A in the previous studies with new Moyal product and new nonstandard commutation relations, we find that the orders of magnitude of noncommutative parameters (Lorentz invariant violation parameters A) is not self-consistent. This inconsistency means that the previous studies of Lorentz invariance violation in noncommutative field theory may not naturally explain massless neutrino oscillation. In other words, it should be impossible to explain neutrino oscillation by Lorentz invariance violation in noncommutative field theory. This conclusion is supported by the latest atmospheric neutrinos experimental results from the super-Kamiokande Collaboration, which show that no evidence of Lorentz invariance violation on atmospheric neutrinos was observed.

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